Index
1 Maximum Clique1.1 Surveys / Theory
1.1.1 Bounds
1.2 Stochastic Local Search algorithms
1.3 Applications
1.4 Exact methods
1.4.1 Bron-Kerbosch and variants
1.4.2 Other exact methods
1.5 Continuous formulations
1.6 Instances
1.6.1 DIMACS
2 Generalisations
2.1 Quasi-Cliques
2.1.1 Stochastic Local Search algorithms
2.1.2 Applications
2.2 Weighted Maximum Clique
2.2.1 Surveys / Theory
2.2.2 Stochastic Local Search algorithms
2.2.3 Applications
2.2.4 Exact methods
2.2.5 Continuous formulations
Bibliography
Download the complete bibliography in BibTeX format, or the single BibTeX entries below. A paper can belong to different categories. In each category papers are sorted from the most recent to the oldest. This commented bibliography (252 references for the time being) does not aim at being complete and is currently under construction.
Applications are labeled with the research field name or the research topic.
References to algorithms for the Maximum Independent set (or Maximum Stable Set) are also reported. The Maximum Independent Set is the same problem as the Maximum Clique on the complementary graph, and algorithms can be easily applied to both problems by switching a logical condition in the code. The Maximum Clique literature has been recently richer than the Maximum Independent Set literature and most of the algorithms have been proposed as Maximum Clique solvers.
1 Maximum Clique
1.1 Surveys / Theory
Qinghua Wu and Jin-Kao Hao. A review on algorithms for maximum clique problems. European Journal of Operational Research, 242(3):693—709, 2015.
The maximum clique problem (MCP) is to determine in a graph a clique (i.e., a complete subgraph) of maximum cardinality. The MCP is notable for its capability of modeling other combinatorial problems and real-world applications. As one of the most studied NP-hard problems, many algorithms are available in the literature and new methods are continually being proposed. Given that the two existing surveys on the MCP date back to 1994 and 1999 respectively, one primary goal of this paper is to provide an updated and comprehensive review on both exact and heuristic MCP algorithms, with a special focus on recent developments. To be informative, we identify the general framework followed by these algorithms and pinpoint the key ingredients that make them successful. By classifying the main search strategies and putting forward the critical elements of the most relevant clique methods, this review intends to encourage future development of more powerful methods and motivate new applications of the clique approaches.
@article{WuH:2015,
author = {Qinghua Wu and Jin{-}Kao Hao},
title = {A review on algorithms for maximum clique problems},
journal = {European Journal of Operational Research},
volume = {242},
number = {3},
pages = {693--709},
year = {2015},
doi = {10.1016/j.ejor.2014.09.064},
}S. Akbari, M. Aryapoor, and M. Jamaali. Chromatic number and clique number of subgraphs of regular graph of matrix algebras. Linear Algebra and Its Applications, 436(7):2419—2424, 2012. Restriction to graph class having special properties.
Let R be a ring and \(X \subseteq R\) be a non-empty set. The regular graph of \(X, \Gamma(X)\), is defined to be the graph with regular elements of X (non-zero divisors of X) as the set of vertices and two vertices are adjacent if their sum is a zero divisor. There is an interesting question posed in BCC22. For a field F, is the chromatic number of \(\Gamma (GL_n(F))\) finite? In this paper, we show that if G is a soluble subgroup of \(GL_n(F)\), then \(\chi(\Gamma(G)) < \infty\). Also, we show that for every field F, \(\chi(\Gamma(M_n(F))) = \chi(\Gamma(M_n(F(x))))\), where x is an indeterminate. Finally, for every algebraically closed field F, we determine the maximum value of the clique number of \(\Gamma(\langle A \rangle)\), where \(\langle A \rangle\) denotes the subgroup generated by \(A \in GL_n(F)\).
@article{AkbariAJ:2012,
author = {Akbari, S. and Aryapoor, M. and Jamaali, M.},
title = {Chromatic number and clique number of subgraphs of regular graph of matrix algebras},
journal = {Linear Algebra and Its Applications},
volume = {436},
number = {7},
pages = {2419-2424},
year = {2012},
doi = {10.1016/j.laa.2011.09.020},
}Türker Bıyıkoğlu and Josef Leydold. Graphs of given order and size and minimum algebraic connectivity. Linear Algebra and Its Applications, 436(7):2067—2077, 2012. Restriction to graph class having special properties.
The structure of connected graphs of given size and order that have minimal algebraic connectivity is investigated. It is shown that they must consist of a chain of cliques. Moreover, an upper bound for the number of maximal cliques of size 2 or larger is derived.
@article{BiyikogluL:2012,
author = {B{\i}y{\i}ko{\ug}lu, T{\"u}rker and Leydold, Josef},
title = {Graphs of given order and size and minimum algebraic connectivity},
journal = {Linear Algebra and Its Applications},
volume = {436},
number = {7},
pages = {2067-2077},
year = {2012},
doi = {10.1016/j.laa.2011.09.026},
}Carmen Ortiz and Mónica Villanueva. Maximal independent sets in caterpillar graphs. Discrete Applied Mathematics, 160(3):259—266, 2012. [Maximum Independent Set] Restriction to graph class having special properties.
A caterpillar graph is a tree in which the removal of all pendant vertices results in a chordless path. In this work, we determine the number of maximal independent sets (mis) in caterpillar graphs. For a general graph, this problem is Pcomplete. We provide a polynomial time algorithm to generate the whole family of mis in a caterpillar graph. We also characterize the independent graph (intersection graph of mis) and the clique graph (intersection graph of cliques) of complete caterpillar graphs.
@article{OrtizV:2012,
author = {Ortiz, Carmen and Villanueva, M{\'o}nica},
title = {Maximal independent sets in caterpillar graphs},
journal = {Discrete Applied Mathematics},
volume = {160},
number = {3},
pages = {259-266},
year = {2012},
doi = {10.1016/j.dam.2011.10.024},
}Sándor Szabó. Parallel algorithms for finding cliques in a graph. Journal of Physics: Conference Series, 268(1):012030, 2011.
A clique is a subgraph in a graph that is complete in the sense that each two of its nodes are connected by an edge. Finding cliques in a given graph is an important procedure in discrete mathematical modeling. The paper will show how concepts such as splitting partitions, quasi coloring, node and edge dominance are related to clique search problems. In particular we will discuss the connection with parallel clique search algorithms. These concepts also suggest practical guide lines to inspect a given graph before starting a large scale search.
@article{Szabo:2011,
author = {S{\'a}ndor Szab{\'o}},
title = {Parallel algorithms for finding cliques in a graph},
journal = {Journal of Physics: Conference Series},
volume = {268},
number = {1},
pages = {012030},
year = {2011},
doi = {10.1088/1742-6596/268/1/012030},
}Tatsuya Akutsu Etsuji Tomita and Tsutomu Matsunaga. Efficient algorithms for finding maximum and maximal cliques: Effective tools for bioinformatics. ISBN 978-953-307-475-7
@incollection{TomitaAM:2011,
author = {Etsuji Tomita, Tatsuya Akutsu and Tsutomu Matsunaga},
title = {Efficient Algorithms for Finding Maximum and Maximal Cliques: Effective Tools for Bioinformatics},
booktitle = {Biomedical Engineering, Trends in Electronics, Communications and Software},
pages = {625-640},
editor = {Anthony N. Laskovski},
publisher = {InTech},
year = {2011},
url = {http://www.intechopen.com/books/biomedical-engineering-trends-in-electronics-communications-and-software/efficient-algorithms-for-finding-maximum-and-maximal-cliques-effective-tools-for-bioinformatics},
}David Eppstein, Marteen Löffler, and Darren Strash. Listing all maximal cliques in sparse graphs in near-optimal time. In Otfried Cheong, Kyung-Yong Chwa, and Kunsoo Park, editors, Algorithms and Computation, volume 6506 of Lecture Notes in Computer Science, pages 403—414. Springer Berlin / Heidelberg, 2010.
Note: Variation of BronK:1973 with nodes ordered by degeneracy \(d\), which runs in \(O(dn3^{d/3})\). The algorithm can be applied to large graphs with low degeneracy number (see EppsteinS:2011).
The degeneracy of an n-vertex graph G is the smallest number d such that every subgraph of G contains a vertex of degree at most \(d\). We show that there exists a nearly-optimal fixed-parameter tractable algorithm for enumerating all maximal cliques, parametrized by degeneracy. To achieve this result, we modify the classic Bron-Kerbosch algorithm and show that it runs in time \(O(dn3^{d/3})\). We also provide matching upper and lower bounds showing that the largest possible number of maximal cliques in an n-vertex graph with degeneracy \(d\) (when \(d\) is a multiple of 3 and \(n \ge d + 3\)) is \((n - d)3^{d/3}\). Therefore, our algorithm matches the \(\Theta(d(n - d)3^{d/3})\) worst-case output size of the problem whenever \(n - d = \Omega(n)\).
@incollection{EppsteinLS:2010,
author = {Eppstein, David and L{\"o}ffler, Marteen and Strash, Darren},
title = {Listing All Maximal Cliques in Sparse Graphs in Near-Optimal Time},
volume = {6506},
booktitle = {Algorithms and Computation},
series = {Lecture Notes in Computer Science},
pages = {403--414},
editor = {Cheong, Otfried and Chwa, Kyung-Yong and Park, Kunsoo},
publisher = {Springer Berlin / Heidelberg},
year = {2010},
doi = {10.1007/978-3-642-17517-6_36},
}Sergiy Butenko and Wilbert E. Wilhelm. Clique-detection models in computational biochemistry and genomics. European Journal of Operational Research, 173(1):1—17, 2006.
Note: Survey on relevant problems in bioinformatics and biochemistry that can be formalised as graph problems and solved with clique-detection models.
Many important problems arising in computational biochemistry and genomics have been formulated in terms of underlying combinatorial optimization models. In particular, a number have been formulated as clique-detection models. The proposed article includes an introduction to the underlying biochemistry and genomic aspects of the problems as well as to the graph-theoretic aspects of the solution approaches. Each subsequent section describes a particular type of problem, gives an example to show how the graph model can be derived, summarizes recent progress, and discusses challenges associated with solving the associated graph-theoretic models.
Clique-detection models include prescribing (a) a maximal clique, (b) a maximum clique, (c) a maximum weighted clique, or (d) all maximal cliques in a graph. The particular types of biochemistry and genomics problems that can be represented by a clique-detection model include integration of genome mapping data, nonoverlapping local alignments, matching and comparing molecular structures, and protein docking.
Clique-detection models include prescribing (a) a maximal clique, (b) a maximum clique, (c) a maximum weighted clique, or (d) all maximal cliques in a graph. The particular types of biochemistry and genomics problems that can be represented by a clique-detection model include integration of genome mapping data, nonoverlapping local alignments, matching and comparing molecular structures, and protein docking.
@article{ButenkoW:2006,
author = {Butenko, Sergiy and Wilhelm, Wilbert E.},
title = {Clique-detection models in computational biochemistry and genomics},
journal = {European Journal of Operational Research},
volume = {173},
number = {1},
pages = {1--17},
year = {2006},
doi = {10.1016/j.ejor.2005.05.026},
}Tobias Storch. How randomized search heuristics find maximum cliques in planar graphs. In GECCO 2006 - Genetic and Evolutionary Computation Conference, volume 1, pages 567—574, New York, NY, USA, 2006. ACM. Restriction to graph class having special properties.
Surprisingly, general search heuristics often solve combinatorial problems quite sufficiently, although they do not outperform specialized algorithms. Here, the behavior of simple randomized optimizers on the maximum clique problem on planar graphs is investigated rigorously. The focus is on the worst-, average-, and semi-average-case behaviors. In semi-random planar graph models an adversary is allowed to modify moderately a random planar graph, where a graph is chosen uniformly at random among all planar graphs. With regard to the heuristics particular interest is given to the influences of the following four popular strategies to overcome local optima: local- vs. global-search, single- vs. multi-start, small vs. large population, and elitism vs. non-elitism selection. Finally, the black-box complexities of the planar graph models are analyzed.
@inproceedings{Storch:2006,
author = {Storch, Tobias},
title = {How randomized search heuristics find maximum cliques in planar graphs},
volume = {1},
booktitle = {GECCO 2006 - Genetic and Evolutionary Computation Conference},
pages = {567--574},
publisher = {ACM},
year = {2006},
address = {New York, NY, USA},
}Etsuji Tomita, Akira Tanaka, and Haruhisa Takahashi. The worst-case time complexity for generating all maximal cliques and computational experiments. Theoretical Computer Science, 363(1):28—42, 2006.
Note: Theoretical work on worst case complexity of generating all maximal cliques with a depth-first search algorithm. The exact algorithm has a pruning methods that are similar to the Bron-Kerbosh algorithm (BronK:1973), and a different, more compact, representation of the enumerated maximal cliques. The algorithm has \(O(3^{n/3})\) worst-case time complexity for enumerating all maximal cliques (which is optimal).
We present a depth-first search algorithm for generating all maximal cliques of an undirected graph, in which pruning methods are employed as in the Bron-Kerbosch algorithm. All the maximal cliques generated are output in a tree-like form. Subsequently, we prove that its worst-case time complexity is \(O(3^{n/3})\) for an n-vertex graph. This is optimal as a function of n, since there exist up to \(3^{n/3}\) maximal cliques in an n-vertex graph. The algorithm is also demonstrated to run very fast in practice by computational experiments.
@article{TomitaTT:2006,
author = {Tomita, Etsuji and Tanaka, Akira and Takahashi, Haruhisa},
title = {The worst-case time complexity for generating all maximal cliques and computational experiments},
journal = {Theoretical Computer Science},
volume = {363},
number = {1},
pages = {28--42},
publisher = {Elsevier},
year = {2006},
doi = {10.1016/j.tcs.2006.06.015},
}Immanuel M. Bomze, Marco Budinich, Panos M. Pardalos, and Marcello Pelillo. The maximum clique problem. Handbook of Combinatorial Optimization (Supplement Volume A), 4:1—74, 1999.
Note: Most recent complete survey on the maximum clique formulations, generalisations, algorithms and applications.
@article{BomzeBPP:1999,
author = {Bomze, Immanuel M. and Budinich, Marco and Pardalos, Panos M. and Pelillo, Marcello},
title = {The maximum clique problem},
journal = {Handbook of Combinatorial Optimization (Supplement Volume A)},
volume = {4},
pages = {1--74},
editor = {Du, D.-Z. and Pardalos, Panos M.},
publisher = {Kluwer Academic Publishers},
city = {Boston, MA},
year = {1999},
url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.56.6221},
}Mihir Bellare, Oded Goldreich, and Madhu Sudan. Free bits, pcps, and nonapproximability - towards tight results. SIAM Journal on Computing, 27(3):804—915, 1998.
This paper continues the investigation of the connection between probabilistically checkable proofs (PCPs) the approximability of NP-optimization problems. The emphasis is on proving tight non-approximability results via consideration of measures like the ‘‘free bit complexity” and the ‘‘amortized free bit complexity” of proof systems.
The first part of the paper presents a collection of new proof systems based on a new errorcorrecting code called the long code. We provide a proof system which has amortized free bit complexity of \(2 + \epsilon\), implying that approximating Max Clique within \(N^{\frac{1}{3}-\epsilon}\), and approximating the Chromatic Number within \(N^{\frac{1}{5}-\epsilon}\), are hard assuming NP \(\neq\) coRP, for any \(\epsilon > 0\). We also derive the first explicit and reasonable constant hardness factors for Min Vertex Cover, Max2SAT, and Max Cut, and improve the hardness factor for Max3SAT. We note that our non-approximability factors for MaxSNP problems are appreciably close to the values known to be achievable by polynomial time algorithms. Finally we note a general approach to the derivation of strong non-approximability results under which the problem reduces to the construction of certain ‘‘gadgets.”
The increasing strength of non-approximability results obtained via the PCP connection motivates us to ask how far this can go, and whether PCPs are inherent in any way. The second part of the paper addresses this. The main result is a ‘‘reversal” of the FGLSS connection: where the latter had shown how to translate proof systems for NP into NP-hardness of approximation results for Max Clique, we show how any NP-hardness of approximation result for Max Clique yields a proof system for NP. Roughly our result says that for any constant \(f\) if Max Clique is NP-hard to approximate within N^{1/(1+f)} then \(NP \subseteq \overline{\text{FPCP}}\left[log, f \right]\), the latter being the class of languages possessing proofs of logarithmic randomness and amortized free bit complexity \(f\). This suggests that PCPs are inherent to obtaining non-approximability results. Furthermore the tight relation suggests that reducing the amortized free bit complexity is necessary for improving the non-approximability results for Max Clique.
The third part of our paper initiates a systematic investigation of the properties of PCP and FPCP as a function of the various parameters: randomness, query complexity, free bit complexity, amortized free bit complexity, proof size, etc. We are particularly interested in ‘‘triviality” results, which indicate which classes are not powerful enough to capture NP. We also distill the role of randomized reductions in this are
The first part of the paper presents a collection of new proof systems based on a new errorcorrecting code called the long code. We provide a proof system which has amortized free bit complexity of \(2 + \epsilon\), implying that approximating Max Clique within \(N^{\frac{1}{3}-\epsilon}\), and approximating the Chromatic Number within \(N^{\frac{1}{5}-\epsilon}\), are hard assuming NP \(\neq\) coRP, for any \(\epsilon > 0\). We also derive the first explicit and reasonable constant hardness factors for Min Vertex Cover, Max2SAT, and Max Cut, and improve the hardness factor for Max3SAT. We note that our non-approximability factors for MaxSNP problems are appreciably close to the values known to be achievable by polynomial time algorithms. Finally we note a general approach to the derivation of strong non-approximability results under which the problem reduces to the construction of certain ‘‘gadgets.”
The increasing strength of non-approximability results obtained via the PCP connection motivates us to ask how far this can go, and whether PCPs are inherent in any way. The second part of the paper addresses this. The main result is a ‘‘reversal” of the FGLSS connection: where the latter had shown how to translate proof systems for NP into NP-hardness of approximation results for Max Clique, we show how any NP-hardness of approximation result for Max Clique yields a proof system for NP. Roughly our result says that for any constant \(f\) if Max Clique is NP-hard to approximate within N^{1/(1+f)} then \(NP \subseteq \overline{\text{FPCP}}\left[log, f \right]\), the latter being the class of languages possessing proofs of logarithmic randomness and amortized free bit complexity \(f\). This suggests that PCPs are inherent to obtaining non-approximability results. Furthermore the tight relation suggests that reducing the amortized free bit complexity is necessary for improving the non-approximability results for Max Clique.
The third part of our paper initiates a systematic investigation of the properties of PCP and FPCP as a function of the various parameters: randomness, query complexity, free bit complexity, amortized free bit complexity, proof size, etc. We are particularly interested in ‘‘triviality” results, which indicate which classes are not powerful enough to capture NP. We also distill the role of randomized reductions in this are
@article{BellareGS:1998,
author = {Bellare, Mihir and Goldreich, Oded and Sudan, Madhu},
title = {Free bits, PCPs, and nonapproximability - towards tight results},
journal = {SIAM Journal on Computing},
volume = {27},
number = {3},
pages = {804--915},
year = {1998},
doi = {10.1137/S0097539796302531},
}Johan Håstad. Clique is hard to approximate within \(n^{1-\epsilon}\). In Proceedings of 37th Ann. IEEE Symp. on Foundations of Computer Science, pages 627—636. IEEE Computer Society, 1996.
The author proves that unless NP=coR, Max Clique is hard to approximate in polynomial time within a factor \(n^{1-\epsilon}\) for any \(\delta \gt 0\). This is done by, for any \(\delta \gt 0\), constructing a proof system for NP which uses \(\delta\) amortized free bits. A central lemma, which might be of independent interest, gives sufficient conditions (in the form of a certain type of agreement) for creating a global function from local functions certain local consistency conditions.
@inproceedings{Hastad:1996,
author = {H{\aa}stad, Johan},
title = {Clique is hard to approximate within $n^{1-\epsilon}$},
booktitle = {Proceedings of 37th Ann. IEEE Symp. on Foundations of Computer Science},
pages = {627--636},
publisher = {IEEE Computer Society},
year = {1996},
doi = {10.1109/SFCS.1996.548522},
}Panos M. Pardalos and Jue Xue. The maximum clique problem. Journal of Global Optimization, 4(3):301—328, 1994.
In this paper we present a survey of results concerning algorithms, complexity, and applications of the maximum clique problem. We discuss enumerative and exact algorithms, heuristics, and a variety of other proposed methods. An up to date bibliography on the maximum clique and related problems is also provided.
@article{PardalosX:1994,
author = {Pardalos, Panos M. and Xue, Jue},
title = {The maximum clique problem},
journal = {Journal of Global Optimization},
volume = {4},
number = {3},
pages = {301--328},
year = {1994},
doi = {10.1007/BF01098364},
}Michael R. Garey and David S. Johnson. Computers and Intractability: A Guide to the Theory of NP-completeness. ISBN 978-0716710455
Note: Classic book on NP-completeness.
@book{GareyJ:1979,
author = {Garey, Michael R. and Johnson, David S.},
title = {Computers and Intractability: A Guide to the Theory of NP-completeness},
publisher = {Freeman&Co., San Francisco},
year = {1979},
}David W. Matula. The largest clique size in a random graph. Technical Report CS 7608, Department of Computer Science, Southern Methodist University, 1976
The size of the largest complete subgraph in a random graph is shown to be a random variable with a very peaked density. The extent to which a specified threshold function is investigated by closed form inequality bounds affording numeric examples and by sharp asymptotic formulas for the limiting behavior.
@techreport{Matula:1976,
author = {Matula, David W.},
title = {The Largest Clique Size in a Random Graph},
number = {CS 7608},
institution = {Department of Computer Science, Southern Methodist University},
year = {1976},
url = {http://lyle.smu.edu/~matula/Tech-Report76.pdf},
}Coen Bron and Joep Kerbosch. Algorithm 457: finding all cliques of an undirected graph. Communications of ACM, 16(9):575—577, sep 1973.
Note: Exact algorithm very popular in computational chemistry and other application domains. Variants with special pivoting rules are among the best performing exact algorithms for the problem. Being complete, it can be applied only to very small instances or to larger instances with small degeneracy number (see EppsteinS:2011).
@article{BronK:1973,
author = {Bron, Coen and Kerbosch, Joep},
title = {Algorithm 457: finding all cliques of an undirected graph},
journal = {Communications of ACM},
volume = {16},
number = {9},
pages = {575--577},
publisher = {ACM},
year = {1973},
month = sep,
address = {New York, NY, USA},
doi = {10.1145/362342.362367},
}Richard M. Karp. Reducibility among combinatorial problems. In R. E. Miller and J. W. Thatcher, editors, Complexity of Computer Computations, pages 85—103. Plenum Press, 1972.
Note: Historical paper in which Karp presents 21 NP-complete decision problems and reductions among them.
A large class of computational problems involve the determination of properties of graphs, digraphs, integers, arrays of integers, finite families of finite sets, boolean formulas and elements of other countable domains. Through simple encodings from such domains into the set of words over a finite alphabet these problems can be converted into language recognition problems, and we can inquire into their computational complexity. It is reasonable to consider such a problem satisfactorily solved when an algorithm for its solution is found which terminates within a number of steps bounded by a polynomial in the length of the input. We show that a large number of classic unsolved problems of covering, matching, packing, routing, assignment and sequencing are equivalent, in the sense that either each of them possesses a polynomial-bounded algorithm or none of them does.
@incollection{Karp:1972,
author = {Karp, Richard M.},
title = {Reducibility Among Combinatorial Problems},
booktitle = {Complexity of Computer Computations},
pages = {85--103},
editor = {Miller, R. E. and Thatcher, J. W.},
publisher = {Plenum Press},
year = {1972},
url = {http://www.cs.berkeley.edu/~luca/cs172/karp.pdf},
}1.1.1 Bounds
Igor Dukanovic and Franz Rendl. Semidefinite programming relaxations for graph coloring and maximal clique problems. Mathematical Programming, 109:345—365, 2007.
The semidefinite programming formulation of the Lovász theta number does not only give one of the best polynomial simultaneous bounds on the chromatic number \(\chi(G)\) or the clique number \(\omega(G)\) of a graph, but also leads to heuristics for graph coloring and extracting large cliques. This semidefinite programming formulation can be tightened toward either \(\chi(G)\) or \(\omega(G)\) by adding several types of cutting planes. We explore several such strengthenings, and show that some of them can be computed with the same effort as the theta number. We also investigate computational simplifications for graphs with rich automorphism groups.
@article{DukanovicR:2007,
author = {Dukanovic, Igor and Rendl, Franz},
title = {Semidefinite programming relaxations for graph coloring and maximal clique problems},
journal = {Mathematical Programming},
volume = {109},
pages = {345-365},
publisher = {Springer Berlin / Heidelberg},
year = {2007},
doi = {10.1007/s10107-006-0026-z},
}Javier Peña, Juan Vera, and Luis F. Zuluaga. Computing the stability number of a graph via linear and semidefinite programming. SIAM Journal on Optimization, 18(1):87—105, 2007.
We study certain linear and semidefinite programming lifting approximation schemes for computing the stability number of a graph. Our work is based on and refines de Klerk and Pasechnik’s approach to approximating the stability number via copositive programming [SIAM J. Optim., 12 (2002), pp. 875-892]. We provide a closed-form expression for the values computed by the linear programming approximations. We also show that the exact value of the stability number \(\alpha(G)\) is attained by the semidefinite approximation of order \(\alpha(G)-1\) as long as \(\alpha(G) \leq 6\). Our results reveal some sharp differences between the linear and the semidefinite approximations. For instance, the value of the linear programming approximation of any order is strictly larger than \(\alpha(G)\) whenever \(\alpha(G) > 1\).
@article{Pena:2008,
author = {Javier Pe{\~n}a and Juan Vera and Luis F. Zuluaga},
title = {Computing the Stability Number of a Graph Via Linear and Semidefinite Programming},
journal = {SIAM Journal on Optimization},
volume = {18},
number = {1},
pages = {87--105},
publisher = {SIAM},
year = {2007},
doi = {10.1137/05064401X},
}Nebojša Gvozdenović and Monique Laurent. Semidefinite bounds for the stability number of a graph via sums of squares of polynomials. Integer Programming and Combinatorial Optimization, pages 285—294, 2005.
Lovász and Schrijver [9] have constructed semidefinite relaxations for the stable set polytope of a graph G = (V,E) by a sequence of lift-and-project operations; their procedure finds the stable set polytope in at most α(G) steps, where \(\alpha(G)\) is the stability number of G. Two other hierarchies of semidefinite bounds for the stability number have been proposed by Lasserre [4],[5] and by de Klerk and Pasechnik [3], which are based on relaxing nonnegativity of a polynomial by requiring the existence of a sum of squares decomposition. The hierarchy of Lasserre is known to converge in \(\alpha(G)\) steps as it refines the hierarchy of Lovász and Schrijver, and de Klerk and Pasechnik conjecture that their hierarchy also finds the stability number after \(\alpha(G)\) steps. We prove this conjecture for graphs with stability number at most 8 and we show that the hierarchy of Lasserre refines the hierarchy of de Klerk and Pasechnik.
@article{GvozdenovicL:2005,
author = {Gvozdenovi{\'c}, Neboj{\vs}a and Laurent, Monique},
title = {Semidefinite bounds for the stability number of a graph via sums of squares of polynomials},
journal = {Integer Programming and Combinatorial Optimization},
pages = {285--294},
publisher = {Springer},
year = {2005},
doi = {10.1007/11496915_11},
}Etienne de Klerk and Dmitrii V. Pasechnik. Approximation of the stability number of a graph via copositive programming. SIAM Journal on Optimization, 12(4):875—892, 2002.
Lovász and Schrijver [SIAM J. Optim., 1 (1991), pp. 166—190] showed how to formulate increasingly tight approximations of the stable set polytope of a graph by solving semidefinite programs (SDPs) of increasing size (lift-and-project method). In this paper we present a similar idea. We show how the stability number can be computed as the solution of a conic linear program (LP) over the cone of copositive matrices. Subsequently, we show how to approximate the copositive cone ever more closely via a hierarchy of linear or semidefinite programs of increasing size (liftings). The latter idea is based on recent work by Parrilo [Structured Semidefinite Programs and Semi-algebraic Geometry Methods in Robustness and Optimization, Ph.D. thesis, California Institute of Technology, Pasadena, CA, 2000]. In this way we can compute the stability number \(\alpha(G)\) of any graph \(G(V,E)\) after at most \(\alpha(G)^2\) successive liftings for the LP-based approximations. One can compare this to the \(n - \alpha(G)-1\) bound for the LP-based lift-and-project scheme of Lovász and Schrijver. Our approach therefore requires fewer liftings for families of graphs where \(\alpha(G) < O(\sqrt{n})\). We show that the first SDP-based approximation for \(\alpha(G)\) in our series of increasingly tight approximations coincides with the \(\vartheta’\)-function of Schrijver [IEEE Trans. Inform. Theory, 25 (1979), pp. 425—429]. We further show that the second approximation is tight for complements of triangle-free graphs and for odd cycles.
@article{deKlerkP:2002,
author = {Etienne de Klerk and Dmitrii V. Pasechnik},
title = {Approximation of the Stability Number of a Graph via Copositive Programming},
journal = {SIAM Journal on Optimization},
volume = {12},
number = {4},
pages = {875--892},
publisher = {SIAM},
year = {2002},
doi = {10.1137/S1052623401383248},
}Subhash Khot. Improved inapproximability results for maxclique, chromatic number and approximate graph coloring. In Foundations of Computer Science, 2001. Proceedings. 42nd IEEE Symposium on, pages 600—609. IEEE, 2001.
The author presents improved inapproximability results for three problems: the problem of finding the maximum clique size in a graph, the problem of finding the chromatic number of a graph, and the problem of coloring a graph with a small chromatic number with a small number of colors. J. Hastad’s (1996) result shows that the maximum clique size in a graph with n vertices is inapproximable in polynomial time within a factor \(n^{1-\epsilon}\) or arbitrarily small constant \(\epsilon>0\) unless NP=ZPP. We aim at getting the best subconstant value of \(\epsilon\) in Hastad’s result. We prove that clique size is inapproximable within a factor \(n/2((log n))^{1-y}\) corresponding to \(\epsilon=1/(log n)^\gamma\) for some constant \(\gamma>0\) unless NP \(\subseteq\) ZPTIME\((2((log n))^{O(1)})\). This improves the previous best inapproximability factor of \(n/2^{O(log n \sqrt{log log n})}\) (corresponding to \(\epsilon=O(1/\sqrt{log log n}))\) due to L. Engebretsen and J. Holmerin (2000). A similar result is obtained for the problem of approximating chromatic number of a graph. We also present a new hardness result for approximate graph coloring. We show that for all sufficiently large constants k, it is NP-hard to color a k-colorable graph with \(k^{1/25 (log k)}\) colors. This improves a result of M. Fürer (1995) that for arbitrarily small constant \(\epsilon>0\), for sufficiently large constants k, it is hard to color a k-colorable graph with \(k^{3/2-\epsilon}\) colors.
@inproceedings{Khot:2001,
author = {Khot, Subhash},
title = {Improved inapproximability results for maxclique, chromatic number and approximate graph coloring},
booktitle = {Foundations of Computer Science, 2001. Proceedings. 42nd IEEE Symposium on},
pages = {600--609},
year = {2001},
doi = {10.1109/SFCS.2001.959936},
}Alexander Schrijver. A comparison of the delsarte and lovász bounds. Information Theory, IEEE Transactions on, 25(4):425—429, 1979.
Delsarte’s linear programming bound (an upper bound on the cardinality of cliques in association schemes) is compared with Lovaász’ s \(\theta\)-function bound (an upper bound on the Shannon capacity of a graph). The two bounds can be treated in a uniform fashion. Delsarte’s linear programming bound can be generalized to a bound \(\theta^\prime(G)\) on the independence number \(\propto(G)\) of an arbitrary graph \(G\), such that \(\theta ^\prime(G) \leq \theta(G)\). On the other hand, if the edge set of \(G\) is a union of classes of a symmetric association scheme, \(\theta(G)\) may be calculated by linear programming, For such graphs the product \(\theta(G) \cdot \theta(\overline{G})\) is equal to the number of vertices of \(G\).
@article{Schrijver:1979,
author = {Schrijver, Alexander},
title = {A comparison of the Delsarte and Lov{\'a}sz bounds},
journal = {Information Theory, IEEE Transactions on},
volume = {25},
number = {4},
pages = {425--429},
publisher = {IEEE},
year = {1979},
doi = {10.1109/TIT.1979.1056072},
}1.2 Stochastic Local Search algorithms
Yan Jin and Jin-Kao Hao. General swap-based multiple neighborhood tabu search for the maximum independent set problem. Engineering Applications of Artificial Intelligence, 37:20—33, 2015.
Given a graph G=(V,E)G=(V,E), the Maximum Independent Set problem (MIS) aims to determine a subset S\(\subseteq\)VS\(\subseteq\)V of maximum cardinality such that no two vertices of S are adjacent. This paper presents a general Swap-Based Tabu Search (SBTS) for solving the MIS. SBTS integrates distinguished features including a general and unified (k,1)-swap operator, four constrained neighborhoods and specific rules for neighborhood exploration. Extensive evaluations on two popular benchmarks (DIMACS and BHOSLIB) of 120 instances show that SBTS attains the best-known results for all the instances. To our knowledge, such a performance was not reported in the literature for a single heuristic. The best-known results on 11 additional instances from code theory are also attained.
@article{JinH:2015,
author = {Yan Jin and Jin{-}Kao Hao},
title = {General swap-based multiple neighborhood tabu search for the maximum independent set problem},
journal = {Engineering Applications of Artificial Intelligence},
volume = {37},
pages = {20--33},
year = {2015},
doi = {10.1016/j.engappai.2014.08.007},
}Franco Mascia, Paola Pellegrini, Mauro Birattari, and Thomas Stützle. An analysis of parameter adaptation in reactive tabu search. International Transactions in Operational Research, 21(1):127—152, jan 2014.
Note: In depth analysis of the dynamics of reactive tabu search focussing on the maximum clique problem (BattitiM:2010), and quadratic assignment problem. It also presents an analysis of the DIMACS instances and the first optimal solution with 1100 nodes for MANN_a81.
On-line parameter adaptation schemes are widely used in metaheuristics. They are sometimes preferred to off-line tuning techniques for two main reasons. First, they promise to achieve good performance even on new instance families that have not been considered during the design or the tuning phase of the algorithm. Second, it is assumed that an on-line scheme could adapt the algorithm’s behaviour to local characteristics of the search space. This paper challenges the second hypothesis by analysing the contribution of the parameter adaptation to the performance of a state-of-the-art reactive tabu search (RTS) algorithm for the maximum clique problem. Our experimental analysis shows that this on-line parameter adaptation scheme converges to good instance-specific settings for the parameters, and that there is no evidence that it adapts to the local characteristics of the search space. The insights gained from the analysis are confirmed by further experiments with an RTS algorithm for the quadratic assignment problem. Together, the results of the two algorithms shed some new light on the reasons behind the effectiveness of RTS.
@article{MasciaPBS:2014,
author = {Franco Mascia and Paola Pellegrini and Mauro Birattari and Thomas St{\"u}tzle},
title = {An Analysis of Parameter Adaptation in Reactive Tabu Search},
journal = {International Transactions in Operational Research},
volume = {21},
number = {1},
pages = {127--152},
year = {2014},
month = jan,
doi = {10.1111/itor.12043},
}Una Benlic and Jin-Kao Hao. Breakout local search for maximum clique problems. Computers and Operations Research, 40(1):192—206, 2013.
The maximum clique problem (MCP) is one of the most popular combinatorial optimization problems with various practical applications. An important generalization of MCP is the maximum weight clique problem (MWCP) where a positive weight is associate to each vertex. In this paper, we present Breakout Local Search (BLS) which can be applied to both MC and MWC problems without any particular adaptation. BLS explores the search space by a joint use of local search and adaptive perturbation strategies. Extensive experimental evaluations using the DIMACS and BOSHLIB benchmarks show that the proposed approach competes favourably with the current state-of-art heuristic methods for MCP. Moreover, it is able to provide some new improved results for a number of MWCP instances. This paper also reports for the first time a detailed landscape analysis, which has been missing in the literature. This analysis not only explains the difficulty of several benchmark instances, but also justifies to some extent the behaviour of the proposed approach and the used parameter settings.
@article{BenlicH:2013,
author = {Una Benlic and Jin{-}Kao Hao},
title = {Breakout Local Search for maximum clique problems},
journal = {Computers and Operations Research},
volume = {40},
number = {1},
pages = {192--206},
year = {2013},
doi = {10.1016/j.cor.2012.06.002},
}Qinghua Wu and Jin-Kao Hao. An adaptive multistart tabu search approach to solve the maximum clique problem. Journal of Combinatorial Optimization, 26(1):86—108, 2013.
Given an undirected graph G=(V,E) with vertex set V={1,…,n} and edge set E\(\subseteq\)VxV. The maximum clique problem is to determine in G a clique (i.e., a complete subgraph) of maximum cardinality. This paper presents an effective algorithm for the maximum clique problem. The proposed multistart tabu search algorithm integrates a constrained neighborhood, a dynamic tabu tenure mechanism and a long term memory based restart strategy. Our proposed algorithm is evaluated on the whole set of 80 DIMACS challenge benchmarks and compared with five state-of-the-art algorithms. Computational results show that our proposed algorithm attains the largest known clique for 79 benchmarks.
@article{WuH:2013,
author = {Qinghua Wu and Jin{-}Kao Hao},
title = {An adaptive multistart tabu search approach to solve the maximum clique problem},
journal = {Journal of Combinatorial Optimization},
volume = {26},
number = {1},
pages = {86--108},
year = {2013},
doi = {10.1007/s10878-011-9437-8},
}Ben-Da Zhou, Hong-Liang Yao, Ming-Hua Shi, Qin Yue, and Hao Wang. An new immune genetic algorithm based on uniform design sampling. Knowledge and Information Systems, pages 1—15, 2012.
The deficiencies of keeping population diversity, prematurity and low success rate of searching the global optimal solution are the shortcomings of genetic algorithm (GA). Based on the bias of samples in the uniform design sampling (UDS) point set, the crossover operation in GA is redesigned. Using the concentrations of antibodies in artificial immune system (AIS), the chromosomes concentration in GA is defined and the clonal selection strategy is designed. In order to solve the maximum clique problem (MCP), an new immune GA (UIGA) is presented based on the clonal selection strategy and UDS. The simulation results show that the UIGA provides superior solution quality, convergence rate, and other various indices to those of the simple and good point GA when solving MCPs.
@article{ZhouYSYW:2012,
author = {Zhou, Ben-Da and Yao, Hong-Liang and Shi, Ming-Hua and Yue, Qin and Wang, Hao},
title = {An new immune genetic algorithm based on uniform design sampling},
journal = {Knowledge and Information Systems},
pages = {1-15},
year = {2012},
doi = {10.1007/s10115-011-0476-3},
}Mohammad M. Javidi and Saeed Mehrabi. On evolutionary algorithms for large cliques in random graphs. International Journal of Applied Mathematics and Statistics, 22(SUPPL. 11):53—60, 2011.
The maximum clique problem (MCP) is an old NP-complete problem which has been frequently used for delivering the NP-completeness of many other problems with respect to computational complexity literature. In this paper, we give a heuristic based genetic algorithm for solving this problem. By incorporating a heuristic into the crossover operator, we speed up the convergence rate of our algorithm - GACP (genetic algorithm for clique problem). GACP has been tested on a variety of challenging benchmarks including DIMACS instances and compared with two recently efficient algorithms. Experimental results show that GACP not only competes consistently with these algorithms but also performed well at solving the maximum clique problem.
@article{JavidiM:2011,
author = {Javidi, Mohammad M. and Mehrabi, Saeed},
title = {On evolutionary algorithms for large cliques in random graphs},
journal = {International Journal of Applied Mathematics and Statistics},
volume = {22},
number = {SUPPL. 11},
pages = {53-60},
year = {2011},
url = {http://ceser.in/ceserp/index.php/ijamas/article/view/259/137},
}Wayne Pullan, Franco Mascia, and Mauro Brunato. Cooperating local search for the maximum clique problem. Journal of Heuristics, 17(2):181—199, apr 2011.
Note: Parallel meta-heuristic with state-of-the-art results on DIMACS and BHOSLIB instances. Components are a greedy reactive tabu search component (BattitiM:2010), a penalty-based dynamic local search (PullanH:2006), and a focussed meta-heuristic that focusses on cliques having nodes with a specific degree.
The advent of desktop multi-core computers has dramatically improved the usability of parallel algorithms which, in the past, have required specialised hardware. This paper introduces cooperating local search (CLS), a parallelised hyper-heuristic for the maximum clique problem. CLS utilises cooperating low level heuristics which alternate between sequences of iterative improvement, during which suitable vertices are added to the current clique, and plateau search, where vertices of the current clique are swapped with vertices not in the current clique. These low level heuristics differ primarily in their vertex selection techniques and their approach to dealing with plateaus. To improve the performance of CLS, guidance information is passed between low level heuristics directing them to particular areas of the search domain. In addition, CLS dynamically reconfigures the allocation of low level heuristics to cores, based on information obtained during a trial, to ensure that the mix of low level heuristics is appropriate for the instance being optimised. CLS has no problem instance dependent parameters, improves the state-of-the-art performance for the maximum clique problem over all the BHOSLIB benchmark instances and attains unprecedented consistency over the state-of-the-art on the DIMACS benchmark instances.
@article{PullanMB:2011,
author = {Pullan, Wayne and Mascia, Franco and Brunato, Mauro},
title = {Cooperating local search for the maximum clique problem},
journal = {Journal of Heuristics},
volume = {17},
number = {2},
pages = {181--199},
publisher = {Springer},
year = {2011},
month = apr,
doi = {10.1007/s10732-010-9131-5},
}Roberto Battiti and Franco Mascia. Reactive and dynamic local search for max-clique: Engineering effective building blocks. Computers and Operations Research, 37(3):534—542, mar 2010.
Note: Latest implementation of the original reactive tabu search for the maximum clique problem (BattitiP:2001). It is a parameter free algorithm which is state-of-the-art results on DIMACS instances.
This paper presents the results of an ongoing investigation about how different algorithmic building blocks contribute to solving the maximum clique problem. We consider greedy constructions, plateau searches, and more complex schemes based on dynamic penalties and/or prohibitions, in particular the recently proposed technique of dynamic local search and the previously proposed reactive local search (RLS). We design a variation of the original RLS algorithm where the role of long-term memory (LTM) is increased (RLS-LTM). In addition, we consider in detail the effect of the low-level implementation choices on the CPU time per iteration. We present experimental results on randomly generated graphs with different statistical properties, showing the crucial effects of the implementation, the robustness of different techniques, and their empirical scalability.
@article{BattitiM:2010,
author = {Battiti, Roberto and Mascia, Franco},
title = {Reactive and dynamic local search for max-clique: Engineering effective building blocks},
journal = {Computers and Operations Research},
volume = {37},
number = {3},
pages = {534--542},
publisher = {Elsevier Science Ltd.},
year = {2010},
month = mar,
address = {Oxford, UK, UK},
doi = {10.1016/j.cor.2009.02.013},
}Duc-Cuong Dang and Aziz Moukrim. Subgraph extraction and memetic algorithm for the maximum clique problem. In ICEC 2010 - Proceedings of the International Conference on Evolutionary Computation, pages 77—84. INSTICC, 2010.
The maximum clique problem involves finding the largest set of pair-wise adjacent vertices in a graph. The problem is classic but still attracts much attention because of its hardness and its prominent applications. Our work is based on the existence of an order on all the vertices whereby those belonging to a maximum clique stay close enough to each other. Such an order can be identified via the extraction of a particular sub-graph from the original graph. The problem can consequently be seen as a permutation problem that can be addressed efficiently with an evolutionary-like algorithm, here we use a memetic algorithm (MA). Computational experiments conducted on DIMACS benchmark instances clearly show our MA which not only outperforms existing genetic approaches, but also compares very well to state-of-the-art algorithms.
@inproceedings{DangM:2010,
author = {Dang, Duc-Cuong and Moukrim, Aziz},
title = {Subgraph extraction and memetic algorithm for the maximum clique problem},
booktitle = {ICEC 2010 - Proceedings of the International Conference on Evolutionary Computation},
pages = {77-84},
publisher = {INSTICC},
year = {2010},
url = {http://hal.archives-ouvertes.fr/hal-00575910/en/},
}Shalini Rajawat, Naveen Hemrajani, and Ekta Menghani. Solving maximal clique problem through genetic algorithm. In R. B. Patel and B. P. Singh, editors, AIP Conference Proceedings, volume 1324, pages 235—238. American Institute of Physics, 2010.
Genetic algorithm is one of the most interesting heuristic search techniques. It depends basically on three operations; selection, crossover and mutation. The outcome of the three operations is a new population for the next generation. Repeating these operations until the termination condition is reached. All the operations in the algorithm are accessible with today’s molecular biotechnology. The simulations show that with this new computing algorithm, it is possible to get a solution from a very small initial data pool, avoiding enumerating all candidate solutions. For randomly generated problems, genetic algorithm can give correct solution within a few cycles at high probability.
@inproceedings{RajawatHM:2010,
author = {Rajawat, Shalini and Hemrajani, Naveen and Menghani, Ekta},
title = {Solving maximal clique problem through genetic algorithm},
volume = {1324},
booktitle = {AIP Conference Proceedings},
pages = {235-238},
editor = {Patel, R. B. and Singh, B. P.},
publisher = {American Institute of Physics},
year = {2010},
doi = {10.1063/1.3526202},
}Shijun Ren and Yadong Wang. An improved aco metaheuristic for solving the mcp. In Proceedings - 2010 6th International Conference on Natural Computation, ICNC 2010, volume 1, pages 106—111, 2010.
In this paper, an ant colony optimization (ACO) algorithm with local pheromone update strategy for solving maximum clique problem (MCP) is proposed. It is based on iteration. During each iteration cycle, ants in the colony guide their decisions by pheromone trails they deposit on vertices of the MCP graph while building solutions. And when an ant has constructed a clique, the local pheromone update procedure is implemented to ensure diversification in an iteration cycle. Once all ants have constructed their solutions, the pheromone is updated according to global pheromone update rule which increases the amount of pheromone on vertices that have been found in high quality solutions so as to intensify the search towards the "promising" areas in the search space. Experiments on DIMACS benchmark instances are presented and the results show that the improved ACO metaheuristic outperforms other population-based metaheuristics such as EA/G algorithm which is the best genetic algorithm on the problem reported so far.
@inproceedings{RenW:2010,
author = {Ren, Shijun and Wang, Yadong},
title = {An improved ACO metaheuristic for solving the MCP},
volume = {1},
booktitle = {Proceedings - 2010 6th International Conference on Natural Computation, ICNC 2010},
pages = {106-111},
year = {2010},
doi = {10.1109/ICNC.2010.5583351},
}Thang N. Bui, ThanhVu Nguyen, and Joseph R. Rizzo Jr. Parallel shared memory strategies for ant-based optimization algorithms. In Proceedings of the 11th Annual Genetic and Evolutionary Computation Conference, GECCO-2009, pages 1—8, New York, NY, USA, 2009. ACM.
This paper describes a general scheme to convert sequential ant-based algorithms into parallel shared memory algorithms. The scheme is applied to an ant-based algorithm for the maximum clique problem. Extensive experimental results indicate that the parallel version provides noticeable improvements to the running time while maintaining comparable solution quality to that of the sequential version. Copyright 2009 ACM.
@inproceedings{BuiNR:2009,
author = {Bui, Thang N. and Nguyen, ThanhVu and Rizzo Jr., Joseph R.},
title = {Parallel shared memory strategies for ant-based optimization algorithms},
booktitle = {Proceedings of the 11th Annual Genetic and Evolutionary Computation Conference, GECCO-2009},
pages = {1--8},
publisher = {ACM},
year = {2009},
address = {New York, NY, USA},
doi = {10.1145/1569901.1569903},
}Andrea Grosso, Marco Locatelli, and Wayne Pullan. Simple ingredients leading to very efficient heuristics for the maximum clique problem. Journal of Heuristics, 14(6):587—612, oct 2007.
Note: Parameter free meta-heuristic. First optimal solution of size 80 for the DIMACS instance C2000.9.
Starting from an algorithm recently proposed by Pullan and Hoos, we formulate and analyze iterated local search algorithms for the maximum clique problem. The basic components of such algorithms are a fast neighbourhood search (not based on node evaluation but on completely random selection) and simple, yet very effective, diversification techniques and restart rules. A detailed computational study is performed in order to identify strengths and weaknesses of the proposed algorithms and the role of the different components on several classes of instances. The tested algorithms are very fast and reliable: most of the DIMACS benchmark instances are solved within very short CPU times. For one of the hardest tests, a new putative optimum was discovered by one of our algorithms. Very good performances were also shown on recently proposed and more difficult instances. It is important to remark that the heuristics tested in this paper are basically parameter free (the appropriate value for the unique parameter is easily identified and was, in fact, the same value for all problem instances used in this paper).
@article{GrossoLP:2007,
author = {Grosso, Andrea and Locatelli, Marco and Pullan, Wayne},
title = {Simple ingredients leading to very efficient heuristics for the maximum clique problem},
journal = {Journal of Heuristics},
volume = {14},
number = {6},
pages = {587--612},
year = {2007},
month = oct,
doi = {10.1007/s10732-007-9055-x},
}Hassan Younies and George O. Wesolowsky. Planar maximal covering location problem under block norm distance measure. Journal of the Operational Research Society, 58(6):740—750, 2007. Clique Partitioning Problem
This paper introduces a new model for the planar maximal covering location problem (PMCLP) under different block norms. The problem involves locating g facilities anywhere on the plane in order to cover the maximum number of n given demand points. The generalization, in this paper, is that the distance measures assigned to facilities are block norms of different types and different proximity measures. First, the PMCLP under different block norms is modelled as a maximum clique partition problem on an equivalent multi-interval graph. Then, the equivalent graph problem is modelled as an unconstrained binary quadratic problem (UQP). Both the maximum clique partition problem and the UQP are NP-hard problems; therefore, we solve the UQP format through a genetic algorithm heuristic. Computational examples are given.
@article{YouniesW:2007,
author = {Younies, Hassan and Wesolowsky, George O.},
title = {Planar maximal covering location problem under block norm distance measure},
journal = {Journal of the Operational Research Society},
volume = {58},
number = {6},
pages = {740-750},
year = {2007},
doi = {10.1057/palgrave.jors.2602172},
}Qingfu Zhang, Jianyong Sun, and Edward Tsang. Combinations of estimation of distribution algorithms and other techniques. ISSN 1476-8186
This paper summaries our recent work on combining estimation of distribution algorithms (EDA) and other techniques for solving hard search and optimization problems: a) guided mutation, an offspring generator in which the ideas from EDAs and genetic algorithms are combined together, we have shown that an evolutionary algorithm with guided mutation outperforms the best GA for the maximum clique problem, b) evolutionary algorithms refining a heuristic, we advocate a strategy for solving a hard optimization problem with complicated data structure, and c) combination of two different local search techniques and EDA for numerical global optimization problems, its basic idea is that not all the new generated points are needed to be improved by an expensive local search.
@article{ZhangST:2007,
author = {Zhang, Qingfu and Sun, Jianyong and Tsang, Edward},
title = {Combinations of estimation of distribution algorithms and other techniques},
journal = {International Journal of Automation and Computing},
volume = {4},
number = {3},
pages = {273-280},
publisher = {Institute of Automation, Chinese Academy of Sciences, co-published with Springer-Verlag GmbH},
year = {2007},
doi = {10.1007/s11633-007-0273-3},
}Wayne Pullan. Phased local search for the maximum clique problem. Journal of Combinatorial Optimization, 12(3):303—323, 2006.
Note: Portfolio of meta-heuristics applied sequentially, with adaptive setting of the penalty delay parameter of (PullanH:2006).
This paper introduces Phased Local Search (PLS), a new stochastic reactive dynamic local search algorithm for the maximum clique problem. (PLS) interleaves sub-algorithms which alternate between sequences of iterative improvement, during which suitable vertices are added to the current clique, and plateau search, where vertices of the current clique are swapped with vertices not contained in the current clique. The sub-algorithms differ in their vertex selection techniques in that selection can be solely based on randomly selecting a vertex, randomly selecting within highest vertex degree or randomly selecting within vertex penalties that are dynamically adjusted during the search. In addition, the perturbation mechanism used to overcome search stagnation differs between the sub-algorithms. (PLS) has no problem instance dependent parameters and achieves state-of-the-art performance for the maximum clique problem over a large range of the commonly used DIMACS benchmark instances.
@article{Pullan:2006,
author = {Pullan, Wayne},
title = {Phased local search for the maximum clique problem},
journal = {Journal of Combinatorial Optimization},
volume = {12},
number = {3},
pages = {303--323},
publisher = {Springer},
year = {2006},
doi = {10.1007/s10878-006-9635-y},
}Wayne Pullan and Holger H. Hoos. Dynamic local search for the maximum clique problem. Journal of Artificial Intelligence Research, 25(1):159—185, 2006.
Note: Penalty based non-greedy meta-heuristic with state-of-the-art performance on the DIMACS benchmark set.
In this paper, we introduce DLS-MC, a new stochastic local search algorithm for the maximum clique problem. DLS-MC alternates between phases of iterative improvement, during which suitable vertices are added to the current clique, and plateau search, during which vertices of the current clique are swapped with vertices not contained in the current clique. The selection of vertices is solely based on vertex penalties that are dynamically adjusted during the search, and a perturbation mechanism is used to overcome search stagnation. The behaviour of DLS-MC is controlled by a single parameter, penalty delay, which controls the frequency at which vertex penalties are reduced. We show empirically that DLS-MC achieves substantial performance improvements over state-of-the-art algorithms for the maximum clique problem over a large range of the commonly used DIMACS benchmark instances.
@article{PullanH:2006,
author = {Pullan, Wayne and Hoos, Holger H.},
title = {Dynamic local search for the maximum clique problem},
journal = {Journal of Artificial Intelligence Research},
volume = {25},
number = {1},
pages = {159--185},
publisher = {AI Access Foundation},
year = {2006},
doi = {10.1613/jair.1815},
}Alok Singh and Ashok Kumar Gupta. A hybrid heuristic for the maximum clique problem. Journal of Heuristics, 12(1-2):5—22, 2006.
In this paper we present a heuristic based steady-state genetic algorithm for the maximum clique problem. The steady-state genetic algorithm generates cliques, which are then extended into maximal cliques by the heuristic. We compare our algorithm with three best evolutionary approaches and the overall best approach, which is non-evolutionary, for the maximum clique problem and find that our algorithm outperforms all the three evolutionary approaches in terms of best and average clique sizes found on majority of DIMACS benchmark instances. However, the obtained results are much inferior to those obtained with the best approach for the maximum clique problem.
@article{SinghG:2006,
author = {Singh, Alok and Gupta, Ashok Kumar},
title = {A hybrid heuristic for the maximum clique problem},
journal = {Journal of Heuristics},
volume = {12},
number = {1-2},
pages = {5-22},
year = {2006},
doi = {10.1007/s10732-006-3750-x},
}Christine Solnon and Serge Fenet. A study of aco capabilities for solving the maximum clique problem. Journal of Heuristics, 12(3):155—180, 2006.
Note: Study on the impact of pheromone trails on the solution process of a memetic algorithm for the maximum clique problem.
This paper investigates the capabilities of the Ant Colony Optimization (ACO) meta-heuristic for solving the maximum clique problem, the goal of which is to find a largest set of pairwise adjacent vertices in a graph. We propose and compare two different instantiations of a generic ACO algorithm for this problem. Basically, the generic ACO algorithm successively generates maximal cliques through the repeated addition of vertices into partial cliques, and uses ‘‘pheromone trails” as a greedy heuristic to choose, at each step, the next vertex to enter the clique. The two instantiations differ in the way pheromone trails are laid and exploited, i.e., on edges or on vertices of the graph.
We illustrate the behavior of the two ACO instantiations on a representative benchmark instance and we study the impact of pheromone on the solution process. We consider two measures—the re-sampling and the dispersion ratio—for providing an insight into the performance at run time. We also study the benefit of integrating a local search procedure within the proposed ACO algorithm, and we show that this improves the solution process. Finally, we compare ACO performance with that of three other representative heuristic approaches, showing that the former obtains competitive results.
We illustrate the behavior of the two ACO instantiations on a representative benchmark instance and we study the impact of pheromone on the solution process. We consider two measures—the re-sampling and the dispersion ratio—for providing an insight into the performance at run time. We also study the benefit of integrating a local search procedure within the proposed ACO algorithm, and we show that this improves the solution process. Finally, we compare ACO performance with that of three other representative heuristic approaches, showing that the former obtains competitive results.
@article{SolnonF:2006,
author = {Solnon, Christine and Fenet, Serge},
title = {A study of aco capabilities for solving the maximum clique problem},
journal = {Journal of Heuristics},
volume = {12},
number = {3},
pages = {155--180},
publisher = {Springer},
year = {2006},
doi = {10.1007/s10732-006-4295-8},
}Tobias Storch. How randomized search heuristics find maximum cliques in planar graphs. In GECCO 2006 - Genetic and Evolutionary Computation Conference, volume 1, pages 567—574, New York, NY, USA, 2006. ACM. Restriction to graph class having special properties.
Surprisingly, general search heuristics often solve combinatorial problems quite sufficiently, although they do not outperform specialized algorithms. Here, the behavior of simple randomized optimizers on the maximum clique problem on planar graphs is investigated rigorously. The focus is on the worst-, average-, and semi-average-case behaviors. In semi-random planar graph models an adversary is allowed to modify moderately a random planar graph, where a graph is chosen uniformly at random among all planar graphs. With regard to the heuristics particular interest is given to the influences of the following four popular strategies to overcome local optima: local- vs. global-search, single- vs. multi-start, small vs. large population, and elitism vs. non-elitism selection. Finally, the black-box complexities of the planar graph models are analyzed.
@inproceedings{Storch:2006,
author = {Storch, Tobias},
title = {How randomized search heuristics find maximum cliques in planar graphs},
volume = {1},
booktitle = {GECCO 2006 - Genetic and Evolutionary Computation Conference},
pages = {567--574},
publisher = {ACM},
year = {2006},
address = {New York, NY, USA},
}Kengo Katayama, Akihiro Hamamoto, and Hiroyuki Narihisa. An effective local search for the maximum clique problem. Information Processing Letters, 95(5):503—511, 2005.
We propose a variable depth search based algorithm, called k-opt localsearch (KLS), for the maximumcliqueproblem. KLS efficiently explores the k-opt neighborhood defined as the set of neighbors that can be obtained by a sequence of several add and drop moves that are adaptively changed in the feasible search space. Computational results on DIMACS benchmark graphs indicate that KLS is capable of finding considerably satisfactory cliques with reasonable running times in comparison with those of state-of-the-art metaheuristics.
@article{KatayamaHN:2005,
author = {Katayama, Kengo and Hamamoto, Akihiro and Narihisa, Hiroyuki},
title = {An effective local search for the maximum clique problem},
journal = {Information Processing Letters},
volume = {95},
number = {5},
pages = {503--511},
publisher = {Elsevier},
year = {2005},
doi = {10.1016/j.ipl.2005.05.010},
}Xiaoming Liu, Jianwei Yin, Jung-Sing Jwo, Zhilin Feng, and Jinxiang Dong. A dna-based genetic algorithm implementation for graph coloring problem. In De-Shuang Huang, Xiao-Ping Zhang, and Guang-Bin Huang, editors, Advances in Intelligent Computing, volume 3645 of Lecture Notes in Computer Science, pages 99—108. Springer Berlin / Heidelberg, 2005.
This paper presents an implementation of Croitoru’s genetic algorithm for graph coloring problem, and some necessary modification and simplifying are made by using DNA operations. In this algorithm, each vertex and edge is encoded with a series of encodings incorporating position information, and the initial diverse candidate population is generated using POA. One crossover operator, two mutation operators, evaluation and selection operators are all implemented using basic operations on DNA. It is shown that the algorithm can be implemented with space complexity much decreased and time complexity \(O(mn^2)\) to get a new generation, where n is the number of vertices and m is the number of edges. Moreover, borrowing ideas from the above implementation, an algorithm for Maximal Clique problem is also presented.
@inproceedings{LiuYJFD:2005,
author = {Liu, Xiaoming and Yin, Jianwei and Jwo, Jung-Sing and Feng, Zhilin and Dong, Jinxiang},
title = {A DNA-Based Genetic Algorithm Implementation for Graph Coloring Problem},
volume = {3645},
booktitle = {Advances in Intelligent Computing},
series = {Lecture Notes in Computer Science},
pages = {99--108},
editor = {Huang, De-Shuang and Zhang, Xiao-Ping and Huang, Guang-Bin},
publisher = {Springer Berlin / Heidelberg},
year = {2005},
doi = {10.1007/11538356_11},
}C. Y. Sun, W. J. Li, and X. Z. Gao. A novel evolutionary algorithm for mcp using mec. In SMCia/05 - Proceedings of the 2005 IEEE Mid-Summer Workshop on Soft Computing in Industrial Applications, volume 2005, pages 99—104, 2005.
A novel evolutionary algorithm for the maximum clique problem (MCP) is presented in the paper. That is called MCP-MEC1 and is based on Mind Evolutionary Computation (MEC). The construction of individuals, groups, operations-similartaxis and dissimilation and the evaluation of individuals are accomplished for MCP. 21 benchmark graphs collected by DIMACS (Discrete Mathematics and Theoretical Computer Science) are used to evaluate the performance of the MCP-MEC1 algorithm. The results obtained by MCP-MEC1 are compared with those obtained by two best algorithms for the MCP, RLS (Reactive Local Search) and HGA (Heuristic Based Genetic Algorithm). It is shown that the MCP-MEC1 outperforms HGA and is as good as RLS. So the MCP-MEC1 is one of the best heuristic algorithms for the MCP.
@inproceedings{SunLG:2005,
author = {Sun, C. Y. and Li, W. J. and Gao, X. Z.},
title = {A novel evolutionary algorithm for MCP using MEC},
volume = {2005},
booktitle = {SMCia/05 - Proceedings of the 2005 IEEE Mid-Summer Workshop on Soft Computing in Industrial Applications},
pages = {99--104},
year = {2005},
doi = {10.1109/SMCIA.2005.1466955},
}Qingfu Zhang, Jianyong Sun, and Edward Tsang. An evolutionary algorithm with guided mutation for the maximum clique problem. Evolutionary Computation, IEEE Transactions on, 9(2):192—200, 2005.
Estimation of distribution algorithms sample new solutions (offspring) from a probability model which characterizes the distribution of promising solutions in the search space at each generation. The location information of solutions found so far (i.e., the actual positions of these solutions in the search space) is not directly used for generating offspring in most existing estimation of distribution algorithms. This paper introduces a new operator, called guided mutation. Guided mutation generates offspring through combination of global statistical information and the location information of solutions found so far. An evolutionary algorithm with guided mutation (EA/G) for the maximum clique problem is proposed in this paper. Besides guided mutation, EA/G adopts a strategy for searching different search areas in different search phases. Marchiori’s heuristic is applied to each new solution to produce a maximal clique in EA/G. Experimental results show that EA/G outperforms the heuristic genetic algorithm of Marchiori (the best evolutionary algorithm reported so far) and a MIMIC algorithm on DIMACS benchmark graphs.
@article{ZhangST:2005,
author = {Zhang, Qingfu and Sun, Jianyong and Tsang, Edward},
title = {An evolutionary algorithm with guided mutation for the maximum clique problem},
journal = {Evolutionary Computation, IEEE Transactions on},
volume = {9},
number = {2},
pages = {192--200},
publisher = {IEEE},
year = {2005},
doi = {10.1109/TEVC.2004.840835},
}Andrea Grosso, Marco Locatelli, and Federico Della Croce. Combining swaps and node weights in an adaptive greedy approach for the maximum clique problem. Journal of Heuristics, 10(2):135—152, 2004.
In this work, the NP-hard maximum clique problem on graphs is considered. Starting from basic greedy heuristics, modifications and improvements are proposed and combined in a two-phase heuristic procedure. In the first phase an improved greedy procedure is applied starting from each node of the graph; on the basis of the results of this phase a reduced subset of nodes is selected and an adaptive greedy algorithm is repeatedly started to build cliques around such nodes. In each restart the selection of nodes is biased by the maximal clique generated in the previous execution. Computational results are reported on the DIMACS benchmarks suite. Remarkably, the two-phase procedure successfully solves the difficult Brockington-Culberson instances, and is generally competitive with state-of-the-art much more complex heuristics.
@article{GrossoLD:2004,
author = {Grosso, Andrea and Locatelli, Marco and Della~Croce, Federico},
title = {Combining Swaps and Node Weights in an Adaptive Greedy Approach for the Maximum Clique Problem},
journal = {Journal of Heuristics},
volume = {10},
number = {2},
pages = {135-152},
publisher = {Springer Netherlands},
year = {2004},
doi = {10.1023/B:HEUR.0000026264.51747.7f},
}Pierre Hansen, Nenad Mladenović, and Dragan Urošević. Variable neighborhood search for the maximum clique. Discrete Applied Mathematics, 145(1):117—125, 2004.
Maximumc lique is one of the most studied NP-hard optimization problem on graphs because of its simplicity and its numerous applications. A basic variable neighborhood search heuristic for maximum clique that combines greedy with the simplicial vertex test in its descent step is proposed and tested on standard test problems from the literature. Despite its simplicity, the proposed heuristic outperforms most of the well-known approximate solution methods. Moreover, it gives solution of equal quality to those of the state-of-the-art heuristic of Battiti and Protasi in half the time.
@article{HansenMU:2004,
author = {Hansen, Pierre and Mladenovi{\'c}, Nenad and Uro{\vs}evi{\'c}, Dragan},
title = {Variable neighborhood search for the maximum clique},
journal = {Discrete Applied Mathematics},
volume = {145},
number = {1},
pages = {117--125},
publisher = {Elsevier},
year = {2004},
doi = {10.1016/j.dam.2003.09.012},
}Kengo Katayama, Akihiro Hamamoto, and Hiroyuki Narihisa. Solving the maximum clique problem by k-opt local search. In Proceedings of the ACM Symposium on Applied Computing, volume 2, pages 1021—1025, New York, NY, USA, 2004. ACM.
This paper presents a local search algorithm based on variable depth search, called the k-opt local search, for the maximum clique problem. The k-opt local search performs add and drop moves, each of which can be interpreted as 1-opt move, to search a k-opt neighborhood solution at each iteration until no better k-opt neighborhood solution can be found. To evaluate our k-opt local search algorithm, we repeatedly apply the local search for each of DIMACS benchmark graphs and compare with the state-of-the-art metaheuristics such as the genetic local search and the iterated local search reported previously. The computational results show that in spite of the absence of major metaheuristic components, the k-opt local search is capable of finding better (at least the same) solutions on average than those obtained by these metaheuristics for all the graphs.
@inproceedings{KatayamaHN:2004,
author = {Katayama, Kengo and Hamamoto, Akihiro and Narihisa, Hiroyuki},
title = {Solving the maximum clique problem by k-opt local search},
volume = {2},
booktitle = {Proceedings of the ACM Symposium on Applied Computing},
pages = {1021-1025},
publisher = {ACM},
year = {2004},
address = {New York, NY, USA},
doi = {10.1145/967900.968107},
}Sherin M. Youssef and Dave G. Elliman. Reactive prohibition-based ant colony optimization (rpaco): A new parallel architecture for constrained clique sub-graphs. In Proceedings - International Conference on Tools with Artificial Intelligence, ICTAI, pages 63—70. IEEE, 2004.
In this paper we introduce a new algorithm that combines the stigmergetic capabilities of the Ant Colony Optimization (ACO) with local search heuristics to solve the maximum and maximum-weighted clique problem. Our new algorithm: A Reactive Prohibition-based Ant Colony Optimization (RPACOMCP), complements the intelligent ant colony search with a prohibition-based diversification technique, where the amount of diversification is determined in an automated way through a feedback (history-sensitive) scheme. Based on prohibition, some local moves are temporarily prohibited in order to avoid repeated cycles in the search trajectory and to explore new parts of the total search space. Diversification could be enforced and the ACO search continued beyond local optimal points. One of the main advantages of this approach is the use of parallelism both to have a number of ant colonies searching simultaneously and to have a function distribution of local search procedures. This architecture thus provides a powerful tool to tackle difficult problems using all available processing power. The algorithm is tested on many representative DIMACS benchmark graph instances and results are compared with GLS [1], a genetic local search approach for MCP. It is shown that the proposed PAGO algorithm finds larger cliques in reasonable time, on average, on a wide majority of benchmark instances of the DIMACS library, even though it does not reach the best known results on a few benchmark instances. We also showed that the PACO algorithm outperforms the non-prohibition version on most hard graph instances.
@inproceedings{YoussefE:2004,
author = {Youssef, Sherin M. and Elliman, Dave G.},
title = {Reactive Prohibition-based Ant Colony Optimization (RPACO): A new parallel architecture for constrained clique sub-graphs},
booktitle = {Proceedings - International Conference on Tools with Artificial Intelligence, ICTAI},
pages = {63-70},
publisher = {IEEE},
year = {2004},
doi = {10.1109/ICTAI.2004.104},
}Jean-Charles Regin. Solving the maximum clique problem with constraint programming. In Fifth International Workshop on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CP-AI-OR’03), May 8-10, 2003, Montreal, Canada., pages 166—179, 2003.
This paper aims to show that Constraint Programming can be an efficient technique to solve a well-known combinatorial optimization problem: the search for a maximum clique in a graph. A clique of a graph \(G = (X,E)\) is a subset \(V\) of \(X\), such that every two nodes in \(V\) are joined by an edge of \(E\). The maximum clique problem consists of finding \(\omega(G)\) the largest cardinality of a clique. We propose two new upper bounds of \(\omega(G)\) and a new strategy to guide the search for an optimal solution. The interest of our approach is emphasized by the results we obtain for the DIMACS Benchmarks. Seven instances are solved for the first time and two better lower bounds for problems remaining open are found. Moreover, we show that the CP method we propose gives good results and quickly.
@inproceedings{Regin:2003,
author = {Regin, Jean-Charles},
title = {Solving the maximum clique problem with constraint programming},
booktitle = {Fifth International Workshop on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CP-AI-OR'03), May 8-10, 2003, Montreal, Canada.},
pages = {166--179},
year = {2003},
url = {http://www.crt.umontreal.ca/cpaior/article-regin.pdf},
}Elena Marchiori. Genetic, iterated and multistart local search for the maximum clique problem. In Stefano Cagnoni, Jens Gottlieb, Emma Hart, Martin Middendorf, and Günther Raidl, editors, Applications of Evolutionary Computing, volume 2279 of Lecture Notes in Computer Science, pages 112—121. Springer Berlin / Heidelberg, 2002.
This paper compares experimentally three heuristic algorithms for the maximum clique problem obtained as instances of an evolutionary algorithm scheme. The algorithms use three popular heuristic methods for combinatorial optimization problems, known as genetic, iterated and multistart local search, respectively.
@incollection{Marchiori:2002,
author = {Marchiori, Elena},
title = {Genetic, Iterated and Multistart Local Search for the Maximum Clique Problem},
volume = {2279},
booktitle = {Applications of Evolutionary Computing},
series = {Lecture Notes in Computer Science},
pages = {112-121},
editor = {Cagnoni, Stefano and Gottlieb, Jens and Hart, Emma and Middendorf, Martin and Raidl, G{\"u}nther},
publisher = {Springer Berlin / Heidelberg},
year = {2002},
doi = {10.1007/3-540-46004-7_12},
}Roberto Battiti and Marco Protasi. Reactive local search for the maximum clique problem. Algorithmica, 29(4):610—637, apr 2001.
Note: Original reactive tabu search for the maximum clique problem. BattitiM:2010, is the updated version with small implementation and algorithmic improvements, which is, on large instances, one order of magnitude faster.
A new Reactive Local Search (RLS) algorithm is proposed for the solution of the Maximum-Clique problem. RLS is based on local search complemented by a feedback (history-sensitive) scheme to determine the amount of diversification. The reaction acts on the single parameter that decides the temporary prohibition of selected moves in the neighborhood, in a manner inspired by Tabu Search. The performance obtained in computational tests appears to be significantly better with respect to all algorithms tested at the the second DIMACS implementation challenge. The worst-case complexity per iteration of the algorithm is O(max{n,m}) where n and m are the number of nodes and edges of the graph. In practice, when a vertex is moved, the number of operations tends to be proportional to its number of missing edges and therefore the iterations are particularly fast in dense graphs.
@article{BattitiP:2001,
author = {Battiti, Roberto and Protasi, Marco},
title = {Reactive Local Search for the Maximum Clique Problem},
journal = {Algorithmica},
volume = {29},
number = {4},
pages = {610--637},
year = {2001},
month = apr,
doi = {10.1007/s004530010074},
}Immanuel M. Bomze and Volker Stix. Genetic engineering via negative fitness:evolutionary dynamics for global optimization. ISSN 0254-5330
In this paper, we provide a novel interpretation of a global optimization procedure for standard quadratic problems (QPs) in terms of selection models. A standard QP consists of maximizing a quadratic form over the standard simplex. Recently, local solutions to standardQPs have been obtained with the help of replicator dynamics, which were designed to modelevolutionary processes. Following trajectories under these dynamics, one obtains a sequence of feasible points with strictly increasing objective values, which approach stationary points.We present regularity conditions which ensure that the limiting points are indeed localsolutions, so that jamming could be avoided. Genetic engineering via negative fitness is ablock pivoting procedure which either delivers a certificate for global optimality of thecurrent local solution, or else enables an escape from its basin of attraction, if it is inefficient.The name originates from the way the block pivot is obtained: via minimization (rather thanmaximization) of a subproblem. We also elaborate on an important application, the searchfor a maximum clique in an undirected graph, and report both theoretical and empiricalresults.
@article{BomzeS:1999,
author = {Bomze, Immanuel M. and Stix, Volker},
title = {Genetic engineering via negative fitness:Evolutionary dynamics for global optimization},
journal = {Annals of Operations Research},
volume = {89},
pages = {297-318},
publisher = {Springer Netherlands},
year = {1999},
doi = {10.1023/A:1018935925761},
}Patrick Soriano and Michel Gendreau. Diversification strategies in tabu search algorithms for the maximum clique problem. ISSN 0254-5330
The purpose of this study is to develop some understanding of the benefits that can be derived from the inclusion of diversification strategies in tabu search methods. To do so, we discuss the implementation of various diversification strategies in several tabu search heuristics developed for the maximum clique problem. Computational results on a large set of randomly generated test problems are reported and compared to assess the impact of these techniques on solution quality and running time.
@article{SorianoG:1996,
author = {Soriano, Patrick and Gendreau, Michel},
title = {Diversification strategies in tabu search algorithms for the maximum clique problem},
journal = {Annals of Operations Research},
volume = {63},
pages = {189--207},
publisher = {Springer Netherlands},
year = {1996},
doi = {10.1007/BF02125454},
}Thang Nguyen Bui and Paul H. Eppley. A hybrid genetic algorithm for the maximum clique problem. In Proceedings of the 6th international conference on genetic algorithms, pages 478—484, San Francisco, CA, USA, 1995. Morgan Kaufmann Publishers Inc.
@inproceedings{BuiE:1995,
author = {Bui, Thang Nguyen and Eppley, Paul H.},
title = {A hybrid genetic algorithm for the maximum clique problem},
booktitle = {Proceedings of the 6th international conference on genetic algorithms},
pages = {478--484},
year = {1995},
address = {San Francisco, CA, USA},
}Thomas Bäck and Sami Khuri. An evolutionary heuristic for the maximum independent set problem. In Evolutionary Computation, 1994. IEEE World Congress on Computational Intelligence., Proceedings of the First IEEE Conference on, pages 531—535. IEEE, 1994. [Maximum Independent Set]
The results obtained from the application of a genetic algorithm, GENEsYs, to the NP-complete maximum independent set problem are reported. In contrast to many other genetic algorithm-based approaches that use domain-specific knowledge, the approach presented in this paper relies on a graded penalty term component of the fitness function to penalize infeasible solutions. The method is applied to several large problem instances of the maximum independent set problem. The results clearly indicate that genetic algorithms can be successfully used as heuristics for finding good approximative solutions for this highly constrained optimization problem.
@inproceedings{BackK:1994,
author = {B{\"a}ck, Thomas and Khuri, Sami},
title = {An evolutionary heuristic for the maximum independent set problem},
booktitle = {Evolutionary Computation, 1994. IEEE World Congress on Computational Intelligence., Proceedings of the First IEEE Conference on},
pages = {531--535},
year = {1994},
doi = {10.1109/ICEC.1994.350004},
}Robert Carter and Kihong Park. How good are genetic algorithms at finding large cliques: an experimental study. Technical report, Boston University Computer Science Department, 1993
This paper investigates the power of genetic algorithms at solving the MAX-CLIQUE problem. We measure the performance of a standard genetic algorithm on an elementary set of problem instances consisting of embedded cliques in random graphs. We indicate the need for improvement, and introduce a new genetic algorithm, the multi-phase annealed GA, which exhibits superior performance on the same problem set.
As we scale up the problem size and test on ‘‘hard” benchmark instances, we notice a degraded performance in the algorithm caused by premature convergence to local minima. To alleviate this problem, a sequence of modi cations are implemented ranging from changes in input representation to systematic local search. The most recent version, called union GA, incorporates the features of union cross-over, greedy replacement, and diversity enhancement. It shows a marked speed-up in the number of iterations required to find a given solution, as well as some improvement in the clique size found.
We discuss issues related to the SIMD implementation of the genetic algorithms on a Thinking Machines CM-5, which was necessitated by the intrinsically high time complexity (O(n3)) of the serial algorithm for computing one iteration.
Our preliminary conclusions are: (1) a genetic algorithm needs to be heavily customized to work ‘‘well” for the clique problem; (2) a GA is computationally very expensive, and its use is only recommended if it is known to a nd larger cliques than other algorithms; (3) although our customization e ort is bringing forth continued improvements, there is no clear evidence, at this time, that a GA will have better success in circumventing local minima.
As we scale up the problem size and test on ‘‘hard” benchmark instances, we notice a degraded performance in the algorithm caused by premature convergence to local minima. To alleviate this problem, a sequence of modi cations are implemented ranging from changes in input representation to systematic local search. The most recent version, called union GA, incorporates the features of union cross-over, greedy replacement, and diversity enhancement. It shows a marked speed-up in the number of iterations required to find a given solution, as well as some improvement in the clique size found.
We discuss issues related to the SIMD implementation of the genetic algorithms on a Thinking Machines CM-5, which was necessitated by the intrinsically high time complexity (O(n3)) of the serial algorithm for computing one iteration.
Our preliminary conclusions are: (1) a genetic algorithm needs to be heavily customized to work ‘‘well” for the clique problem; (2) a GA is computationally very expensive, and its use is only recommended if it is known to a nd larger cliques than other algorithms; (3) although our customization e ort is bringing forth continued improvements, there is no clear evidence, at this time, that a GA will have better success in circumventing local minima.
@techreport{CarterP:1993,
author = {Carter, Robert and Park, Kihong},
title = {How good are genetic algorithms at finding large cliques: an experimental study},
institution = {Boston University Computer Science Department},
year = {1993},
url = {http://dcommon.bu.edu/xmlui/bitstream/handle/2144/1469/1993-015-ga-clique.pdf?sequence=1},
}Michel Gendreau, Patrick Soriano, and Louis Salvail. Solving the maximum clique problem using a tabu search approach. Annals of Operations Research, 41(4):385—403, 1993.
We describe two variants of a tabu search heuristic, a deterministic one and a probabilistic one, for the maximum clique problem. This heuristic may be viewed as a natural alternative implementation of tabu search for this problem when compared to existing ones. We also present a new random graph generator, the \(\hat{p}\)-generator, which produces graphs with larger clique sizes than comparable ones obtained by classical random graph generating techniques. Computational results on a large set of test problems randomly generated with this new generator are reported and compared with those of other approximate methods.
@article{GendreauSS:1993,
author = {Gendreau, Michel and Soriano, Patrick and Salvail, Louis},
title = {Solving the maximum clique problem using a tabu search approach},
journal = {Annals of Operations Research},
volume = {41},
number = {4},
pages = {385--403},
publisher = {Springer},
year = {1993},
doi = {10.1007/BF02023002},
}C. Friden, A. Hertz, and D. Werra. Stabulus: a technique for finding stable sets in large graphs with tabu search. Computing, 42(1):35—44, 1989. [Maximum Independent Set]
Numerical experiments with tabu search have been carried out for constructing independent sets in large graphs. We present some variations on the independent set problem and discuss the results obtained by the tabu search technique.
As for graph coloring, this method seems to be a very efficient heuristic procedure.
As for graph coloring, this method seems to be a very efficient heuristic procedure.
@article{FridenHW:1989,
author = {Friden, C. and Hertz, A. and Werra, D.},
title = {Stabulus: a technique for finding stable sets in large graphs with tabu search},
journal = {Computing},
volume = {42},
number = {1},
pages = {35--44},
publisher = {Springer},
year = {1989},
doi = {10.1007/BF02243141},
}1.3 Applications
Carina Curto, Anda Degeratu, and Vladimir Itskov. Flexible memory networks. Bulletin of Mathematical Biology, 74(3):590—614, mar 2012. [neuroscience]
Networks of neurons in some brain areas are flexible enough to encode new memories quickly. Using a standard firing rate model of recurrent networks, we develop a theory of flexible memory networks. Our main results characterize networks having the maximal number of flexible memory patterns, given a constraint graph on the network’s connectivity matrix. Modulo a mild topological condition, we find a close connection between maximally flexible networks and rank 1 matrices. The topological condition is H (1)(X;Z)=0, where X is the clique complex associated to the network’s constraint graph; this condition is generically satisfied for large random networks that are not overly sparse. In order to prove our main results, we develop some matrix-theoretic tools and present them in a self-contained section independent of the neuroscience context. ccurto2@math.unl.edu
@article{CurtoDI:2012,
author = {Curto, Carina and Degeratu, Anda and Itskov, Vladimir},
title = {Flexible memory networks.},
journal = {Bulletin of Mathematical Biology},
volume = {74},
number = {3},
pages = {590-614},
year = {2012},
month = mar,
doi = {10.1007/s11538-011-9678-9},
}Seung Kwan Kim, Jee Hyung Lee, Keun Ho Ryu, and Ungmo Kim. A framework of spatial co-location pattern mining for ubiquitous gis. Multimedia Tools and Applications, pages 1—20, 2012. [spatial data mining]
A spatial co-location pattern represents relationships between spatial features that are frequently located in close proximity to one another. Such a pattern is one of the most important concepts for geographic context awareness of ubiquitous Geographic Information System (GIS). We constructed a framework for co-location pattern mining using the transaction-based approach, which employs maximal cliques as a transaction-type dataset; we first define transaction-type data and verify that the definition satisfies the requirements, and we also propose an efficient way to generate all transaction-type data. The constructed framework can play a role as a theoretical methodology of co-location pattern mining, which supports geographic context awareness of ubiquitous GIS.
@article{KimLRK:2012,
author = {Kim, Seung Kwan and Lee, Jee Hyung and Ryu, Keun Ho and Kim, Ungmo},
title = {A framework of spatial co-location pattern mining for ubiquitous GIS},
journal = {Multimedia Tools and Applications},
pages = {1-20},
year = {2012},
doi = {10.1007/s11042-012-1007-2},
}Xiaoke Ma and Lin Gao. Predicting protein complexes in protein interaction networks using a core-attachment algorithm based on graph communicability. Information Sciences, 189:233—254, 2012. [bioinformatics - proteomics - protein complexes]
Studying protein complexes is very important in biological processes because it helps reveal the structure-functionality relationships in a protein complex. Much attention has been paid to accurately predicting the protein complexes from the increasing amount of protein-protein interaction (PPI) data. Almost all of the current algorithms that concern the detection of protein complexes focus on discovering dense subgraphs based on the observation that dense subgraphs in a biological network may correspond to protein complexes. However, such an assumption would throw away further topological information about complexes. In this paper introducing the core-attachment concept, a novel core-attachment algorithm is developed by detecting the cores and attachments, respectively. To detect the cores of protein complexes, a virtual network is constructed using the eigenvalues and eigenvectors of the network involved, where each maximal clique corresponds to a protein complex core. With this notion, the problem of detecting protein complex cores is transformed into the classic all-cliques problem. The attachments are then merged into their cores to yield biologically meaningful complexes. A comprehensive comparison between MCL, DPClus, Coach, DECAFF and our algorithm has been made by comparing the predicted protein complexes with the benchmarked complexes. Experimental results indicate that our algorithm outperforms the MCL, DPClus and DECAFF and has comparative performance with the Coach algorithm in terms of the accuracy of prediction. Moreover, the detected complexes with core-attachment structures match well with the benchmark data, demonstrating that our algorithm can provide more insightful perspectives. Robustness analysis further shows that the algorithm is very robust.
@article{MaG:2012,
author = {Ma, Xiaoke and Gao, Lin},
title = {Predicting protein complexes in protein interaction networks using a core-attachment algorithm based on graph communicability},
journal = {Information Sciences},
volume = {189},
pages = {233-254},
year = {2012},
doi = {10.1016/j.ins.2011.11.033},
}Dana M. Sepe, Thomas McWilliams, Jinbo Chen, Aaron Kershenbaum, Huaqing Zhao, Mei La, Meenakshi Devidas, Beverly Lange, Timothy R. Rebbeck, and Richard Aplenc. Germline genetic variation and treatment response on ccg-1891. Pediatric Blood & Cancer, 58(5):695—700, may 2012. [medicine - gene-gene interaction networks]
Background
Recent studies suggest that polymorphisms in genes encoding enzymes involved in drug detoxification and metabolism may influence disease outcome in pediatric acute lymphoblastic leukemia (ALL). We sought to extend current knowledge by using standard and novel statistical methodology to examine polymorphic variants of genes and relapse risk, toxicity, and drug dose delivery in standard risk ALL.
Procedure
We genotyped and abstracted chemotherapy drug dose data from treatment roadmaps on 557 patients on the Children’s Cancer Group ALL study, CCG-1891. Fourteen common polymorphisms in genes involved in folate metabolism and/or phase I and II drug detoxification were evaluated individually and clique-finding methodology was employed for detection of significant gene-gene interactions.
Results
After controlling for known risk factors, polymorphisms in four genes: GSTP1*B (HR = 1.94, P = 0.047), MTHFR (HR = 1.61, P = 0.034), MTRR (HR = 1.95, P = 0.01), and TS (3R/4R, HR = 3.69, P = 0.007) were found to significantly increase relapse risk. One gene-gene pair, MTRR A/G and GSTM1 null genotype, significantly increased the risk of relapse after correction for multiple comparisons (P = 0.012). Multiple polymorphisms were associated with various toxicities and there was no significant difference in dose of chemotherapy delivered by genotypes.
Conclusions
These data suggest that various polymorphisms play a role in relapse risk and toxicity during childhood ALL therapy and that genotype does not play a role in adjustment of drug dose administered. Additionally, gene-gene interactions may increase the risk of relapse in childhood ALL and the clique method may have utility in further exploring these interactions. childhood ALL therapy. USA. sepe@email.chop.edu
Recent studies suggest that polymorphisms in genes encoding enzymes involved in drug detoxification and metabolism may influence disease outcome in pediatric acute lymphoblastic leukemia (ALL). We sought to extend current knowledge by using standard and novel statistical methodology to examine polymorphic variants of genes and relapse risk, toxicity, and drug dose delivery in standard risk ALL.
Procedure
We genotyped and abstracted chemotherapy drug dose data from treatment roadmaps on 557 patients on the Children’s Cancer Group ALL study, CCG-1891. Fourteen common polymorphisms in genes involved in folate metabolism and/or phase I and II drug detoxification were evaluated individually and clique-finding methodology was employed for detection of significant gene-gene interactions.
Results
After controlling for known risk factors, polymorphisms in four genes: GSTP1*B (HR = 1.94, P = 0.047), MTHFR (HR = 1.61, P = 0.034), MTRR (HR = 1.95, P = 0.01), and TS (3R/4R, HR = 3.69, P = 0.007) were found to significantly increase relapse risk. One gene-gene pair, MTRR A/G and GSTM1 null genotype, significantly increased the risk of relapse after correction for multiple comparisons (P = 0.012). Multiple polymorphisms were associated with various toxicities and there was no significant difference in dose of chemotherapy delivered by genotypes.
Conclusions
These data suggest that various polymorphisms play a role in relapse risk and toxicity during childhood ALL therapy and that genotype does not play a role in adjustment of drug dose administered. Additionally, gene-gene interactions may increase the risk of relapse in childhood ALL and the clique method may have utility in further exploring these interactions. childhood ALL therapy. USA. sepe@email.chop.edu
@article{SepeMCKZLDLRA:2012,
author = {Sepe, Dana M. and McWilliams, Thomas and Chen, Jinbo and Kershenbaum, Aaron and Zhao, Huaqing and La, Mei and Devidas, Meenakshi and Lange, Beverly and Rebbeck, Timothy R. and Aplenc, Richard},
title = {Germline genetic variation and treatment response on CCG-1891.},
journal = {Pediatric Blood & Cancer},
volume = {58},
number = {5},
pages = {695-700},
year = {2012},
month = may,
doi = {10.1002/pbc.23192},
}S. Joshua Swamidass, Bradley T. Calhoun, Joshua A. Bittker, Nicole E. Bodycombe, and Paul A. Clemons. Utility-aware screening with clique-oriented prioritization. Journal of Chemical Information and Modeling, 52(1):29—37, jan 2012. [chemistry / molecular biology - high-throughput-screening]
Most methods of deciding which hits from a screen to send for confirmatory testing assume that all confirmed actives are equally valuable and aim only to maximize the number of confirmed hits. In contrast, "utility-aware" methods are informed by models of screeners’ preferences and can increase the rate at which the useful information is discovered. Clique-oriented prioritization (COP) extends a recently proposed economic framework and aims—by changing which hits are sent for confirmatory testing—to maximize the number of scaffolds with at least two confirmed active examples. In both retrospective and prospective experiments, COP enables accurate predictions of the number of clique discoveries in a batch of confirmatory experiments and improves the rate of clique discovery by more than 3-fold. In contrast, other similarity-based methods like ontology-based pattern identification (OPI) and local hit-rate analysis (LHR) reduce the rate of scaffold discovery by about half. The utility-aware algorithm used to implement COP is general enough to implement several other important models of screener preferences. Immunology, Washington University School of Medicine, St. Louis, Missouri, USA. swamidass@wustl.edu
@article{SwamidassCBBC:2012,
author = {Swamidass, S. Joshua and Calhoun, Bradley T. and Bittker, Joshua A. and Bodycombe, Nicole E. and Clemons, Paul A.},
title = {Utility-aware screening with clique-oriented prioritization.},
journal = {Journal of Chemical Information and Modeling},
volume = {52},
number = {1},
pages = {29-37},
year = {2012},
month = jan,
doi = {10.1021/ci2003285},
}Sanjeev Arora, Rong Ge, Sushant Sachdeva, and Grant Schoenebeck. Finding overlapping communities in social networks: Toward a rigorous approach. CoRR, abs/1112.1831, 2011.
A ‘‘community” in a social network is usually understood to be a group of nodes more densely connected with each other than with the rest of the network. This is an important concept in most domains where networks arise: social, technological, biological, etc. For many years algorithms for finding communities implicitly assumed communities are nonoverlapping (leading to use of clustering-based approaches) but there is increasing interest in finding overlapping communities. A barrier to finding communities is that the solution concept is often defined in terms of an NP-complete problem such as Clique or Hierarchical Clustering.
This paper seeks to initiate a rigorous approach to the problem of finding overlapping communities, where ‘‘rigorous” means that we clearly state the following: (a) the object sought by our algorithm (b) the assumptions about the underlying network (c) the (worst-case) running time.
Our assumptions about the network lie between worst-case and average-case. An average case analysis would require a precise probabilistic model of the network, on which there is currently no consensus. However, some plausible assumptions about network parameters can be gleaned from a long body of work in the sociology community spanning five decades focusing on the study of individual communities and ego-centric networks. Thus our assumptions are somewhat ‘‘local” in nature. Nevertheless they suffice to permit a rigorous analysis of running time of algorithms that recover global structure.
Our algorithms use random sampling similar to that in property testing and algorithms for dense graphs. However, our networks are not necessarily dense graphs, not even in local neighborhoods.
Our algorithms explore a local-global relationship between ego-centric and socio-centric networks that we hope will provide a fruitful framework for future work both in computer science and sociology.
This paper seeks to initiate a rigorous approach to the problem of finding overlapping communities, where ‘‘rigorous” means that we clearly state the following: (a) the object sought by our algorithm (b) the assumptions about the underlying network (c) the (worst-case) running time.
Our assumptions about the network lie between worst-case and average-case. An average case analysis would require a precise probabilistic model of the network, on which there is currently no consensus. However, some plausible assumptions about network parameters can be gleaned from a long body of work in the sociology community spanning five decades focusing on the study of individual communities and ego-centric networks. Thus our assumptions are somewhat ‘‘local” in nature. Nevertheless they suffice to permit a rigorous analysis of running time of algorithms that recover global structure.
Our algorithms use random sampling similar to that in property testing and algorithms for dense graphs. However, our networks are not necessarily dense graphs, not even in local neighborhoods.
Our algorithms explore a local-global relationship between ego-centric and socio-centric networks that we hope will provide a fruitful framework for future work both in computer science and sociology.
@article{AroraGSS:2011,
author = {Sanjeev Arora and Rong Ge and Sushant Sachdeva and Grant Schoenebeck},
title = {Finding Overlapping Communities in Social Networks: Toward a Rigorous Approach},
journal = {CoRR},
volume = {abs/1112.1831},
year = {2011},
url = {http://arxiv.org/abs/1112.1831},
}Sankar Basu, Dhananjay Bhattacharyya, and Rahul Banerjee. Mapping the distribution of packing topologies within protein interiors shows predominant preference for specific packing motifs. BMC Bioinformatics, 12:195, 2011.
Background
Mapping protein primary sequences to their three dimensional folds referred to as the ’second genetic code’ remains an unsolved scientific problem. A crucial part of the problem concerns the geometrical specificity in side chain association leading to densely packed protein cores, a hallmark of correctly folded native structures. Thus, any model of packing within proteins should constitute an indispensable component of protein folding and design.
Results
In this study an attempt has been made to find, characterize and classify recurring patterns in the packing of side chain atoms within a protein which sustains its native fold. The interaction of side chain atoms within the protein core has been represented as a contact network based on the surface complementarity and overlap between associating side chain surfaces. Some network topologies definitely appear to be preferred and they have been termed ’packing motifs’, analogous to super secondary structures in proteins. Study of the distribution of these motifs reveals the ubiquitous presence of typical smaller graphs, which appear to get linked or coalesce to give larger graphs, reminiscent of the nucleation-condensation model in protein folding. One such frequently occurring motif, also envisaged as the unit of clustering, the three residue clique was invariably found in regions of dense packing. Finally, topological measures based on surface contact networks appeared to be effective in discriminating sequences native to a specific fold amongst a set of decoys.
Conclusions
Out of innumerable topological possibilities, only a finite number of specific packing motifs are actually realized in proteins. This small number of motifs could serve as a basis set in the construction of larger networks. Of these, the triplet clique exhibits distinct preference both in terms of composition and geometry. Physics, Bidhannagar, Kolkata, India.
Mapping protein primary sequences to their three dimensional folds referred to as the ’second genetic code’ remains an unsolved scientific problem. A crucial part of the problem concerns the geometrical specificity in side chain association leading to densely packed protein cores, a hallmark of correctly folded native structures. Thus, any model of packing within proteins should constitute an indispensable component of protein folding and design.
Results
In this study an attempt has been made to find, characterize and classify recurring patterns in the packing of side chain atoms within a protein which sustains its native fold. The interaction of side chain atoms within the protein core has been represented as a contact network based on the surface complementarity and overlap between associating side chain surfaces. Some network topologies definitely appear to be preferred and they have been termed ’packing motifs’, analogous to super secondary structures in proteins. Study of the distribution of these motifs reveals the ubiquitous presence of typical smaller graphs, which appear to get linked or coalesce to give larger graphs, reminiscent of the nucleation-condensation model in protein folding. One such frequently occurring motif, also envisaged as the unit of clustering, the three residue clique was invariably found in regions of dense packing. Finally, topological measures based on surface contact networks appeared to be effective in discriminating sequences native to a specific fold amongst a set of decoys.
Conclusions
Out of innumerable topological possibilities, only a finite number of specific packing motifs are actually realized in proteins. This small number of motifs could serve as a basis set in the construction of larger networks. Of these, the triplet clique exhibits distinct preference both in terms of composition and geometry. Physics, Bidhannagar, Kolkata, India.
@article{BasuBB:2011,
author = {Basu, Sankar and Bhattacharyya, Dhananjay and Banerjee, Rahul},
title = {Mapping the distribution of packing topologies within protein interiors shows predominant preference for specific packing motifs.},
journal = {BMC Bioinformatics},
volume = {12},
pages = {195},
year = {2011},
doi = {10.1186/1471-2105-12-195},
}Ming-Huang Chen, Wu-Lung R. Yang, Kuan-Ting Lin, Chia-Hung Liu, Yu-Wen Liu, Kai-Wen Huang, Peter Mu-Hsin Chang, Jin-Mei Lai, Chun-Nan Hsu, Kun-Mao Chao, Cheng-Yan Kao, and Chi-Ying F. Huang. Gene expression-based chemical genomics identifies potential therapeutic drugs in hepatocellular carcinoma. Plos One, 6(11):e27186, 2011.
Hepatocellular carcinoma (HCC) is an aggressive tumor with a poor prognosis. Currently, only sorafenib is approved by the FDA for advanced HCC treatment; therefore, there is an urgent need to discover candidate therapeutic drugs for HCC. We hypothesized that if a drug signature could reverse, at least in part, the gene expression signature of HCC, it might have the potential to inhibit HCC-related pathways and thereby treat HCC. To test this hypothesis, we first built an integrative platform, the "Encyclopedia of Hepatocellular Carcinoma genes Online 2", dubbed EHCO2, to systematically collect, organize and compare the publicly available data from HCC studies. The resulting collection includes a total of 4,020 genes. To systematically query the Connectivity Map (CMap), which includes 6,100 drug-mediated expression profiles, we further designed various gene signature selection and enrichment methods, including a randomization technique, majority vote, and clique analysis. Subsequently, 28 out of 50 prioritized drugs, including tanespimycin, trichostatin A, thioguanosine, and several anti-psychotic drugs with anti-tumor activities, were validated via MTT cell viability assays and clonogenic assays in HCC cell lines. To accelerate their future clinical use, possibly through drug-repurposing, we selected two well-established drugs to test in mice, chlorpromazine and trifluoperazine. Both drugs inhibited orthotopic liver tumor growth. In conclusion, we successfully discovered and validated existing drugs for potential HCC therapeutic use with the pipeline of Connectivity Map analysis and lab verification, thereby suggesting the usefulness of this procedure to accelerate drug repurposing for HCC treatment.
@article{ChenYLLLHCLHCKH:2011,
author = {Chen, Ming-Huang and Yang, Wu-Lung R. and Lin, Kuan-Ting and Liu, Chia-Hung and Liu, Yu-Wen and Huang, Kai-Wen and Chang, Peter Mu-Hsin and Lai, Jin-Mei and Hsu, Chun-Nan and Chao, Kun-Mao and Kao, Cheng-Yan and Huang, Chi-Ying F.},
title = {Gene expression-based chemical genomics identifies potential therapeutic drugs in hepatocellular carcinoma.},
journal = {Plos One},
volume = {6},
number = {11},
pages = {e27186},
year = {2011},
doi = {10.1371/journal.pone.0027186},
}Daiji Fukagawa, Takeyuki Tamura, Atsuhiro Takasu, Etsuji Tomita, and Tatsuya Akutsu. A clique-based method for the edit distance between unordered trees and its application to analysis of glycan structures. BMC Bioinformatics, 12 Suppl 1:S13, 2011.
Background
Measuring similarities between tree structured data is important for analysis of RNA secondary structures, phylogenetic trees, glycan structures, and vascular trees. The edit distance is one of the most widely used measures for comparison of tree structured data. However, it is known that computation of the edit distance for rooted unordered trees is NP-hard. Furthermore, there is almost no available software tool that can compute the exact edit distance for unordered trees.
Results
In this paper, we present a practical method for computing the edit distance between rooted unordered trees. In this method, the edit distance problem for unordered trees is transformed into the maximum clique problem and then efficient solvers for the maximum clique problem are applied. We applied the proposed method to similar structure search for glycan structures. The result suggests that our proposed method can efficiently compute the edit distance for moderate size unordered trees. It also suggests that the proposed method has the accuracy comparative to those by the edit distance for ordered trees and by an existing method for glycan search.
Conclusions
The proposed method is simple but useful for computation of the edit distance between unordered trees. The object code is available upon request. Japan. dfukagaw@mail.doshisha.ac.jp
Measuring similarities between tree structured data is important for analysis of RNA secondary structures, phylogenetic trees, glycan structures, and vascular trees. The edit distance is one of the most widely used measures for comparison of tree structured data. However, it is known that computation of the edit distance for rooted unordered trees is NP-hard. Furthermore, there is almost no available software tool that can compute the exact edit distance for unordered trees.
Results
In this paper, we present a practical method for computing the edit distance between rooted unordered trees. In this method, the edit distance problem for unordered trees is transformed into the maximum clique problem and then efficient solvers for the maximum clique problem are applied. We applied the proposed method to similar structure search for glycan structures. The result suggests that our proposed method can efficiently compute the edit distance for moderate size unordered trees. It also suggests that the proposed method has the accuracy comparative to those by the edit distance for ordered trees and by an existing method for glycan search.
Conclusions
The proposed method is simple but useful for computation of the edit distance between unordered trees. The object code is available upon request. Japan. dfukagaw@mail.doshisha.ac.jp
@article{FukagawaTTTA:2011,
author = {Fukagawa, Daiji and Tamura, Takeyuki and Takasu, Atsuhiro and Tomita, Etsuji and Akutsu, Tatsuya},
title = {A clique-based method for the edit distance between unordered trees and its application to analysis of glycan structures.},
journal = {BMC Bioinformatics},
volume = {12 Suppl 1},
pages = {S13},
year = {2011},
doi = {10.1186/1471-2105-12-S1-S13},
}Hiroshi Ishikawa. Transformation of general binary mrf minimization to the first-order case. IEEE Transactions On Pattern Analysis and Machine Intelligence, 33(6):1234—49, jun 2011.
We introduce a transformation of general higher-order Markov random field with binary labels into a first-order one that has the same minima as the original. Moreover, we formalize a framework for approximately minimizing higher-order multi-label MRF energies that combines the new reduction with the fusion-move and QPBO algorithms. While many computer vision problems today are formulated as energy minimization problems, they have mostly been limited to using first-order energies, which consist of unary and pairwise clique potentials, with a few exceptions that consider triples. This is because of the lack of efficient algorithms to optimize energies with higher-order interactions. Our algorithm challenges this restriction that limits the representational power of the models so that higher-order energies can be used to capture the rich statistics of natural scenes. We also show that some minimization methods can be considered special cases of the present framework, as well as comparing the new method experimentally with other such techniques. 169-8555, Japan. hfs@waseda.jp
@article{Ishikawa:2011,
author = {Ishikawa, Hiroshi},
title = {Transformation of general binary MRF minimization to the first-order case.},
journal = {IEEE Transactions On Pattern Analysis and Machine Intelligence},
volume = {33},
number = {6},
pages = {1234-49},
year = {2011},
month = jun,
doi = {10.1109/TPAMI.2010.91},
}Qing-Ju Jiao, Yan Huang, and Hong-Bin Shen. Large-scale mining co-expressed genes in arabidopsis anther: from pair to group. Computational Biology and Chemistry, 35(2):62—8, apr 2011.
Research on gene co-expression not only plays an important role in understanding the complex regulatory relationships, but also contributes to our understanding of gene regulatory network. Beyond the co-expression knowledge between two genes, investigating the co-expression relationships among multiple target genes is more informative for understanding the basic working mechanisms in a cell. In this paper, all the Arabidopsis anther genes and every gene’s potential co-expressed partners are collected by cross-database search. By combining simple pair gene co-expression networks, a complex Arabidopsis anther co-expression network is constructed. Maximum-clique algorithm is then applied to mine the groups reflecting co-expression relationships among multiple Arabidopsis anther genes that are represented by completely connected graphs. As a result, 254 Arabidopsis anther complete co-expression groups are obtained and our analysis shows that all the genes in the same group have high propensity to be functionally related and co-expressed together. We also demonstrate the efficacy of the proposed maximum-clique algorithm by comparing its results with the known Arabidopsis genome pathways, K-means clustering algorithm derived results and randomized data. It is expected that the 254 Arabidopsis anther complete co-expression groups generated in this paper can be a valuable knowledge source for further studies of molecular mechanisms of anther and its transcription regulations. Control and Information Processing, Ministry of Education of China, Shanghai, China.
@article{JiaoHS:2011,
author = {Jiao, Qing-Ju and Huang, Yan and Shen, Hong-Bin},
title = {Large-scale mining co-expressed genes in Arabidopsis anther: from pair to group.},
journal = {Computational Biology and Chemistry},
volume = {35},
number = {2},
pages = {62-8},
year = {2011},
month = apr,
doi = {10.1016/j.compbiolchem.2011.01.003},
}Takeshi Kawabata. Build-up algorithm for atomic correspondence between chemical structures. Journal of Chemical Information and Modeling, 51(8):1775—87, aug 2011.
Determining a one-to-one atom correspondence between two chemical compounds is important to measure molecular similarities and to find compounds with similar biological activities. This calculation can be formalized as the maximum common substructure (MCS) problem, which is well-studied and has been shown to be NP-complete. Although many rigorous and heuristic algorithms have been developed, none of these algorithms is sufficiently fast and accurate. We developed a new program, called "kcombu" using a build-up algorithm, which is a type of the greedy heuristic algorithms. The program can search connected and disconnected MCSs as well as topologically constrained disconnected MCS (TD-MCS), which is introduced in this study. To evaluate the performance of our program, we prepared two correct standards: the exact correspondences generated by the maximum clique algorithms and the 3D correspondences obtained from superimposed 3D structure of the molecules in a complex 3D structure with the same protein. For the five sets of molecules taken from the protein structure database, the agreement value between the build-up and the exact correspondences for the connected MCS is sufficiently high, but the computation time of the build-up algorithm is much smaller than that of the exact algorithm. The comparison between the build-up and the 3D correspondences shows that the TD-MCS has the best agreement value among the other types of MCS. Additionally, we observed a strong correlation between the molecular similarity and the agreement with the correct and 3D correspondences; more similar molecule pairs are more correctly matched. Molecular pairs with more than 40% Tanimoto similarities can be correctly matched for more than half of the atoms with the 3D correspondences. kawabata@protein.osaka-u.ac.jp
@article{Kawabata:2011,
author = {Kawabata, Takeshi},
title = {Build-up algorithm for atomic correspondence between chemical structures.},
journal = {Journal of Chemical Information and Modeling},
volume = {51},
number = {8},
pages = {1775-87},
year = {2011},
month = aug,
doi = {10.1021/ci2001023},
}Conrad Lee, Fergal Reid, Aaron McDaid, and Neil Hurley. Seeding for pervasively overlapping communities. Phys. Rev. E, 83(6):066107, 2011.
In some social and biological networks, the majority of nodes belong to multiple communities. It has recently been shown that a number of the algorithms specifically designed to detect overlapping communities do not perform well in such highly overlapping settings. Here, we consider one class of these algorithms, those which optimize a local fitness measure, typically by using a greedy heuristic to expand a seed into a community. We perform synthetic benchmarks which indicate that an appropriate seeding strategy becomes more important as the extent of community overlap increases. We find that distinct cliques provide the best seeds. We find further support for this seeding strategy with benchmarks on a Facebook network and the yeast interactome.
@article{LeeRMH:2011,
author = {Lee, Conrad and Reid, Fergal and McDaid, Aaron and Hurley, Neil},
title = {Seeding for pervasively overlapping communities},
journal = {Phys. Rev. E},
volume = {83},
number = {6},
pages = {066107},
publisher = {American Physical Society},
year = {2011},
doi = {10.1103/PhysRevE.83.066107},
}Sheng-An Lee, Theresa Tsun-Hui Tsao, Ko-Chun Yang, Han Lin, Yu-Lun Kuo, Chien-Hsiang Hsu, Wen-Kuei Lee, Kuo-Chuan Huang, and Cheng-Yan Kao. Construction and analysis of the protein-protein interaction networks for schizophrenia, bipolar disorder, and major depression. BMC Bioinformatics, 12 Suppl 13:S20, nov 2011.
Background
Schizophrenia, bipolar disorder, and major depression are devastating mental diseases, each with distinctive yet overlapping epidemiologic characteristics. Microarray and proteomics data have revealed genes which expressed abnormally in patients. Several single nucleotide polymorphisms (SNPs) and mutations are associated with one or more of the three diseases. Nevertheless, there are few studies on the interactions among the disease-associated genes and proteins.
Results
This study, for the first time, incorporated microarray and protein-protein interaction (PPI) databases to construct the PPI network of abnormally expressed genes in postmortem brain samples of schizophrenia, bipolar disorder, and major depression patients. The samples were collected from Brodmann area (BA) 10 of the prefrontal cortex. Abnormally expressed disease genes were selected by t-tests comparing the disease and control samples. These genes were involved in housekeeping functions (e.g. translation, transcription, energy conversion, and metabolism), in brain specific functions (e.g. signal transduction, neuron cell differentiation, and cytoskeleton), or in stress responses (e.g. heat shocks and biotic stress).The diseases were interconnected through several "switchboard"-like nodes in the PPI network or shared abnormally expressed genes. A "core" functional module which consisted of a tightly knitted sub-network of clique-5 and -4s was also observed. These cliques were formed by 12 genes highly expressed in both disease and control samples.
Conclusions
Several previously unidentified disease marker genes and drug targets, such as SBNO2 (schizophrenia), SEC24C (bipolar disorder), and SRRT (major depression), were identified based on statistical and topological analyses of the PPI network. The shared or interconnecting marker genes may explain the shared symptoms of the studied diseases. Furthermore, the "switchboard" genes, such as APP, UBC, and YWHAZ, are proposed as potential targets for developing new treatments due to their functional and topological significance.
Schizophrenia, bipolar disorder, and major depression are devastating mental diseases, each with distinctive yet overlapping epidemiologic characteristics. Microarray and proteomics data have revealed genes which expressed abnormally in patients. Several single nucleotide polymorphisms (SNPs) and mutations are associated with one or more of the three diseases. Nevertheless, there are few studies on the interactions among the disease-associated genes and proteins.
Results
This study, for the first time, incorporated microarray and protein-protein interaction (PPI) databases to construct the PPI network of abnormally expressed genes in postmortem brain samples of schizophrenia, bipolar disorder, and major depression patients. The samples were collected from Brodmann area (BA) 10 of the prefrontal cortex. Abnormally expressed disease genes were selected by t-tests comparing the disease and control samples. These genes were involved in housekeeping functions (e.g. translation, transcription, energy conversion, and metabolism), in brain specific functions (e.g. signal transduction, neuron cell differentiation, and cytoskeleton), or in stress responses (e.g. heat shocks and biotic stress).The diseases were interconnected through several "switchboard"-like nodes in the PPI network or shared abnormally expressed genes. A "core" functional module which consisted of a tightly knitted sub-network of clique-5 and -4s was also observed. These cliques were formed by 12 genes highly expressed in both disease and control samples.
Conclusions
Several previously unidentified disease marker genes and drug targets, such as SBNO2 (schizophrenia), SEC24C (bipolar disorder), and SRRT (major depression), were identified based on statistical and topological analyses of the PPI network. The shared or interconnecting marker genes may explain the shared symptoms of the studied diseases. Furthermore, the "switchboard" genes, such as APP, UBC, and YWHAZ, are proposed as potential targets for developing new treatments due to their functional and topological significance.
@article{LeeTYLKHLHK:2011,
author = {Lee, Sheng-An and Tsao, Theresa Tsun-Hui and Yang, Ko-Chun and Lin, Han and Kuo, Yu-Lun and Hsu, Chien-Hsiang and Lee, Wen-Kuei and Huang, Kuo-Chuan and Kao, Cheng-Yan},
title = {Construction and analysis of the protein-protein interaction networks for schizophrenia, bipolar disorder, and major depression.},
journal = {BMC Bioinformatics},
volume = {12 Suppl 13},
pages = {S20},
year = {2011},
month = nov,
doi = {10.1186/1471-2105-12-S13-S20},
}Xia Li, Chunquan Li, Desi Shang, Jing Li, Junwei Han, Yingbo Miao, Yan Wang, Qianghu Wang, Wei Li, Chao Wu, Yunpeng Zhang, Xiang Li, and Qianlan Yao. The implications of relationships between human diseases and metabolic subpathways. Plos One, 6(6):e21131, 2011.
One of the challenging problems in the etiology of diseases is to explore the relationships between initiation and progression of diseases and abnormalities in local regions of metabolic pathways. To gain insight into such relationships, we applied the "k-clique" subpathway identification method to all disease-related gene sets. For each disease, the disease risk regions of metabolic pathways were then identified and considered as subpathways associated with the disease. We finally built a disease-metabolic subpathway network (DMSPN). Through analyses based on network biology, we found that a few subpathways, such as that of cytochrome P450, were highly connected with many diseases, and most belonged to fundamental metabolisms, suggesting that abnormalities of fundamental metabolic processes tend to cause more types of diseases. According to the categories of diseases and subpathways, we tested the clustering phenomenon of diseases and metabolic subpathways in the DMSPN. The results showed that both disease nodes and subpathway nodes displayed slight clustering phenomenon. We also tested correlations between network topology and genes within disease-related metabolic subpathways, and found that within a disease-related subpathway in the DMSPN, the ratio of disease genes and the ratio of tissue-specific genes significantly increased as the number of diseases caused by the subpathway increased. Surprisingly, the ratio of essential genes significantly decreased and the ratio of housekeeping genes remained relatively unchanged. Furthermore, the coexpression levels between disease genes and other types of genes were calculated for each subpathway in the DMSPN. The results indicated that those genes intensely influenced by disease genes, including essential genes and tissue-specific genes, might be significantly associated with the disease diversity of subpathways, suggesting that different kinds of genes within a disease-related subpathway may play significantly differential roles on the diversity of diseases caused by the corresponding subpathway. Bioinformatics Science and Technology, Harbin Medical University, Harbin, China. lixia@hrbmu.edu.cn
@article{LiLSLHMWWLWZLY:2011,
author = {Li, Xia and Li, Chunquan and Shang, Desi and Li, Jing and Han, Junwei and Miao, Yingbo and Wang, Yan and Wang, Qianghu and Li, Wei and Wu, Chao and Zhang, Yunpeng and Li, Xiang and Yao, Qianlan},
title = {The implications of relationships between human diseases and metabolic subpathways.},
journal = {Plos One},
volume = {6},
number = {6},
pages = {e21131},
year = {2011},
doi = {10.1371/journal.pone.0021131},
}Pedro Nunez, Ricardo Vazquez-Martin, and Antonio Bandera. Visual odometry based on structural matching of local invariant features using stereo camera sensor. Sensors, 11(7):7262—84, 2011.
This paper describes a novel sensor system to estimate the motion of a stereo camera. Local invariant image features are matched between pairs of frames and linked into image trajectories at video rate, providing the so-called visual odometry, i.e., motion estimates from visual input alone. Our proposal conducts two matching sessions: the first one between sets of features associated to the images of the stereo pairs and the second one between sets of features associated to consecutive frames. With respect to previously proposed approaches, the main novelty of this proposal is that both matching algorithms are conducted by means of a fast matching algorithm which combines absolute and relative feature constraints. Finding the largest-valued set of mutually consistent matches is equivalent to finding the maximum-weighted clique on a graph. The stereo matching allows to represent the scene view as a graph which emerge from the features of the accepted clique. On the other hand, the frame-to-frame matching defines a graph whose vertices are features in 3D space. The efficiency of the approach is increased by minimizing the geometric and algebraic errors to estimate the final displacement of the stereo camera between consecutive acquired frames. The proposed approach has been tested for mobile robotics navigation purposes in real environments and using different features. Experimental results demonstrate the performance of the proposal, which could be applied in both industrial and service robot fields. of Extremadura, Escuela Politecnica, Avda. Universidad s/n, 10071 Caceres, Spain. pnuntru@unex.es
@article{NunezVB:2011,
author = {Nunez, Pedro and Vazquez-Martin, Ricardo and Bandera, Antonio},
title = {Visual odometry based on structural matching of local invariant features using stereo camera sensor.},
journal = {Sensors},
volume = {11},
number = {7},
pages = {7262-84},
year = {2011},
doi = {10.3390/s110707262},
}Alex Rodionov, Alexandr Bezginov, Jonathan Rose, and Elisabeth Rm Tillier. A new, fast algorithm for detecting protein coevolution using maximum compatible cliques. Algorithms for Molecular Biology, 6:17, 2011.
Background
The MatrixMatchMaker algorithm was recently introduced to detect the similarity between phylogenetic trees and thus the coevolution between proteins. MMM finds the largest common submatrices between pairs of phylogenetic distance matrices, and has numerous advantages over existing methods of coevolution detection. However, these advantages came at the cost of a very long execution time.
Results
In this paper, we show that the problem of finding the maximum submatrix reduces to a multiple maximum clique subproblem on a graph of protein pairs. This allowed us to develop a new algorithm and program implementation, MMMvII, which achieved more than 600x speedup with comparable accuracy to the original MMM.
Conclusions
MMMvII will thus allow for more more extensive and intricate analyses of coevolution.
Availability
An implementation of the MMMvII algorithm is available at: http://www.uhnresearch.ca/labs/tillier/MMMWEBvII/MMMWEBvII.php. University of Toronto, Toronto, Canada. arod@eecg.toronto.edu.
The MatrixMatchMaker algorithm was recently introduced to detect the similarity between phylogenetic trees and thus the coevolution between proteins. MMM finds the largest common submatrices between pairs of phylogenetic distance matrices, and has numerous advantages over existing methods of coevolution detection. However, these advantages came at the cost of a very long execution time.
Results
In this paper, we show that the problem of finding the maximum submatrix reduces to a multiple maximum clique subproblem on a graph of protein pairs. This allowed us to develop a new algorithm and program implementation, MMMvII, which achieved more than 600x speedup with comparable accuracy to the original MMM.
Conclusions
MMMvII will thus allow for more more extensive and intricate analyses of coevolution.
Availability
An implementation of the MMMvII algorithm is available at: http://www.uhnresearch.ca/labs/tillier/MMMWEBvII/MMMWEBvII.php. University of Toronto, Toronto, Canada. arod@eecg.toronto.edu.
@article{RodionovBRT:2011,
author = {Rodionov, Alex and Bezginov, Alexandr and Rose, Jonathan and Tillier, Elisabeth Rm},
title = {A new, fast algorithm for detecting protein coevolution using maximum compatible cliques.},
journal = {Algorithms for Molecular Biology},
volume = {6},
pages = {17},
year = {2011},
doi = {10.1186/1748-7188-6-17},
}Matthew C. Schmidt, Andrea M. Rocha, Kanchana Padmanabhan, Zhengzhang Chen, Kathleen Scott, James R. Mihelcic, and Nagiza F. Samatova. Efficient alpha, beta-motif finder for identification of phenotype-related functional modules. BMC Bioinformatics, 12:440, 2011.
Background
Microbial communities in their natural environments exhibit phenotypes that can directly cause particular diseases, convert biomass or wastewater to energy, or degrade various environmental contaminants. Understanding how these communities realize specific phenotypic traits (e.g., carbon fixation, hydrogen production) is critical for addressing health, bioremediation, or bioenergy problems.
Results
In this paper, we describe a graph-theoretical method for in silico prediction of the cellular subsystems that are related to the expression of a target phenotype. The proposed (alpha, beta)-motif finder approach allows for identification of these phenotype-related subsystems that, in addition to metabolic subsystems, could include their regulators, sensors, transporters, and even uncharacterized proteins. By comparing dozens of genome-scale networks of functionally associated proteins, our method efficiently identifies those statistically significant functional modules that are in at least alpha networks of phenotype-expressing organisms but appear in no more than beta networks of organisms that do not exhibit the target phenotype. It has been shown via various experiments that the enumerated modules are indeed related to phenotype-expression when tested with different target phenotypes like hydrogen production, motility, aerobic respiration, and acid-tolerance.
Conclusion
Thus, we have proposed a methodology that can identify potential statistically significant phenotype-related functional modules. The functional module is modeled as an (alpha, beta)-clique, where alpha and beta are two criteria introduced in this work. We also propose a novel network model, called the two-typed, divided network. The new network model and the criteria make the problem tractable even while very large networks are being compared. The code can be downloaded from http://www.freescience.org/cs/ABClique/ 27695, USA.
Microbial communities in their natural environments exhibit phenotypes that can directly cause particular diseases, convert biomass or wastewater to energy, or degrade various environmental contaminants. Understanding how these communities realize specific phenotypic traits (e.g., carbon fixation, hydrogen production) is critical for addressing health, bioremediation, or bioenergy problems.
Results
In this paper, we describe a graph-theoretical method for in silico prediction of the cellular subsystems that are related to the expression of a target phenotype. The proposed (alpha, beta)-motif finder approach allows for identification of these phenotype-related subsystems that, in addition to metabolic subsystems, could include their regulators, sensors, transporters, and even uncharacterized proteins. By comparing dozens of genome-scale networks of functionally associated proteins, our method efficiently identifies those statistically significant functional modules that are in at least alpha networks of phenotype-expressing organisms but appear in no more than beta networks of organisms that do not exhibit the target phenotype. It has been shown via various experiments that the enumerated modules are indeed related to phenotype-expression when tested with different target phenotypes like hydrogen production, motility, aerobic respiration, and acid-tolerance.
Conclusion
Thus, we have proposed a methodology that can identify potential statistically significant phenotype-related functional modules. The functional module is modeled as an (alpha, beta)-clique, where alpha and beta are two criteria introduced in this work. We also propose a novel network model, called the two-typed, divided network. The new network model and the criteria make the problem tractable even while very large networks are being compared. The code can be downloaded from http://www.freescience.org/cs/ABClique/ 27695, USA.
@article{SchmidtRPCSMS:2011,
author = {Schmidt, Matthew C. and Rocha, Andrea M. and Padmanabhan, Kanchana and Chen, Zhengzhang and Scott, Kathleen and Mihelcic, James R. and Samatova, Nagiza F.},
title = {Efficient alpha, beta-motif finder for identification of phenotype-related functional modules.},
journal = {BMC Bioinformatics},
volume = {12},
pages = {440},
year = {2011},
doi = {10.1186/1471-2105-12-440},
}Elizabeth Skippington and Mark A. Ragan. Lateral genetic transfer and the construction of genetic exchange communities. Fems Microbiology Reviews, 35(5):707—35, sep 2011.
Lateral genetic transfer (LGT) is a major source of phenotypic innovation among bacteria. Determinants for antibiotic resistance and other adaptive traits can spread rapidly, particularly by conjugative plasmids, but also phages and natural transformation. Each successive step from the uptake of foreign DNA, its genetic recombination and regulatory integration, to its establishment in the host population presents differential barriers and opportunities. The emergence of successive multidrug-resistant strains of Staphylococcus aureus illustrates the ongoing role of LGT in the combinatorial assembly of pathogens. The dynamic interplay among hosts, vectors, DNA elements, combinations of genetic determinants and environments constructs communities of genetic exchange. These relations can be abstracted as a graph, within which an exchange community might correspond to a path, transitively closed set, clique or near-clique. We provide a set-based definition, and review the features of actual genetic exchange communities (GECs), adopting first a knowledge-driven approach based on literature, and then a synoptic data-centric bioinformatic approach. GECs are diverse, but share some common features. Differential opportunity and barriers to lateral genetic transfer create bacterial communities of exchange. Publishing Ltd. All rights reserved. The University of Queensland, Brisbane, Qld, Australia.
@article{SkippingtonR:2011,
author = {Skippington, Elizabeth and Ragan, Mark A.},
title = {Lateral genetic transfer and the construction of genetic exchange communities.},
journal = {Fems Microbiology Reviews},
volume = {35},
number = {5},
pages = {707-35},
year = {2011},
month = sep,
doi = {10.1111/j.1574-6976.2010.00261.x},
}I-Lin Wang and Chia-Yuan Chang. Mathematical properties and bounds on haplotyping populations by pure parsimony. Mathematical Biosciences, 231(2):120—5, jun 2011.
Although the haplotype data can be used to analyze the function of DNA, due to the significant efforts required in collecting the haplotype data, usually the genotype data is collected and then the population haplotype inference (PHI) problem is solved to infer haplotype data from genotype data for a population. This paper investigates the PHI problem based on the pure parsimony criterion (HIPP), which seeks the minimum number of distinct haplotypes to infer a given genotype data. We analyze the mathematical structure and properties for the HIPP problem, propose techniques to reduce the given genotype data into an equivalent one of much smaller size, and analyze the relations of genotype data using a compatible graph. Based on the mathematical properties in the compatible graph, we propose a maximal clique heuristic to obtain an upper bound, and a new polynomial-sized integer linear programming formulation to obtain a lower bound for the HIPP problem. University, No.1 University Rd., Tainan 701, Taiwan. ilinwang@mail.ncku.edu.tw
@article{WangC:2011,
author = {Wang, I-Lin and Chang, Chia-Yuan},
title = {Mathematical properties and bounds on haplotyping populations by pure parsimony.},
journal = {Mathematical Biosciences},
volume = {231},
number = {2},
pages = {120-5},
year = {2011},
month = jun,
doi = {10.1016/j.mbs.2011.02.008},
}Michael Wels, Yefeng Zheng, Martin Huber, Joachim Hornegger, and Dorin Comaniciu. A discriminative model-constrained em approach to 3d mri brain tissue classification and intensity non-uniformity correction. Physics in Medicine and Biology, 56(11):3269—300, jun 2011.
We describe a fully automated method for tissue classification, which is the segmentation into cerebral gray matter (GM), cerebral white matter (WM), and cerebral spinal fluid (CSF), and intensity non-uniformity (INU) correction in brain magnetic resonance imaging (MRI) volumes. It combines supervised MRI modality-specific discriminative modeling and unsupervised statistical expectation maximization (EM) segmentation into an integrated Bayesian framework. While both the parametric observation models and the non-parametrically modeled INUs are estimated via EM during segmentation itself, a Markov random field (MRF) prior model regularizes segmentation and parameter estimation. Firstly, the regularization takes into account knowledge about spatial and appearance-related homogeneity of segments in terms of pairwise clique potentials of adjacent voxels. Secondly and more importantly, patient-specific knowledge about the global spatial distribution of brain tissue is incorporated into the segmentation process via unary clique potentials. They are based on a strong discriminative model provided by a probabilistic boosting tree (PBT) for classifying image voxels. It relies on the surrounding context and alignment-based features derived from a probabilistic anatomical atlas. The context considered is encoded by 3D Haar-like features of reduced INU sensitivity. Alignment is carried out fully automatically by means of an affine registration algorithm minimizing cross-correlation. Both types of features do not immediately use the observed intensities provided by the MRI modality but instead rely on specifically transformed features, which are less sensitive to MRI artifacts. Detailed quantitative evaluations on standard phantom scans and standard real-world data show the accuracy and robustness of the proposed method. They also demonstrate relative superiority in comparison to other state-of-the-art approaches to this kind of computational task: our method achieves average Dice coefficients of 0.93 +/- 0.03 (WM) and 0.90 +/- 0.05 (GM) on simulated mono-spectral and 0.94 +/- 0.02 (WM) and 0.92 +/- 0.04 (GM) on simulated multi-spectral data from the BrainWeb repository. The scores are 0.81 +/- 0.09 (WM) and 0.82 +/- 0.06 (GM) and 0.87 +/- 0.05 (WM) and 0.83 +/- 0.12 (GM) for the two collections of real-world data sets-consisting of 20 and 18 volumes, respectively-provided by the Internet Brain Segmentation Repository. University Erlangen-Nuremberg, Martensstr. 3, 91058 Erlangen, Germany. michael.wels@informatik.uni-erlangen.de
@article{WelsZHHC:2011,
author = {Wels, Michael and Zheng, Yefeng and Huber, Martin and Hornegger, Joachim and Comaniciu, Dorin},
title = {A discriminative model-constrained EM approach to 3D MRI brain tissue classification and intensity non-uniformity correction.},
journal = {Physics in Medicine and Biology},
volume = {56},
number = {11},
pages = {3269-300},
year = {2011},
month = jun,
doi = {10.1088/0031-9155/56/11/007},
}Yan Yan, Shenggui Zhang, and Fang-Xiang Wu. Applications of graph theory in protein structure identification. Proteome Science, 9 Suppl 1:S17, 2011.
There is a growing interest in the identification of proteins on the proteome wide scale. Among different kinds of protein structure identification methods, graph-theoretic methods are very sharp ones. Due to their lower costs, higher effectiveness and many other advantages, they have drawn more and more researchers’ attention nowadays. Specifically, graph-theoretic methods have been widely used in homology identification, side-chain cluster identification, peptide sequencing and so on. This paper reviews several methods in solving protein structure identification problems using graph theory. We mainly introduce classical methods and mathematical models including homology modeling based on clique finding, identification of side-chain clusters in protein structures upon graph spectrum, and de novo peptide sequencing via tandem mass spectrometry using the spectrum graph model. In addition, concluding remarks and future priorities of each method are given. 5A9, Canada. faw341@mail.usask.ca.
@article{YanZW:2011,
author = {Yan, Yan and Zhang, Shenggui and Wu, Fang-Xiang},
title = {Applications of graph theory in protein structure identification.},
journal = {Proteome Science},
volume = {9 Suppl 1},
pages = {S17},
year = {2011},
doi = {10.1186/1477-5956-9-S1-S17},
}Zhanli Zhang, Xin Jiang, Lili Ma, Shaoting Tang, and Zhiming Zheng. Detecting communities in clustered networks based on group action on set. Physica A: Statistical Mechanics and its Applications, 390(6):1171—1181, 2011.
In this paper, we propose a well targeted algorithm (GAS algorithm) for detecting communities in high clustered networks by presenting group action technology on community division. During the processing of this algorithm, the underlying community structure of a clustered network emerges simultaneously as the corresponding partition of orbits by the permutation groups acting on the node set are achieved. As the derivation of the orbit partition, an algebraic structure r-cycle can be considered as the origin of the community. To be a priori estimation for the community structure of the algorithm, the community separability is introduced to indicate whether a network has distinct community structure. By executing the algorithm on several typical networks and the LFR benchmark, it shows that this GAS algorithm can detect communities accurately and effectively in high clustered networks. Furthermore, we compare the GAS algorithm and the clique percolation algorithm on the LFR benchmark. It is shown that the GAS algorithm is more accurate at detecting non-overlapping communities in clustered networks. It is suggested that algebraic techniques can uncover fresh light on detecting communities in complex networks.
@article{ZhangJMTZ:2011,
author = {Zhanli Zhang and Xin Jiang and Lili Ma and Shaoting Tang and Zhiming Zheng},
title = {Detecting communities in clustered networks based on group action on set},
journal = {Physica A: Statistical Mechanics and its Applications},
volume = {390},
number = {6},
pages = {1171--1181},
year = {2011},
doi = {10.1016/j.physa.2010.11.029},
}Hongyan Zhang and Xiyu Liu. A clique algorithm using dna computing techniques based on closed-circle dna sequences. Bio Systems, 105(1):73—82, jul 2011.
DNA computing has been applied in broad fields such as graph theory, finite state problems, and combinatorial problem. DNA computing approaches are more suitable used to solve many combinatorial problems because of the vast parallelism and high-density storage. The CLIQUE algorithm is one of the gird-based clustering techniques for spatial data. It is the combinatorial problem of the density cells. Therefore we utilize DNA computing using the closed-circle DNA sequences to execute the CLIQUE algorithm for the two-dimensional data. In our study, the process of clustering becomes a parallel bio-chemical reaction and the DNA sequences representing the marked cells can be combined to form a closed-circle DNA sequences. This strategy is a new application of DNA computing. Although the strategy is only for the two-dimensional data, it provides a new idea to consider the grids to be vertexes in a graph and transform the search problem into a combinatorial problem. China. zswanz@yahoo.com.cn
@article{ZhangL:2011,
author = {Zhang, Hongyan and Liu, Xiyu},
title = {A CLIQUE algorithm using DNA computing techniques based on closed-circle DNA sequences.},
journal = {Bio Systems},
volume = {105},
number = {1},
pages = {73-82},
year = {2011},
month = jul,
doi = {10.1016/j.biosystems.2011.03.004},
}Xiaoqi Zheng, Taigang Liu, Zhongnan Yang, and Jun Wang. Large cliques in arabidopsis gene coexpression network and motif discovery. Journal of Plant Physiology, 168(6):611—8, apr 2011.
Identification of cis-regulatory elements in Arabidopsis is a key step to understanding its transcriptional regulation scheme. In this study, the Arabidopsis gene coexpression network was constructed using the ATTED-II data, and thereafter a subgraph-induced approach and clique-finding algorithm were used to extract gene coexpression groups from the gene coexpression network. A total of 23 large coexpression gene groups were obtained, with each consisting of more than 100 highly correlated genes. Four classical tools were used to predict motifs in the promoter regions of coexpressed genes. Consequently, we detected a large number of candidate biologically relevant regulatory elements, and many of them are consistent with known cis-regulatory elements from AGRIS and AthaMap. Experiments on coexpressed groups, including E2Fa target genes, showed that our method had a high probability of returning the real binding motif. Our study provides the basis for future cis-regulatory module analysis and creates a starting point to unravel regulatory networks of Arabidopsis thaliana.
@article{ZhengLYW:2011,
author = {Zheng, Xiaoqi and Liu, Taigang and Yang, Zhongnan and Wang, Jun},
title = {Large cliques in Arabidopsis gene coexpression network and motif discovery.},
journal = {Journal of Plant Physiology},
volume = {168},
number = {6},
pages = {611-8},
year = {2011},
month = apr,
doi = {10.1016/j.jplph.2010.09.010},
}Ashis Kumer Biswas, Nasimul Noman, and Abdur Rahman Sikder. Machine learning approach to predict protein phosphorylation sites by incorporating evolutionary information. BMC Bioinformatics, 11:273, 2010.
Background
Most of the existing in silico phosphorylation site prediction systems use machine learning approach that requires preparing a good set of classification data in order to build the classification knowledge. Furthermore, phosphorylation is catalyzed by kinase enzymes and hence the kinase information of the phosphorylated sites has been used as major classification data in most of the existing systems. Since the number of kinase annotations in protein sequences is far less than that of the proteins being sequenced to date, the prediction systems that use the information found from the small clique of kinase annotated proteins can not be considered as completely perfect for predicting outside the clique. Hence the systems are certainly not generalized. In this paper, a novel generalized prediction system, PPRED (Phosphorylation PREDictor) is proposed that ignores the kinase information and only uses the evolutionary information of proteins for classifying phosphorylation sites.
Results
Experimental results based on cross validations and an independent benchmark reveal the significance of using the evolutionary information alone to classify phosphorylation sites from protein sequences. The prediction performance of the proposed system is better than those of the existing prediction systems that also do not incorporate kinase information. The system is also comparable to systems that incorporate kinase information in predicting such sites.
Conclusions
The approach presented in this paper provides an efficient way to identify phosphorylation sites in a given protein primary sequence that would be a valuable information for the molecular biologists working on protein phosphorylation sites and for bioinformaticians developing generalized prediction systems for the post translational modifications like phosphorylation or glycosylation. PPRED is publicly available at the URL http://www.cse.univdhaka.edu/ ashis/ppred/index.php. 1000, Bangladesh. ashis.csedu@gmail.com
Most of the existing in silico phosphorylation site prediction systems use machine learning approach that requires preparing a good set of classification data in order to build the classification knowledge. Furthermore, phosphorylation is catalyzed by kinase enzymes and hence the kinase information of the phosphorylated sites has been used as major classification data in most of the existing systems. Since the number of kinase annotations in protein sequences is far less than that of the proteins being sequenced to date, the prediction systems that use the information found from the small clique of kinase annotated proteins can not be considered as completely perfect for predicting outside the clique. Hence the systems are certainly not generalized. In this paper, a novel generalized prediction system, PPRED (Phosphorylation PREDictor) is proposed that ignores the kinase information and only uses the evolutionary information of proteins for classifying phosphorylation sites.
Results
Experimental results based on cross validations and an independent benchmark reveal the significance of using the evolutionary information alone to classify phosphorylation sites from protein sequences. The prediction performance of the proposed system is better than those of the existing prediction systems that also do not incorporate kinase information. The system is also comparable to systems that incorporate kinase information in predicting such sites.
Conclusions
The approach presented in this paper provides an efficient way to identify phosphorylation sites in a given protein primary sequence that would be a valuable information for the molecular biologists working on protein phosphorylation sites and for bioinformaticians developing generalized prediction systems for the post translational modifications like phosphorylation or glycosylation. PPRED is publicly available at the URL http://www.cse.univdhaka.edu/ ashis/ppred/index.php. 1000, Bangladesh. ashis.csedu@gmail.com
@article{BiswasNS:2010,
author = {Biswas, Ashis Kumer and Noman, Nasimul and Sikder, Abdur Rahman},
title = {Machine learning approach to predict protein phosphorylation sites by incorporating evolutionary information.},
journal = {BMC Bioinformatics},
volume = {11},
pages = {273},
year = {2010},
doi = {10.1186/1471-2105-11-273},
}Rick C. S Chen and Stephen J. H. Yang. Applying dna computation to intractable problems in social network analysis. Bio Systems, 101(3):222—32, sep 2010.
From ancient times to the present day, social networks have played an important role in the formation of various organizations for a range of social behaviors. As such, social networks inherently describe the complicated relationships between elements around the world. Based on mathematical graph theory, social network analysis (SNA) has been developed in and applied to various fields such as Web 2.0 for Web applications and product developments in industries, etc. However, some definitions of SNA, such as finding a clique, N-clique, N-clan, N-club and K-plex, are NP-complete problems, which are not easily solved via traditional computer architecture. These challenges have restricted the uses of SNA. This paper provides DNA-computing-based approaches with inherently high information density and massive parallelism. Using these approaches, we aim to solve the three primary problems of social networks: N-clique, N-clan, and N-club. Their accuracy and feasible time complexities discussed in the paper will demonstrate that DNA computing can be used to facilitate the development of SNA. University, Taiwan.
@article{ChenY:2010,
author = {Chen, Rick C. S and Yang, Stephen J. H.},
title = {Applying DNA computation to intractable problems in social network analysis.},
journal = {Bio Systems},
volume = {101},
number = {3},
pages = {222-32},
year = {2010},
month = sep,
doi = {10.1016/j.biosystems.2010.05.006},
}David L. Cooper, James E. Gentle, Ernest Barreto, and James L. Olds. Synchronized changes to relative neuron populations in postnatal human neocortical development. Cognitive Neurodynamics, 4(2):151—63, jun 2010.
Mammalian prenatal neocortical development is dominated by the synchronized formation of the laminae and migration of neurons. Postnatal development likewise contains "sensitive periods" during which functions such as ocular dominance emerge. Here we introduce a novel neuroinformatics approach to identify and study these periods of active development. Although many aspects of the approach can be used in other studies, some specific techniques were chosen because of a legacy dataset of human histological data (Conel in The postnatal development of the human cerebral cortex, vol 1-8. Harvard University Press, Cambridge, 1939-1967). Our method calculates normalized change vectors from the raw histological data, and then employs k-means cluster analysis of the change vectors to explore the population dynamics of neurons from 37 neocortical areas across eight postnatal developmental stages from birth to 72 months in 54 subjects. We show that the cortical "address" (Brodmann area/sub-area and layer) provides the necessary resolution to segregate neuron population changes into seven correlated "k-clusters" in k-means cluster analysis. The members in each k-cluster share a single change interval where the relative share of the cortex by the members undergoes its maximum change. The maximum change occurs in a different change interval for each k-cluster. Each k-cluster has at least one totally connected maximal "clique" which appears to correspond to cortical function. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s11571-010-9103-3) contains supplementary material, which is available to authorized users.
@article{CooperGBO:2010,
author = {Cooper, David L. and Gentle, James E. and Barreto, Ernest and Olds, James L.},
title = {Synchronized changes to relative neuron populations in postnatal human neocortical development.},
journal = {Cognitive Neurodynamics},
volume = {4},
number = {2},
pages = {151-63},
year = {2010},
month = jun,
doi = {10.1007/s11571-010-9103-3},
}Ryan Day, Kristin P. Lennox, David B. Dahl, Marina Vannucci, and Jerry W. Tsai. Characterizing the regularity of tetrahedral packing motifs in protein tertiary structure. Bioinformatics, 26(24):3059—66, dec 2010.
Motivation
While protein secondary structure is well understood, representing the repetitive nature of tertiary packing in proteins remains difficult. We have developed a construct called the relative packing group (RPG) that applies the clique concept from graph theory as a natural basis for defining the packing motifs in proteins. An RPG is defined as a clique of residues, where every member contacts all others as determined by the Delaunay tessellation. Geometrically similar RPGs define a regular element of tertiary structure or tertiary motif (TerMo). This intuitive construct provides a simple approach to characterize general repetitive elements of tertiary structure.
Results
A dataset of over 4 million tetrahedral RPGs was clustered using different criteria to characterize the various aspects of regular tertiary structure in TerMos. Grouping this data within the SCOP classification levels of Family, Superfamily, Fold, Class and PDB showed that similar packing is shared across different folds. Classification of RPGs based on residue sequence locality reveals topological preferences according to protein sizes and secondary structure. We find that larger proteins favor RPGs with three local residues packed against a non-local residue. Classifying by secondary structure, helices prefer mostly local residues, sheets favor at least two local residues, while turns and coil populate with more local residues. To depict these TerMos, we have developed 2 complementary and intuitive representations: (i) Dirichlet process mixture density estimation of the torsion angle distributions and (ii) kernel density estimation of the Cartesian coordinate distribution. The TerMo library and representations software are available upon request.
While protein secondary structure is well understood, representing the repetitive nature of tertiary packing in proteins remains difficult. We have developed a construct called the relative packing group (RPG) that applies the clique concept from graph theory as a natural basis for defining the packing motifs in proteins. An RPG is defined as a clique of residues, where every member contacts all others as determined by the Delaunay tessellation. Geometrically similar RPGs define a regular element of tertiary structure or tertiary motif (TerMo). This intuitive construct provides a simple approach to characterize general repetitive elements of tertiary structure.
Results
A dataset of over 4 million tetrahedral RPGs was clustered using different criteria to characterize the various aspects of regular tertiary structure in TerMos. Grouping this data within the SCOP classification levels of Family, Superfamily, Fold, Class and PDB showed that similar packing is shared across different folds. Classification of RPGs based on residue sequence locality reveals topological preferences according to protein sizes and secondary structure. We find that larger proteins favor RPGs with three local residues packed against a non-local residue. Classifying by secondary structure, helices prefer mostly local residues, sheets favor at least two local residues, while turns and coil populate with more local residues. To depict these TerMos, we have developed 2 complementary and intuitive representations: (i) Dirichlet process mixture density estimation of the torsion angle distributions and (ii) kernel density estimation of the Cartesian coordinate distribution. The TerMo library and representations software are available upon request.
@article{DayLDVT:2010,
author = {Day, Ryan and Lennox, Kristin P. and Dahl, David B. and Vannucci, Marina and Tsai, Jerry W.},
title = {Characterizing the regularity of tetrahedral packing motifs in protein tertiary structure.},
journal = {Bioinformatics},
volume = {26},
number = {24},
pages = {3059-66},
year = {2010},
month = dec,
doi = {10.1093/bioinformatics/btq573},
}Janez Konc and Dusanka Janezic. Probis algorithm for detection of structurally similar protein binding sites by local structural alignment. Bioinformatics, 26(9):1160—8, may 2010.
Motivation
Exploitation of locally similar 3D patterns of physicochemical properties on the surface of a protein for detection of binding sites that may lack sequence and global structural conservation.
Results
An algorithm, ProBiS is described that detects structurally similar sites on protein surfaces by local surface structure alignment. It compares the query protein to members of a database of protein 3D structures and detects with sub-residue precision, structurally similar sites as patterns of physicochemical properties on the protein surface. Using an efficient maximum clique algorithm, the program identifies proteins that share local structural similarities with the query protein and generates structure-based alignments of these proteins with the query. Structural similarity scores are calculated for the query protein’s surface residues, and are expressed as different colors on the query protein surface. The algorithm has been used successfully for the detection of protein-protein, protein-small ligand and protein-DNA binding sites.
Availability
The software is available, as a web tool, free of charge for academic users at http://probis.cmm.ki.si.
Exploitation of locally similar 3D patterns of physicochemical properties on the surface of a protein for detection of binding sites that may lack sequence and global structural conservation.
Results
An algorithm, ProBiS is described that detects structurally similar sites on protein surfaces by local surface structure alignment. It compares the query protein to members of a database of protein 3D structures and detects with sub-residue precision, structurally similar sites as patterns of physicochemical properties on the protein surface. Using an efficient maximum clique algorithm, the program identifies proteins that share local structural similarities with the query protein and generates structure-based alignments of these proteins with the query. Structural similarity scores are calculated for the query protein’s surface residues, and are expressed as different colors on the query protein surface. The algorithm has been used successfully for the detection of protein-protein, protein-small ligand and protein-DNA binding sites.
Availability
The software is available, as a web tool, free of charge for academic users at http://probis.cmm.ki.si.
@article{KoncJ:2010,
author = {Konc, Janez and Janezic, Dusanka},
title = {ProBiS algorithm for detection of structurally similar protein binding sites by local structural alignment.},
journal = {Bioinformatics},
volume = {26},
number = {9},
pages = {1160-8},
year = {2010},
month = may,
doi = {10.1093/bioinformatics/btq100},
}M. Pawan Kumar, P. H S. Torr, and A. Zisserman. Objcut: efficient segmentation using top-down and bottom-up cues. IEEE Transactions On Pattern Analysis and Machine Intelligence, 32(3):530—45, mar 2010.
We present a probabilistic method for segmenting instances of a particular object category within an image. Our approach overcomes the deficiencies of previous segmentation techniques based on traditional grid conditional random fields (CRF), namely that 1) they require the user to provide seed pixels for the foreground and the background and 2) they provide a poor prior for specific shapes due to the small neighborhood size of grid CRF. Specifically, we automatically obtain the pose of the object in a given image instead of relying on manual interaction. Furthermore, we employ a probabilistic model which includes shape potentials for the object to incorporate top-down information that is global across the image, in addition to the grid clique potentials which provide the bottom-up information used in previous approaches. The shape potentials are provided by the pose of the object obtained using an object category model. We represent articulated object categories using a novel layered pictorial structures model. Nonarticulated object categories are modeled using a set of exemplars. These object category models have the advantage that they can handle large intraclass shape, appearance, and spatial variation. We develop an efficient method, OBJCUT, to obtain segmentations using our probabilistic framework. Novel aspects of this method include: 1) efficient algorithms for sampling the object category models of our choice and 2) the observation that a sampling-based approximation of the expected log-likelihood of the model can be increased by a single graph cut. Results are presented on several articulated (e.g., animals) and nonarticulated (e.g., fruits) object categories. We provide a favorable comparison of our method with the state of the art in object category specific image segmentation, specifically the methods of Leibe and Schiele and Schoenemann and Cremers.
@article{KumarTZ:2010,
author = {Kumar, M. Pawan and Torr, P. H S. and Zisserman, A.},
title = {OBJCUT: efficient segmentation using top-down and bottom-up cues.},
journal = {IEEE Transactions On Pattern Analysis and Machine Intelligence},
volume = {32},
number = {3},
pages = {530-45},
year = {2010},
month = mar,
doi = {10.1109/TPAMI.2009.16},
}Ming-Ying Lan, Chi-Long Chen, Kuan-Ting Lin, Sheng-An Lee, Wu-Lung R. Yang, Chun-Nan Hsu, Jaw-Ching Wu, Ching-Yin Ho, Jin-Ching Lin, and Chi-Ying F. Huang. From npc therapeutic target identification to potential treatment strategy. Molecular Cancer Therapeutics, 9(9):2511—23, sep 2010.
Nasopharyngeal carcinoma (NPC) is relatively rare in Western countries but is a common cancer in southern Asia. Many differentially expressed genes have been linked to NPC; however, how to prioritize therapeutic targets and potential drugs from unsorted gene lists remains largely unknown. We first collected 558 upregulated and 993 downregulated NPC genes from published microarray data and the primary literatures. We then postulated that conversion of gene signatures into the protein-protein interaction network and analyzing the network topologically could provide insight into key regulators involved in tumorigenesis of NPC. Of particular interest was the presence of cliques, called fully connected subgraphs, in the inferred NPC networks. These clique-based hubs, connecting with more than three queries and ranked higher than other nodes in the NPC protein-protein interaction network, were further narrowed down by pathway analysis to retrieve 24 upregulated and 6 downregulated bottleneck genes for predicting NPC carcinogenesis. Moreover, additional oncogenes, tumor suppressor genes, genes involved in protein complexes, and genes obtained after functional profiling were merged with the bottleneck genes to form the final gene signature of 38 upregulated and 10 downregulated genes. We used the initial and final NPC gene signatures to query the Connectivity Map, respectively, and found that target reduction through our pipeline could efficiently uncover potential drugs with cytotoxicity to NPC cancer cells. An integrative Web site (http://140.109.23.188:8080/NPC) was established to facilitate future NPC research. This in silico approach, from target prioritization to potential drugs identification, might be an effective method for various cancer researches. Taiwan.
@article{LanCLLYHWHLH:2010,
author = {Lan, Ming-Ying and Chen, Chi-Long and Lin, Kuan-Ting and Lee, Sheng-An and Yang, Wu-Lung R. and Hsu, Chun-Nan and Wu, Jaw-Ching and Ho, Ching-Yin and Lin, Jin-Ching and Huang, Chi-Ying F.},
title = {From NPC therapeutic target identification to potential treatment strategy.},
journal = {Molecular Cancer Therapeutics},
volume = {9},
number = {9},
pages = {2511-23},
year = {2010},
month = sep,
doi = {10.1158/1535-7163.MCT-09-0966},
}Min Li, Jianxin Wang, Jianer Chen, Zhao Cai, and Gang Chen. Identifying the overlapping complexes in protein interaction networks. International Journal of Data Mining and Bioinformatics (IJDMB), 4(1):91—108, 2010.
Identification of protein complexes in large interaction networks is crucial to understanding principles of cellular organisation and predict protein functions. In this paper, a new algorithm of Identifying Protein Complexes based on Maximal Clique Extension (IPC-MCE) is proposed. The maximal clique is considered as the core of the protein complex. Proteins in a complex are classed into core vertices and peripheral vertices. The relation between the core vertices and peripheral vertices is measured by the Interaction Probability. The algorithm IPC-MCE is applied to the protein interaction network of Saccharomyces cerevisiae. Many well-known protein complexes are detected.
@article{LiWCCC:2010,
author = {Min Li and Jianxin Wang and Jianer Chen and Zhao Cai and Gang Chen},
title = {Identifying the overlapping complexes in protein interaction networks},
journal = {International Journal of Data Mining and Bioinformatics (IJDMB)},
volume = {4},
number = {1},
pages = {91--108},
publisher = {Inderscience Publishers},
year = {2010},
address = {Geneva, Switzerland},
doi = {10.1504/IJDMB.2010.030969},
}Ryan R. Rahrig, Neocles B. Leontis, and Craig L. Zirbel. R3d align: global pairwise alignment of rna 3d structures using local superpositions. Bioinformatics, 26(21):2689—97, nov 2010.
Motivation
Comparing 3D structures of homologous RNA molecules yields information about sequence and structural variability. To compare large RNA 3D structures, accurate automatic comparison tools are needed. In this article, we introduce a new algorithm and web server to align large homologous RNA structures nucleotide by nucleotide using local superpositions that accommodate the flexibility of RNA molecules. Local alignments are merged to form a global alignment by employing a maximum clique algorithm on a specially defined graph that we call the ’local alignment’ graph.
Results
The algorithm is implemented in a program suite and web server called ’R3D Align’. The R3D Align alignment of homologous 3D structures of 5S, 16S and 23S rRNA was compared to a high-quality hand alignment. A full comparison of the 16S alignment with the other state-of-the-art methods is also provided. The R3D Align program suite includes new diagnostic tools for the structural evaluation of RNA alignments. The R3D Align alignments were compared to those produced by other programs and were found to be the most accurate, in comparison with a high quality hand-crafted alignment and in conjunction with a series of other diagnostics presented. The number of aligned base pairs as well as measures of geometric similarity are used to evaluate the accuracy of the alignments.
Availability
R3D Align is freely available through a web server http://rna.bgsu.edu/R3DAlign. The MATLAB source code of the program suite is also freely available for download at that location. 45810, USA. r-rahrig@onu.edu
Comparing 3D structures of homologous RNA molecules yields information about sequence and structural variability. To compare large RNA 3D structures, accurate automatic comparison tools are needed. In this article, we introduce a new algorithm and web server to align large homologous RNA structures nucleotide by nucleotide using local superpositions that accommodate the flexibility of RNA molecules. Local alignments are merged to form a global alignment by employing a maximum clique algorithm on a specially defined graph that we call the ’local alignment’ graph.
Results
The algorithm is implemented in a program suite and web server called ’R3D Align’. The R3D Align alignment of homologous 3D structures of 5S, 16S and 23S rRNA was compared to a high-quality hand alignment. A full comparison of the 16S alignment with the other state-of-the-art methods is also provided. The R3D Align program suite includes new diagnostic tools for the structural evaluation of RNA alignments. The R3D Align alignments were compared to those produced by other programs and were found to be the most accurate, in comparison with a high quality hand-crafted alignment and in conjunction with a series of other diagnostics presented. The number of aligned base pairs as well as measures of geometric similarity are used to evaluate the accuracy of the alignments.
Availability
R3D Align is freely available through a web server http://rna.bgsu.edu/R3DAlign. The MATLAB source code of the program suite is also freely available for download at that location. 45810, USA. r-rahrig@onu.edu
@article{RahrigLZ:2010,
author = {Rahrig, Ryan R. and Leontis, Neocles B. and Zirbel, Craig L.},
title = {R3D Align: global pairwise alignment of RNA 3D structures using local superpositions.},
journal = {Bioinformatics},
volume = {26},
number = {21},
pages = {2689-97},
year = {2010},
month = nov,
doi = {10.1093/bioinformatics/btq506},
}Felix Reisen, Martin Weisel, Jan M. Kriegl, and Gisbert Schneider. Self-organizing fuzzy graphs for structure-based comparison of protein pockets. Journal of Proteome Research, 9(12):6498—510, dec 2010.
Patterns of receptor-ligand interaction can be conserved in functionally equivalent proteins even in the absence of sequence homology. Therefore, structural comparison of ligand-binding pockets and their pharmacophoric features allow for the characterization of so-called "orphan" proteins with known three-dimensional structure but unknown function, and predict ligand promiscuity of binding pockets. We present an algorithm for rapid pocket comparison (PoLiMorph), in which protein pockets are represented by self-organizing graphs that fill the volume of the cavity. Vertices in these three-dimensional frameworks contain information about the local ligand-receptor interaction potential coded by fuzzy property labels. For framework matching, we developed a fast heuristic based on the maximum dispersion problem, as an alternative to techniques utilizing clique detection or geometric hashing algorithms. A sophisticated scoring function was applied that incorporates knowledge about property distributions and ligand-receptor interaction patterns. In an all-against-all virtual screening experiment with 207 pocket frameworks extracted from a subset of PDBbind, PoLiMorph correctly assigned 81% of 69 distinct structural classes and demonstrated sustained ability to group pockets accommodating the same ligand chemotype. We determined a score threshold that indicates "true" pocket similarity with high reliability, which not only supports structure-based drug design but also allows for sequence-independent studies of the proteome. Zurich, Switzerland.
@article{ReisenWKS:2010,
author = {Reisen, Felix and Weisel, Martin and Kriegl, Jan M. and Schneider, Gisbert},
title = {Self-organizing fuzzy graphs for structure-based comparison of protein pockets.},
journal = {Journal of Proteome Research},
volume = {9},
number = {12},
pages = {6498-510},
year = {2010},
month = dec,
doi = {10.1021/pr100719n},
}Zhiao Shi, Catherine K. Derow, and Bing Zhang. Co-expression module analysis reveals biological processes, genomic gain, and regulatory mechanisms associated with breast cancer progression. BMC Systems Biology, 4:74, 2010.
Background
Gene expression signatures are typically identified by correlating gene expression patterns to a disease phenotype of interest. However, individual gene-based signatures usually suffer from low reproducibility and interpretability.
Results
We have developed a novel algorithm Iterative Clique Enumeration (ICE) for identifying relatively independent maximal cliques as co-expression modules and a module-based approach to the analysis of gene expression data. Applying this approach on a public breast cancer dataset identified 19 modules whose expression levels were significantly correlated with tumor grade. The correlations were reproducible for 17 modules in an independent breast cancer dataset, and the reproducibility was considerably higher than that based on individual genes or modules identified by other algorithms. Sixteen out of the 17 modules showed significant enrichment in certain Gene Ontology (GO) categories. Specifically, modules related to cell proliferation and immune response were up-regulated in high-grade tumors while those related to cell adhesion was down-regulated. Further analyses showed that transcription factors NYFB, E2F1/E2F3, NRF1, and ELK1 were responsible for the up-regulation of the cell proliferation modules. IRF family and ETS family proteins were responsible for the up-regulation of the immune response modules. Moreover, inhibition of the PPARA signaling pathway may also play an important role in tumor progression. The module without GO enrichment was found to be associated with a potential genomic gain in 8q21-23 in high-grade tumors. The 17-module signature of breast tumor progression clustered patients into subgroups with significantly different relapse-free survival times. Namely, patients with lower cell proliferation and higher cell adhesion levels had significantly lower risk of recurrence, both for all patients (p = 0.004) and for those with grade 2 tumors (p = 0.017).
Conclusions
The ICE algorithm is effective in identifying relatively independent co-expression modules from gene co-expression networks and the module-based approach illustrated in this study provides a robust, interpretable, and mechanistic characterization of transcriptional changes. Nashville, TN 37240, USA.
Gene expression signatures are typically identified by correlating gene expression patterns to a disease phenotype of interest. However, individual gene-based signatures usually suffer from low reproducibility and interpretability.
Results
We have developed a novel algorithm Iterative Clique Enumeration (ICE) for identifying relatively independent maximal cliques as co-expression modules and a module-based approach to the analysis of gene expression data. Applying this approach on a public breast cancer dataset identified 19 modules whose expression levels were significantly correlated with tumor grade. The correlations were reproducible for 17 modules in an independent breast cancer dataset, and the reproducibility was considerably higher than that based on individual genes or modules identified by other algorithms. Sixteen out of the 17 modules showed significant enrichment in certain Gene Ontology (GO) categories. Specifically, modules related to cell proliferation and immune response were up-regulated in high-grade tumors while those related to cell adhesion was down-regulated. Further analyses showed that transcription factors NYFB, E2F1/E2F3, NRF1, and ELK1 were responsible for the up-regulation of the cell proliferation modules. IRF family and ETS family proteins were responsible for the up-regulation of the immune response modules. Moreover, inhibition of the PPARA signaling pathway may also play an important role in tumor progression. The module without GO enrichment was found to be associated with a potential genomic gain in 8q21-23 in high-grade tumors. The 17-module signature of breast tumor progression clustered patients into subgroups with significantly different relapse-free survival times. Namely, patients with lower cell proliferation and higher cell adhesion levels had significantly lower risk of recurrence, both for all patients (p = 0.004) and for those with grade 2 tumors (p = 0.017).
Conclusions
The ICE algorithm is effective in identifying relatively independent co-expression modules from gene co-expression networks and the module-based approach illustrated in this study provides a robust, interpretable, and mechanistic characterization of transcriptional changes. Nashville, TN 37240, USA.
@article{ShiDZ:2010,
author = {Shi, Zhiao and Derow, Catherine K. and Zhang, Bing},
title = {Co-expression module analysis reveals biological processes, genomic gain, and regulatory mechanisms associated with breast cancer progression.},
journal = {BMC Systems Biology},
volume = {4},
pages = {74},
year = {2010},
doi = {10.1186/1752-0509-4-74},
}Shellie R. Simons and Barbara Mawn. Bullying in the workplace—a qualitative study of newly licensed registered nurses. Aaohn Journal, 58(7):305—11, jul 2010.
Bullying in the workplace is associated with negative job satisfaction and retention. It has also been found to have adverse effects on the health of employees. Using a qualitative descriptive design, this study examined the stories of bullying among nurses based on actual or witnessed experiences. One hundred eighty-four newly licensed U.S. nurses responded to an open-ended question on a survey about bullying mailed to their homes. Four major themes emerged that related to varying types of bullying behaviors, perceived causes of bullying, and the impact of bullying behaviors. The themes included structural bullying; nurses "eating their young"; being out of the clique; and leaving the job. Bullying is experienced firsthand and secondhand by nurses, and particularly by vulnerable, newly graduated nurses. Workplace bullying must be explored fully to develop effective strategies to eliminate it. shellie_simons@uml.edu
@article{SimonsM:2010,
author = {Simons, Shellie R. and Mawn, Barbara},
title = {Bullying in the workplace--a qualitative study of newly licensed registered nurses.},
journal = {Aaohn Journal},
volume = {58},
number = {7},
pages = {305-11},
year = {2010},
month = jul,
doi = {10.3928/08910162-20100616-02},
}Jianxin Wang, Binbin Liu, Min Li, and Yi Pan. Identifying protein complexes from interaction networks based on clique percolation and distance restriction. BMC Genomics, 11(Suppl 2):S10, 2010.
Background
Identification of protein complexes in large interaction networks is crucial to understand principles of cellular organization and predict protein functions, which is one of the most important issues in the post-genomic era. Each protein might be subordinate multiple protein complexes in the real protein-protein interaction networks. Identifying overlapping protein complexes from protein-protein interaction networks is a considerable research topic.
Result
As an effective algorithm in identifying overlapping module structures, clique percolation method (CPM) has a wide range of application in social networks and biological networks. However, the recognition accuracy of algorithm CPM is lowly. Furthermore, algorithm CPM is unfit to identifying protein complexes with meso-scale when it applied in protein-protein interaction networks. In this paper, we propose a new topological model by extending the definition of k-clique community of algorithm CPM and introduced distance restriction, and develop a novel algorithm called CP-DR based on the new topological model for identifying protein complexes. In this new algorithm, the protein complex size is restricted by distance constraint to conquer the shortcomings of algorithm CPM. The algorithm CP-DR is applied to the protein interaction network of Sacchromyces cerevisiae and identifies many well known complexes.
Conclusion
The proposed algorithm CP-DR based on clique percolation and distance restriction makes it possible to identify dense subgraphs in protein interaction networks, a large number of which correspond to known protein complexes. Compared to algorithm CPM, algorithm CP-DR has more outstanding performance.
Identification of protein complexes in large interaction networks is crucial to understand principles of cellular organization and predict protein functions, which is one of the most important issues in the post-genomic era. Each protein might be subordinate multiple protein complexes in the real protein-protein interaction networks. Identifying overlapping protein complexes from protein-protein interaction networks is a considerable research topic.
Result
As an effective algorithm in identifying overlapping module structures, clique percolation method (CPM) has a wide range of application in social networks and biological networks. However, the recognition accuracy of algorithm CPM is lowly. Furthermore, algorithm CPM is unfit to identifying protein complexes with meso-scale when it applied in protein-protein interaction networks. In this paper, we propose a new topological model by extending the definition of k-clique community of algorithm CPM and introduced distance restriction, and develop a novel algorithm called CP-DR based on the new topological model for identifying protein complexes. In this new algorithm, the protein complex size is restricted by distance constraint to conquer the shortcomings of algorithm CPM. The algorithm CP-DR is applied to the protein interaction network of Sacchromyces cerevisiae and identifies many well known complexes.
Conclusion
The proposed algorithm CP-DR based on clique percolation and distance restriction makes it possible to identify dense subgraphs in protein interaction networks, a large number of which correspond to known protein complexes. Compared to algorithm CPM, algorithm CP-DR has more outstanding performance.
@article{WangLLP:2010,
author = {Wang, Jianxin and Liu, Binbin and Li, Min and Pan, Yi},
title = {Identifying protein complexes from interaction networks based on clique percolation and distance restriction},
journal = {BMC Genomics},
volume = {11},
number = {Suppl 2},
pages = {S10},
year = {2010},
doi = {10.1186/1471-2164-11-S2-S10},
}Miranda Witvliet, Mara Brendgen, Pol A. C van Lier, Hans M. Koot, and Frank Vitaro. Early adolescent depressive symptoms: prediction from clique isolation, loneliness, and perceived social acceptance. Journal of Abnormal Child Psychology, 38(8):1045—56, nov 2010.
This study examined whether clique isolation predicted an increase in depressive symptoms and whether this association was mediated by loneliness and perceived social acceptance in 310 children followed from age 11-14 years. Clique isolation was identified through social network analysis, whereas depressive symptoms, loneliness, and perceived social acceptance were assessed using self ratings. While accounting for initial levels of depressive symptoms, peer rejection, and friendlessness at age 11 years, a high probability of being isolated from cliques from age 11 to 13 years predicted depressive symptoms at age 14 years. The link between clique isolation and depressive symptoms was mediated by loneliness, but not by perceived social acceptance. No sex differences were found in the associations between clique isolation and depressive symptoms. These results suggest that clique isolation is a social risk factor for the escalation of depressive symptoms in early adolescence. Implications for research and prevention are discussed. Amsterdam, Amsterdam, the Netherlands.
@article{WitvlietBvKV:2010,
author = {Witvliet, Miranda and Brendgen, Mara and van Lier, Pol A. C and Koot, Hans M. and Vitaro, Frank},
title = {Early adolescent depressive symptoms: prediction from clique isolation, loneliness, and perceived social acceptance.},
journal = {Journal of Abnormal Child Psychology},
volume = {38},
number = {8},
pages = {1045-56},
year = {2010},
month = nov,
doi = {10.1007/s10802-010-9426-x},
}Miranda Witvliet, Pol A. C van Lier, Mara Brendgen, Hans M. Koot, and Frank Vitaro. Longitudinal associations between clique membership status and internalizing and externalizing problems during late childhood. Journal of Clinical Child and Adolescent Psychology, 39(5):693—704, 2010.
This study examined the longitudinal link between clique membership status and the development of psychopathology in 451 children followed annually from age 9 to 12 years. Classroom clique membership status was identified through social network analysis, and internalizing and externalizing problems were assessed using peer nominations. Controlling for concurrent experiences of social preference and dyadic friendships, a high clique membership probability was found to be related to low levels of internalizing problems and to an increase in externalizing problems across 4 years. This link between clique membership and an increase in externalizing problems was found for boys only.
@article{WitvlietvBKV:2010,
author = {Witvliet, Miranda and van Lier, Pol A. C and Brendgen, Mara and Koot, Hans M. and Vitaro, Frank},
title = {Longitudinal associations between clique membership status and internalizing and externalizing problems during late childhood.},
journal = {Journal of Clinical Child and Adolescent Psychology},
volume = {39},
number = {5},
pages = {693-704},
year = {2010},
doi = {10.1080/15374416.2010.501678},
}Miranda Witvliet, Pol A. C van Lier, Pim Cuijpers, and Hans M. Koot. Change and stability in childhood clique membership, isolation from cliques, and associated child characteristics. Journal of Clinical Child and Adolescent Psychology, 39(1):12—24, 2010.
This study explored the role of clique membership and clique isolation in children’s psychosocial adjustment. We identified change and stability in early elementary school clique membership and investigated behavioral characteristics related to this change and stability. Participants were first-grade pupils (N = 300), followed over a 1-year period. Clique membership was identified through social network analysis. Differences between children with a stable versus changing clique membership status were tested using peer nominations and teacher ratings. Clique members were better adjusted than nonclique members. Externalizing behavior, less prosocial behavior, and low social preference preceded clique estrangement. Stable-isolates increased in externalizing behavior, whereas children who became part of a dyad or included in a clique showed a decrease in externalizing behavior. Netherlands. m.witvliet@psy.vu.nl
@article{WitvlietvCK:2010,
author = {Witvliet, Miranda and van Lier, Pol A. C and Cuijpers, Pim and Koot, Hans M.},
title = {Change and stability in childhood clique membership, isolation from cliques, and associated child characteristics.},
journal = {Journal of Clinical Child and Adolescent Psychology},
volume = {39},
number = {1},
pages = {12-24},
year = {2010},
doi = {10.1080/15374410903401161},
}Yi Yang, Dong Xu, Feiping Nie, Shuicheng Yan, and Yueting Zhuang. Image clustering using local discriminant models and global integration. IEEE Transactions On Image Processing, 19(10):2761—73, oct 2010.
In this paper, we propose a new image clustering algorithm, referred to as clustering using local discriminant models and global integration (LDMGI). To deal with the data points sampled from a nonlinear manifold, for each data point, we construct a local clique comprising this data point and its neighboring data points. Inspired by the Fisher criterion, we use a local discriminant model for each local clique to evaluate the clustering performance of samples within the local clique. To obtain the clustering result, we further propose a unified objective function to globally integrate the local models of all the local cliques. With the unified objective function, spectral relaxation and spectral rotation are used to obtain the binary cluster indicator matrix for all the samples. We show that LDMGI shares a similar objective function with the spectral clustering (SC) algorithms, e.g., normalized cut (NCut). In contrast to NCut in which the Laplacian matrix is directly calculated based upon a Gaussian function, a new Laplacian matrix is learnt in LDMGI by exploiting both manifold structure and local discriminant information. We also prove that K-means and discriminative K-means (DisKmeans) are both special cases of LDMGI. Extensive experiments on several benchmark image datasets demonstrate the effectiveness of LDMGI. We observe in the experiments that LDMGI is more robust to algorithmic parameter, when compared with NCut. Thus, LDMGI is more appealing for the real image clustering applications in which the ground truth is generally not available for tuning algorithmic parameters. 310027, P R China.
@article{YangXNYZ:2010,
author = {Yang, Yi and Xu, Dong and Nie, Feiping and Yan, Shuicheng and Zhuang, Yueting},
title = {Image clustering using local discriminant models and global integration.},
journal = {IEEE Transactions On Image Processing},
volume = {19},
number = {10},
pages = {2761-73},
year = {2010},
month = oct,
doi = {10.1109/TIP.2010.2049235},
}Corin Yeats, Oliver C. Redfern, and Christine Orengo. A fast and automated solution for accurately resolving protein domain architectures. Bioinformatics, 26(6):745—51, mar 2010.
Motivation
Accurate prediction of the domain content and arrangement in multi-domain proteins (which make up >65% of the large-scale protein databases) provides a valuable tool for function prediction, comparative genomics and studies of molecular evolution. However, scanning a multi-domain protein against a database of domain sequence profiles can often produce conflicting and overlapping matches. We have developed a novel method that employs heaviest weighted clique-finding (HCF), which we show significantly outperforms standard published approaches based on successively assigning the best non-overlapping match (Best Match Cascade, BMC).
Results
We created benchmark data set of structural domain assignments in the CATH database and a corresponding set of Hidden Markov Model-based domain predictions. Using these, we demonstrate that by considering all possible combinations of matches using the HCF approach, we achieve much higher prediction accuracy than the standard BMC method. We also show that it is essential to allow overlapping domain matches to a query in order to identify correct domain assignments. Furthermore, we introduce a straightforward and effective protocol for resolving any overlapping assignments, and producing a single set of non-overlapping predicted domains. AVAILABILITY AND IMPLEMENTATION: The new approach will be used to determine MDAs for UniProt and Ensembl, and made available via the Gene3D website: http://gene3d.biochem.ucl.ac.uk/Gene3D/. The software has been implemented in C++ and compiled for Linux: source code and binaries can be found at: ftp://ftp.biochem.ucl.ac.uk/pub/gene3d_data/DomainFinder3/
Contact
yeats@biochem.ucl.ac.uk SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online. yeats@biochem.ucl.ac.uk
Accurate prediction of the domain content and arrangement in multi-domain proteins (which make up >65% of the large-scale protein databases) provides a valuable tool for function prediction, comparative genomics and studies of molecular evolution. However, scanning a multi-domain protein against a database of domain sequence profiles can often produce conflicting and overlapping matches. We have developed a novel method that employs heaviest weighted clique-finding (HCF), which we show significantly outperforms standard published approaches based on successively assigning the best non-overlapping match (Best Match Cascade, BMC).
Results
We created benchmark data set of structural domain assignments in the CATH database and a corresponding set of Hidden Markov Model-based domain predictions. Using these, we demonstrate that by considering all possible combinations of matches using the HCF approach, we achieve much higher prediction accuracy than the standard BMC method. We also show that it is essential to allow overlapping domain matches to a query in order to identify correct domain assignments. Furthermore, we introduce a straightforward and effective protocol for resolving any overlapping assignments, and producing a single set of non-overlapping predicted domains. AVAILABILITY AND IMPLEMENTATION: The new approach will be used to determine MDAs for UniProt and Ensembl, and made available via the Gene3D website: http://gene3d.biochem.ucl.ac.uk/Gene3D/. The software has been implemented in C++ and compiled for Linux: source code and binaries can be found at: ftp://ftp.biochem.ucl.ac.uk/pub/gene3d_data/DomainFinder3/
Contact
yeats@biochem.ucl.ac.uk SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online. yeats@biochem.ucl.ac.uk
@article{YeatsRO:2010,
author = {Yeats, Corin and Redfern, Oliver C. and Orengo, Christine},
title = {A fast and automated solution for accurately resolving protein domain architectures.},
journal = {Bioinformatics},
volume = {26},
number = {6},
pages = {745-51},
year = {2010},
month = mar,
doi = {10.1093/bioinformatics/btq034},
}Kun Zhao, Shao-Wu Zhang, and Quan Pan. Fuzzy analysis for overlapping community structure of complex network. In Control and Decision Conference (CCDC), 2010 Chinese, pages 3976—3981. IEEE Computer Society, 2010.
We consider the problem of fuzzy community detection in networks, which complements the concept of overlapping community structure. Using the optimization method to approximate network feature matrix is an important approach for conventional fuzzy community detection. In order to retain valuable physical meaning of the approximation, we discard redundant constraints in the process of approximation which is accordingly reduced to a problem of symmetrical non-negative matrix factorization (s-NMF). The resulting fuzzy metric, which is termed clique-node similarity degree (CNSD), is able to grasp very subtle topology information of the node’s neighborhood. Based on the CNSD, we introduce a new measure that is able to identify the key nodes that are critical to the connection of the adjacent communities. The technique is able to discover the fuzzy community structure of different real world networks with high confidence.
@inproceedings{ZhaoZP:2011,
author = {Kun Zhao and Shao-Wu Zhang and Quan Pan},
title = {Fuzzy analysis for overlapping community structure of complex network},
booktitle = {Control and Decision Conference (CCDC), 2010 Chinese},
pages = {3976--3981},
publisher = {IEEE Computer Society},
year = {2010},
doi = {10.1109/CCDC.2010.5498458},
}David Barber. Identifying graph clusters using variational inference and links to covariance parametrization. Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences, 367(1906):4407—26, nov 2009.
Finding clusters of well-connected nodes in a graph is a problem common to many domains, including social networks, the Internet and bioinformatics. From a computational viewpoint, finding these clusters or graph communities is a difficult problem. We use a clique matrix decomposition based on a statistical description that encourages clusters to be well connected and few in number. The formal intractability of inferring the clusters is addressed using a variational approximation inspired by mean-field theories in statistical mechanics. Clique matrices also play a natural role in parametrizing positive definite matrices under zero constraints on elements of the matrix. We show that clique matrices can parametrize all positive definite matrices restricted according to a decomposable graph and form a structured factor analysis approximation in the non-decomposable case. Extensions to conjugate Bayesian covariance priors and more general non-Gaussian independence models are briefly discussed. d.barber@cs.ucl.ac.uk
@article{Barber:2009,
author = {Barber, David},
title = {Identifying graph clusters using variational inference and links to covariance parametrization.},
journal = {Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences},
volume = {367},
number = {1906},
pages = {4407-26},
year = {2009},
month = nov,
doi = {10.1098/rsta.2009.0117},
}Tiberio S. Caetano and Julian J. McAuley. Faster graphical models for point-pattern matching. Spatial Vision, 22(5):443—53, 2009.
It has been shown that isometric matching problems can be solved exactly in polynomial time, by means of a Junction Tree with small maximal clique size. Recently, an iterative algorithm was presented which converges to the same solution an order of magnitude faster. Here, we build on both of these ideas to produce an algorithm with the same asymptotic running time as the iterative solution, but which requires only a single iteration of belief propagation. Thus our algorithm is much faster in practice, while maintaining similar error rates. Information Sciences and Engineering, ANU, Canberra, Australia.
@article{CaetanoM:2009,
author = {Caetano, Tiberio S. and McAuley, Julian J.},
title = {Faster graphical models for point-pattern matching.},
journal = {Spatial Vision},
volume = {22},
number = {5},
pages = {443-53},
year = {2009},
doi = {10.1163/156856809789476083},
}Jiun-Rung Chen and Ye-In Chang. A condition-enumeration tree method for mining biclusters from dna microarray data sets. Bio Systems, 97(1):44—59, jul 2009.
Biclustering, which performs simultaneous clustering of rows (e.g., genes) and columns (e.g., conditions), has proved of great value for finding interesting patterns from microarray data. To find biclusters, a model called pCluster was proposed. A pCluster consists of a set of genes and a set of conditions, where the expression levels of these genes have a similar variation under these conditions. Based on this model, most of the previous methods need to compute MDSs (maximum dimension sets) for every two genes in the microarray data. Since the number of genes is far larger than the number of conditions, this step is inefficient. Another method called MicroCluster was proposed. This method does not compute MDSs for every two genes, and transforms the problem into a graph problem. However, it needs to solve the Maximal Clique problem, which is NP-Complete. To avoid the above disadvantages, in this paper, we propose a new method, CE-Tree (Condition-Enumeration Tree), for finding pClusters. Instead of generating MDSs for every two genes, we generate only MDSs for every two conditions. Then, based only on these MDSs, we expand the CE-Tree in a special local breadth-first within global depth-first manner to efficiently find all pClusters. We also utilize the idea of the traditional hash join approach to efficiently support the CE-Tree. From the simulation results, we show that the CE-Tree method could find pClusters more efficiently than those previous methods. 70, Lienhai Rd., Kaohsiung 80424, Taiwan, ROC. jiunrung@gmail.com
@article{ChenC:2009,
author = {Chen, Jiun-Rung and Chang, Ye-In},
title = {A Condition-Enumeration Tree method for mining biclusters from DNA microarray data sets.},
journal = {Bio Systems},
volume = {97},
number = {1},
pages = {44-59},
year = {2009},
month = jul,
doi = {10.1016/j.biosystems.2009.04.003},
}Majid Darehmiraki. A new solution for maximal clique problem based sticker model. Bio Systems, 95(2):145—9, feb 2009.
In this paper, we use stickers to construct a solution space of DNA for the maximal clique problem (MCP). Simultaneously, we also apply the DNA operation in the sticker-based model to develop a DNA algorithm. The results of the proposed algorithm show that the MCP is resolved with biological operations in the sticker-based model for the solution space of the sticker. Moreover, this work presents clear evidence of the ability of DNA computing to solve the NP-complete problem. The potential of DNA computing for the MCP is promising given the operational time complexity of O(nxk). Birjand, South Khorasan, Iran. darehmiraki@yahoo.com
@article{Darehmiraki:2009,
author = {Darehmiraki, Majid},
title = {A new solution for maximal clique problem based sticker model.},
journal = {Bio Systems},
volume = {95},
number = {2},
pages = {145-9},
year = {2009},
month = feb,
doi = {10.1016/j.biosystems.2008.09.007},
}Dhruba Deb, Saraswathi Vishveshwara, and Smitha Vishveshwara. Understanding protein structure from a percolation perspective. Biophysical Journal, 97(6):1787—94, sep 2009.
Underlying the unique structures and diverse functions of proteins are a vast range of amino-acid sequences and a highly limited number of folds taken up by the polypeptide backbone. By investigating the role of noncovalent connections at the backbone level and at the detailed side-chain level, we show that these unique structures emerge from interplay between random and selected features. Primarily, the protein structure network formed by these connections shows simple (bond) and higher order (clique) percolation behavior distinctly reminiscent of random network models. However, the clique percolation specific to the side-chain interaction network bears signatures unique to proteins characterized by a larger degree of connectivity than in random networks. These studies reflect some salient features of the manner in which amino acid sequences select the unique structure of proteins from the pool of a limited number of available folds.
@article{DebVV:2009,
author = {Deb, Dhruba and Vishveshwara, Saraswathi and Vishveshwara, Smitha},
title = {Understanding protein structure from a percolation perspective.},
journal = {Biophysical Journal},
volume = {97},
number = {6},
pages = {1787-94},
year = {2009},
month = sep,
doi = {10.1016/j.bpj.2009.07.016},
}Sarosh N. Fatakia, Stefano Costanzi, and Carson C. Chow. Computing highly correlated positions using mutual information and graph theory for g protein-coupled receptors. Plos One, 4(3):e4681, 2009.
G protein-coupled receptors (GPCRs) are a superfamily of seven transmembrane-spanning proteins involved in a wide array of physiological functions and are the most common targets of pharmaceuticals. This study aims to identify a cohort or clique of positions that share high mutual information. Using a multiple sequence alignment of the transmembrane (TM) domains, we calculated the mutual information between all inter-TM pairs of aligned positions and ranked the pairs by mutual information. A mutual information graph was constructed with vertices that corresponded to TM positions and edges between vertices were drawn if the mutual information exceeded a threshold of statistical significance. Positions with high degree (i.e. had significant mutual information with a large number of other positions) were found to line a well defined inter-TM ligand binding cavity for class A as well as class C GPCRs. Although the natural ligands of class C receptors bind to their extracellular N-terminal domains, the possibility of modulating their activity through ligands that bind to their helical bundle has been reported. Such positions were not found for class B GPCRs, in agreement with the observation that there are not known ligands that bind within their TM helical bundle. All identified key positions formed a clique within the MI graph of interest. For a subset of class A receptors we also considered the alignment of a portion of the second extracellular loop, and found that the two positions adjacent to the conserved Cys that bridges the loop with the TM3 qualified as key positions. Our algorithm may be useful for localizing topologically conserved regions in other protein families. and Kidney Diseases, National Institutes of Health, Bethesda, Maryland, USA.
@article{FatakiaCC:2009,
author = {Fatakia, Sarosh N. and Costanzi, Stefano and Chow, Carson C.},
title = {Computing highly correlated positions using mutual information and graph theory for G protein-coupled receptors.},
journal = {Plos One},
volume = {4},
number = {3},
pages = {e4681},
year = {2009},
doi = {10.1371/journal.pone.0004681},
}Eleanor J. Gardiner, David A. Cosgrove, Robin Taylor, and Valerie J. Gillet. Multiobjective optimization of pharmacophore hypotheses: bias toward low-energy conformations. Journal of Chemical Information and Modeling, 49(12):2761—73, dec 2009.
Two methods are described for biasing conformational search during pharmacophore elucidation using a multiobjective genetic algorithm (MOGA). The MOGA explores conformation on-the-fly while simultaneously aligning a set of molecules such that their pharmacophoric features are maximally overlaid. By using a clique detection method to generate overlays of precomputed conformations to initialize the population (rather than starting from random), the speed of the algorithm has been increased by 2 orders of magnitude. This increase in speed has enabled the program to be applied to greater numbers of molecules than was previously possible. Furthermore, it was found that biasing the conformations explored during search time to those found in the Cambridge Structural Database could also improve the quality of the results. Portobello Street, Sheffield S1 4DP, United Kingdom. e.gardiner@sheffield.ac.uk
@article{GardinerCTG:2009,
author = {Gardiner, Eleanor J. and Cosgrove, David A. and Taylor, Robin and Gillet, Valerie J.},
title = {Multiobjective optimization of pharmacophore hypotheses: bias toward low-energy conformations.},
journal = {Journal of Chemical Information and Modeling},
volume = {49},
number = {12},
pages = {2761-73},
year = {2009},
month = dec,
doi = {10.1021/ci9002816},
}Thomas T. Hills, Mounir Maouene, Josita Maouene, Adam Sheya, and Linda Smith. Categorical structure among shared features in networks of early-learned nouns. Cognition, 112(3):381—96, sep 2009.
The shared features that characterize the noun categories that young children learn first are a formative basis of the human category system. To investigate the potential categorical information contained in the features of early-learned nouns, we examine the graph-theoretic properties of noun-feature networks. The networks are built from the overlap of words normatively acquired by children prior to 2(1/2) years of age and perceptual and conceptual (functional) features acquired from adult feature generation norms. The resulting networks have small-world structure, indicative of a high degree of feature overlap in local clusters. However, perceptual features—due to their abundance and redundancy—generate networks more robust to feature omissions, while conceptual features are more discriminating and, per feature, offer more categorical information than perceptual features. Using a network specific cluster identification algorithm (the clique percolation method) we also show that shared features among these early-learned nouns create higher-order groupings common to adult taxonomic designations. Again, perceptual and conceptual features play distinct roles among different categories, typically with perceptual features being more inclusive and conceptual features being more exclusive of category memberships. The results offer new and testable hypotheses about the role of shared features in human category knowledge. thomas.hills@unibas.ch
@article{HillsMMSS:2009,
author = {Hills, Thomas T. and Maouene, Mounir and Maouene, Josita and Sheya, Adam and Smith, Linda},
title = {Categorical structure among shared features in networks of early-learned nouns.},
journal = {Cognition},
volume = {112},
number = {3},
pages = {381-96},
year = {2009},
month = sep,
doi = {10.1016/j.cognition.2009.06.002},
}Pushmeet Kohli, M. Pawan Kumar, and Philip H. S. Torr. P3 & beyond: move making algorithms for solving higher order functions. IEEE Transactions On Pattern Analysis and Machine Intelligence, 31(9):1645—56, sep 2009.
In this paper, we extend the class of energy functions for which the optimal \alpha-expansion and \alpha \beta-swap moves can be computed in polynomial time. Specifically, we introduce a novel family of higher order clique potentials, and show that the expansion and swap moves for any energy function composed of these potentials can be found by minimizing a submodular function. We also show that for a subset of these potentials, the optimal move can be found by solving an st-mincut problem. We refer to this subset as the {\cal P};n Potts model. Our results enable the use of powerful \alpha-expansion and \alpha \beta-swap move making algorithms for minimization of energy functions involving higher order cliques. Such functions have the capability of modeling the rich statistics of natural scenes and can be used for many applications in Computer Vision. We demonstrate their use in one such application, i.e., the texture-based image or video-segmentation problem.
@article{KohliPT:2009,
author = {Kohli, Pushmeet and Pawan Kumar, M. and Torr, Philip H. S.},
title = {P3 & beyond: move making algorithms for solving higher order functions.},
journal = {IEEE Transactions On Pattern Analysis and Machine Intelligence},
volume = {31},
number = {9},
pages = {1645-56},
year = {2009},
month = sep,
doi = {10.1109/TPAMI.2008.217},
}Jing Li, Lisa J. Zimmerman, Byung-Hoon Park, David L. Tabb, Daniel C. Liebler, and Bing Zhang. Network-assisted protein identification and data interpretation in shotgun proteomics. Molecular Systems Biology, 5:303, 2009.
Protein assembly and biological interpretation of the assembled protein lists are critical steps in shotgun proteomics data analysis. Although most biological functions arise from interactions among proteins, current protein assembly pipelines treat proteins as independent entities. Usually, only individual proteins with strong experimental evidence, that is, confident proteins, are reported, whereas many possible proteins of biological interest are eliminated. We have developed a clique-enrichment approach (CEA) to rescue eliminated proteins by incorporating the relationship among proteins as embedded in a protein interaction network. In several data sets tested, CEA increased protein identification by 8-23% with an estimated accuracy of 85%. Rescued proteins were supported by existing literature or transcriptome profiling studies at similar levels as confident proteins and at a significantly higher level than abandoned ones. Applying CEA on a breast cancer data set, rescued proteins coded by well-known breast cancer genes. In addition, CEA generated a network view of the proteins and helped show the modular organization of proteins that may underpin the molecular mechanisms of the disease. Nashville, TN 37232-8340, USA.
@article{LiZPTLZ:2009,
author = {Li, Jing and Zimmerman, Lisa J. and Park, Byung-Hoon and Tabb, David L. and Liebler, Daniel C. and Zhang, Bing},
title = {Network-assisted protein identification and data interpretation in shotgun proteomics.},
journal = {Molecular Systems Biology},
volume = {5},
pages = {303},
year = {2009},
doi = {10.1038/msb.2009.54},
}Chen-Ching Lin, Hsueh-Fen Juan, Jen-Tsung Hsiang, Yih-Chii Hwang, Hirotada Mori, and Hsuan-Cheng Huang. Essential core of protein-protein interaction network in escherichia coli. Journal of Proteome Research, 8(4):1925—31, apr 2009.
Essential genes are responsible for the viability of an organism. Global protein interaction network analysis provides an effective way to understand the relationships between protein products of genes. By means of large-scale identification of essential genes and protein-protein interactions, we investigated the substructure of the protein interaction network in Escherichia coli and identified all the cliques in the network. Our analysis showed that larger cliques tend to have larger fractions of proteins encoded by essential genes. By merging the maximum clique with overlapping neighboring cliques, we observed a dense core of the protein interaction network in Escherichia coliwith significantly higher ratio of essential genes. The protein network of Saccharomyces cerevisiae also shows strong correlation between clique and essentiality, and there exist similar dense clusters with high essentiality. Our results indicated that the observed structure of essential cores might exist in higher organisms and play important roles in their respective protein networks. National Yang-Ming University, Taipei 112, Taiwan.
@article{LinJHHMH:2009,
author = {Lin, Chen-Ching and Juan, Hsueh-Fen and Hsiang, Jen-Tsung and Hwang, Yih-Chii and Mori, Hirotada and Huang, Hsuan-Cheng},
title = {Essential core of protein-protein interaction network in Escherichia coli.},
journal = {Journal of Proteome Research},
volume = {8},
number = {4},
pages = {1925-31},
year = {2009},
month = apr,
doi = {10.1021/pr8008786},
}Ville-Petteri Makinen, Carol Forsblom, Lena M. Thorn, Johan Waden, Kimmo Kaski, Mika Ala-Korpela, and Per-Henrik Groop. Network of vascular diseases, death and biochemical characteristics in a set of 4,197 patients with type 1 diabetes (the finndiane study). Cardiovascular Diabetology, 8:54, 2009.
Background
Cardiovascular disease is the main cause of premature death in patients with type 1 diabetes. Patients with diabetic kidney disease have an increased risk of heart attack or stroke. Accurate knowledge of the complex inter-dependencies between the risk factors is critical for pinpointing the best targets for research and treatment. Therefore, the aim of this study was to describe the association patterns between clinical and biochemical features of diabetic complications.
Methods
Medical records and serum and urine samples of 4,197 patients with type 1 diabetes were collected from health care centers in Finland. At baseline, the mean diabetes duration was 22 years, 52% were male, 23% had kidney disease (urine albumin excretion over 300 mg/24 h or end-stage renal disease) and 8% had a history of macrovascular events. All-cause mortality was evaluated after an average of 6.5 years of follow-up (25,714 patient years). The dataset comprised 28 clinical and 25 biochemical variables that were regarded as the nodes of a network to assess their mutual relationships.
Results
The networks contained cliques that were densely inter-connected (r > 0.6), including cliques for high-density lipoprotein (HDL) markers, for triglycerides and cholesterol, for urinary excretion and for indices of body mass. The links between the cliques showed biologically relevant interactions: an inverse relationship between HDL cholesterol and the triglyceride clique (r < -0.3, P < 10(-16)), a connection between triglycerides and body mass via C-reactive protein (r > 0.3, P < 10(-16)) and intermediate-density cholesterol as the connector between lipoprotein metabolism and albuminuria (r > 0.3, P < 10(-16)). Aging and macrovascular disease were linked to death via working ability and retinopathy. Diabetic kidney disease, serum creatinine and potassium, retinopathy and blood pressure were inter-connected. Blood pressure correlations indicated accelerated vascular aging in individuals with kidney disease (P < 0.001).
Conclusion
The complex pattern of links between diverse characteristics and the lack of a single dominant factor suggests a need for multifactorial and multidisciplinary paradigms for the research, treatment and prevention of diabetic complications. Helsinki, Finland. ville-petteri.makinen@finndiane.fi
Cardiovascular disease is the main cause of premature death in patients with type 1 diabetes. Patients with diabetic kidney disease have an increased risk of heart attack or stroke. Accurate knowledge of the complex inter-dependencies between the risk factors is critical for pinpointing the best targets for research and treatment. Therefore, the aim of this study was to describe the association patterns between clinical and biochemical features of diabetic complications.
Methods
Medical records and serum and urine samples of 4,197 patients with type 1 diabetes were collected from health care centers in Finland. At baseline, the mean diabetes duration was 22 years, 52% were male, 23% had kidney disease (urine albumin excretion over 300 mg/24 h or end-stage renal disease) and 8% had a history of macrovascular events. All-cause mortality was evaluated after an average of 6.5 years of follow-up (25,714 patient years). The dataset comprised 28 clinical and 25 biochemical variables that were regarded as the nodes of a network to assess their mutual relationships.
Results
The networks contained cliques that were densely inter-connected (r > 0.6), including cliques for high-density lipoprotein (HDL) markers, for triglycerides and cholesterol, for urinary excretion and for indices of body mass. The links between the cliques showed biologically relevant interactions: an inverse relationship between HDL cholesterol and the triglyceride clique (r < -0.3, P < 10(-16)), a connection between triglycerides and body mass via C-reactive protein (r > 0.3, P < 10(-16)) and intermediate-density cholesterol as the connector between lipoprotein metabolism and albuminuria (r > 0.3, P < 10(-16)). Aging and macrovascular disease were linked to death via working ability and retinopathy. Diabetic kidney disease, serum creatinine and potassium, retinopathy and blood pressure were inter-connected. Blood pressure correlations indicated accelerated vascular aging in individuals with kidney disease (P < 0.001).
Conclusion
The complex pattern of links between diverse characteristics and the lack of a single dominant factor suggests a need for multifactorial and multidisciplinary paradigms for the research, treatment and prevention of diabetic complications. Helsinki, Finland. ville-petteri.makinen@finndiane.fi
@article{MakinenFTWKAG:2009,
author = {Makinen, Ville-Petteri and Forsblom, Carol and Thorn, Lena M. and Waden, Johan and Kaski, Kimmo and Ala-Korpela, Mika and Groop, Per-Henrik},
title = {Network of vascular diseases, death and biochemical characteristics in a set of 4,197 patients with type 1 diabetes (the FinnDiane Study).},
journal = {Cardiovascular Diabetology},
volume = {8},
pages = {54},
year = {2009},
doi = {10.1186/1475-2840-8-54},
}Linyong Mao, John L. Van Hemert, Sudhansu Dash, and Julie A. Dickerson. Arabidopsis gene co-expression network and its functional modules. BMC Bioinformatics, 10:346, 2009.
Background
Biological networks characterize the interactions of biomolecules at a systems-level. One important property of biological networks is the modular structure, in which nodes are densely connected with each other, but between which there are only sparse connections. In this report, we attempted to find the relationship between the network topology and formation of modular structure by comparing gene co-expression networks with random networks. The organization of gene functional modules was also investigated.
Results
We constructed a genome-wide Arabidopsis gene co-expression network (AGCN) by using 1094 microarrays. We then analyzed the topological properties of AGCN and partitioned the network into modules by using an efficient graph clustering algorithm. In the AGCN, 382 hub genes formed a clique, and they were densely connected only to a small subset of the network. At the module level, the network clustering results provide a systems-level understanding of the gene modules that coordinate multiple biological processes to carry out specific biological functions. For instance, the photosynthesis module in AGCN involves a very large number (> 1000) of genes which participate in various biological processes including photosynthesis, electron transport, pigment metabolism, chloroplast organization and biogenesis, cofactor metabolism, protein biosynthesis, and vitamin metabolism. The cell cycle module orchestrated the coordinated expression of hundreds of genes involved in cell cycle, DNA metabolism, and cytoskeleton organization and biogenesis. We also compared the AGCN constructed in this study with a graphical Gaussian model (GGM) based Arabidopsis gene network. The photosynthesis, protein biosynthesis, and cell cycle modules identified from the GGM network had much smaller module sizes compared with the modules found in the AGCN, respectively.
Conclusion
This study reveals new insight into the topological properties of biological networks. The preferential hub-hub connections might be necessary for the formation of modular structure in gene co-expression networks. The study also reveals new insight into the organization of gene functional modules. linyongmao@gmail.com
Biological networks characterize the interactions of biomolecules at a systems-level. One important property of biological networks is the modular structure, in which nodes are densely connected with each other, but between which there are only sparse connections. In this report, we attempted to find the relationship between the network topology and formation of modular structure by comparing gene co-expression networks with random networks. The organization of gene functional modules was also investigated.
Results
We constructed a genome-wide Arabidopsis gene co-expression network (AGCN) by using 1094 microarrays. We then analyzed the topological properties of AGCN and partitioned the network into modules by using an efficient graph clustering algorithm. In the AGCN, 382 hub genes formed a clique, and they were densely connected only to a small subset of the network. At the module level, the network clustering results provide a systems-level understanding of the gene modules that coordinate multiple biological processes to carry out specific biological functions. For instance, the photosynthesis module in AGCN involves a very large number (> 1000) of genes which participate in various biological processes including photosynthesis, electron transport, pigment metabolism, chloroplast organization and biogenesis, cofactor metabolism, protein biosynthesis, and vitamin metabolism. The cell cycle module orchestrated the coordinated expression of hundreds of genes involved in cell cycle, DNA metabolism, and cytoskeleton organization and biogenesis. We also compared the AGCN constructed in this study with a graphical Gaussian model (GGM) based Arabidopsis gene network. The photosynthesis, protein biosynthesis, and cell cycle modules identified from the GGM network had much smaller module sizes compared with the modules found in the AGCN, respectively.
Conclusion
This study reveals new insight into the topological properties of biological networks. The preferential hub-hub connections might be necessary for the formation of modular structure in gene co-expression networks. The study also reveals new insight into the organization of gene functional modules. linyongmao@gmail.com
@article{MaoVDD:2009,
author = {Mao, Linyong and Van Hemert, John L. and Dash, Sudhansu and Dickerson, Julie A.},
title = {Arabidopsis gene co-expression network and its functional modules.},
journal = {BMC Bioinformatics},
volume = {10},
pages = {346},
year = {2009},
doi = {10.1186/1471-2105-10-346},
}Tsutomu Matsunaga, Chikara Yonemori, Etsuji Tomita, and Masaaki Muramatsu. Clique-based data mining for related genes in a biomedical database. BMC Bioinformatics, 10:205, 2009.
Background
Progress in the life sciences cannot be made without integrating biomedical knowledge on numerous genes in order to help formulate hypotheses on the genetic mechanisms behind various biological phenomena, including diseases. There is thus a strong need for a way to automatically and comprehensively search from biomedical databases for related genes, such as genes in the same families and genes encoding components of the same pathways. Here we address the extraction of related genes by searching for densely-connected subgraphs, which are modeled as cliques, in a biomedical relational graph.
Results
We constructed a graph whose nodes were gene or disease pages, and edges were the hyperlink connections between those pages in the Online Mendelian Inheritance in Man (OMIM) database. We obtained over 20,000 sets of related genes (called ’gene modules’) by enumerating cliques computationally. The modules included genes in the same family, genes for proteins that form a complex, and genes for components of the same signaling pathway. The results of experiments using ’metabolic syndrome’-related gene modules show that the gene modules can be used to get a coherent holistic picture helpful for interpreting relations among genes.
Conclusion
We presented a data mining approach extracting related genes by enumerating cliques. The extracted gene sets provide a holistic picture useful for comprehending complex disease mechanisms. Japan. matsunagat@nttdata.co.jp
Progress in the life sciences cannot be made without integrating biomedical knowledge on numerous genes in order to help formulate hypotheses on the genetic mechanisms behind various biological phenomena, including diseases. There is thus a strong need for a way to automatically and comprehensively search from biomedical databases for related genes, such as genes in the same families and genes encoding components of the same pathways. Here we address the extraction of related genes by searching for densely-connected subgraphs, which are modeled as cliques, in a biomedical relational graph.
Results
We constructed a graph whose nodes were gene or disease pages, and edges were the hyperlink connections between those pages in the Online Mendelian Inheritance in Man (OMIM) database. We obtained over 20,000 sets of related genes (called ’gene modules’) by enumerating cliques computationally. The modules included genes in the same family, genes for proteins that form a complex, and genes for components of the same signaling pathway. The results of experiments using ’metabolic syndrome’-related gene modules show that the gene modules can be used to get a coherent holistic picture helpful for interpreting relations among genes.
Conclusion
We presented a data mining approach extracting related genes by enumerating cliques. The extracted gene sets provide a holistic picture useful for comprehending complex disease mechanisms. Japan. matsunagat@nttdata.co.jp
@article{MatsunagaYTM:2009,
author = {Matsunaga, Tsutomu and Yonemori, Chikara and Tomita, Etsuji and Muramatsu, Masaaki},
title = {Clique-based data mining for related genes in a biomedical database.},
journal = {BMC Bioinformatics},
volume = {10},
pages = {205},
year = {2009},
doi = {10.1186/1471-2105-10-205},
}Richard A. Mushlin, Stephen Gallagher, Aaron Kershenbaum, and Timothy R. Rebbeck. Clique-finding for heterogeneity and multidimensionality in biomarker epidemiology research: the chamber algorithm. Plos One, 4(3):e4862, 2009.
Background
Commonly-occurring disease etiology may involve complex combinations of genes and exposures resulting in etiologic heterogeneity. We present a computational algorithm that employs clique-finding for heterogeneity and multidimensionality in biomedical and epidemiological research (the "CHAMBER" algorithm). METHODOLOGY/PRINCIPAL FINDINGS: This algorithm uses graph-building to (1) identify genetic variants that influence disease risk and (2) predict individuals at risk for disease based on inherited genotype. We use a set-covering algorithm to identify optimal cliques and a Boolean function that identifies etiologically heterogeneous groups of individuals. We evaluated this approach using simulated case-control genotype-disease associations involving two- and four-gene patterns. The CHAMBER algorithm correctly identified these simulated etiologies. We also used two population-based case-control studies of breast and endometrial cancer in African American and Caucasian women considering data on genotypes involved in steroid hormone metabolism. We identified novel patterns in both cancer sites that involved genes that sulfate or glucuronidate estrogens or catecholestrogens. These associations were consistent with the hypothesized biological functions of these genes. We also identified cliques representing the joint effect of multiple candidate genes in all groups, suggesting the existence of biologically plausible combinations of hormone metabolism genes in both breast and endometrial cancer in both races.
Conclusions
The CHAMBER algorithm may have utility in exploring the multifactorial etiology and etiologic heterogeneity in complex disease.
Commonly-occurring disease etiology may involve complex combinations of genes and exposures resulting in etiologic heterogeneity. We present a computational algorithm that employs clique-finding for heterogeneity and multidimensionality in biomedical and epidemiological research (the "CHAMBER" algorithm). METHODOLOGY/PRINCIPAL FINDINGS: This algorithm uses graph-building to (1) identify genetic variants that influence disease risk and (2) predict individuals at risk for disease based on inherited genotype. We use a set-covering algorithm to identify optimal cliques and a Boolean function that identifies etiologically heterogeneous groups of individuals. We evaluated this approach using simulated case-control genotype-disease associations involving two- and four-gene patterns. The CHAMBER algorithm correctly identified these simulated etiologies. We also used two population-based case-control studies of breast and endometrial cancer in African American and Caucasian women considering data on genotypes involved in steroid hormone metabolism. We identified novel patterns in both cancer sites that involved genes that sulfate or glucuronidate estrogens or catecholestrogens. These associations were consistent with the hypothesized biological functions of these genes. We also identified cliques representing the joint effect of multiple candidate genes in all groups, suggesting the existence of biologically plausible combinations of hormone metabolism genes in both breast and endometrial cancer in both races.
Conclusions
The CHAMBER algorithm may have utility in exploring the multifactorial etiology and etiologic heterogeneity in complex disease.
@article{MushlinGKR:2009,
author = {Mushlin, Richard A. and Gallagher, Stephen and Kershenbaum, Aaron and Rebbeck, Timothy R.},
title = {Clique-finding for heterogeneity and multidimensionality in biomarker epidemiology research: the CHAMBER algorithm.},
journal = {Plos One},
volume = {4},
number = {3},
pages = {e4862},
year = {2009},
doi = {10.1371/journal.pone.0004862},
}Georgios A. Pavlopoulos, Charalampos N. Moschopoulos, Sean D. Hooper, Reinhard Schneider, and Sophia Kossida. jclust: a clustering and visualization toolbox. Bioinformatics, 25(15):1994—6, aug 2009.
jClust is a user-friendly application which provides access to a set of widely used clustering and clique finding algorithms. The toolbox allows a range of filtering procedures to be applied and is combined with an advanced implementation of the Medusa interactive visualization module. These implemented algorithms are k-Means, Affinity propagation, Bron-Kerbosch, MULIC, Restricted neighborhood search cluster algorithm, Markov clustering and Spectral clustering, while the supported filtering procedures are haircut, outside-inside, best neighbors and density control operations. The combination of a simple input file format, a set of clustering and filtering algorithms linked together with the visualization tool provides a powerful tool for data analysis and information extraction.
Availability
http://jclust.embl.de/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online. Germany. pavlopou@embl.de
Availability
http://jclust.embl.de/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online. Germany. pavlopou@embl.de
@article{PavlopoulosMHSK:2009,
author = {Pavlopoulos, Georgios A. and Moschopoulos, Charalampos N. and Hooper, Sean D. and Schneider, Reinhard and Kossida, Sophia},
title = {jClust: a clustering and visualization toolbox.},
journal = {Bioinformatics},
volume = {25},
number = {15},
pages = {1994-6},
year = {2009},
month = aug,
doi = {10.1093/bioinformatics/btp330},
}Yevgeniy Podolyan and George Karypis. Common pharmacophore identification using frequent clique detection algorithm. Journal of Chemical Information and Modeling, 49(1):13—21, jan 2009.
The knowledge of a pharmacophore, or the 3D arrangement of features in the biologically active molecule that is responsible for its pharmacological activity, can help in the search and design of a new or better drug acting upon the same or related target. In this paper, we describe two new algorithms based on the frequent clique detection in the molecular graphs. The first algorithm mines all frequent cliques that are present in at least one of the conformers of each (or a portion of all) molecules. The second algorithm exploits the similarities among the different conformers of the same molecule and achieves an order of magnitude performance speedup compared to the first algorithm. Both algorithms are guaranteed to find all common pharmacophores in the data set, which is confirmed by the validation on the set of molecules for which pharmacophores have been determined experimentally. In addition, these algorithms are able to scale to data sets with arbitrarily large number of conformers per molecule and identify multiple ligand binding modes or multiple binding sites of the target. Minneapolis, Minnesota 55455, USA.
@article{PodolyanK:2009,
author = {Podolyan, Yevgeniy and Karypis, George},
title = {Common pharmacophore identification using frequent clique detection algorithm.},
journal = {Journal of Chemical Information and Modeling},
volume = {49},
number = {1},
pages = {13-21},
year = {2009},
month = jan,
doi = {10.1021/ci8002478},
}John Thomas, Naren Ramakrishnan, and Chris Bailey-Kellogg. Protein design by sampling an undirected graphical model of residue constraints. IEEE/Acm Transactions On Computational Biology and Bioinformatics / IEEE, Acm, 6(3):506—16, jul 2009.
This paper develops an approach for designing protein variants by sampling sequences that satisfy residue constraints encoded in an undirected probabilistic graphical model. Due to evolutionary pressures on proteins to maintain structure and function, the sequence record of a protein family contains valuable information regarding position-specific residue conservation and coupling (or covariation) constraints. Representing these constraints with a graphical model provides two key benefits for protein design: a probabilistic semantics enabling evaluation of possible sequences for consistency with the constraints, and an explicit factorization of residue dependence and independence supporting efficient exploration of the constrained sequence space. We leverage these benefits in developing two complementary MCMC algorithms for protein design: constrained shuffling mixes wild-type sequences positionwise and evaluates graphical model likelihood, while component sampling directly generates sequences by sampling clique values and propagating to other cliques. We apply our methods to design WW domains. We demonstrate that likelihood under a model of wild-type WWs is highly predictive of foldedness of new WWs. We then show both theoretical and rapid empirical convergence of our algorithms in generating high-likelihood, diverse new sequences. We further show that these sequences capture the original sequence constraints, yielding a model as predictive of foldedness as the original one. Hanover, NH 03755, USA. jthomas@cs.dartmouth.edu
@article{ThomasRB:2009,
author = {Thomas, John and Ramakrishnan, Naren and Bailey-Kellogg, Chris},
title = {Protein design by sampling an undirected graphical model of residue constraints.},
journal = {IEEE/Acm Transactions On Computational Biology and Bioinformatics / IEEE, Acm},
volume = {6},
number = {3},
pages = {506-16},
year = {2009},
month = jul,
doi = {10.1109/TCBB.2008.124},
}Thiago M. Venancio, S. Balaji, Lakshminarayan M. Iyer, and L. Aravind. Reconstructing the ubiquitin network: cross-talk with other systems and identification of novel functions. Genome Biology, 10(3):R33, 2009.
Background
The ubiquitin system (Ub-system) can be defined as the ensemble of components including Ub/ubiquitin-like proteins, their conjugation and deconjugation apparatus, binding partners and the proteasomal system. While several studies have concentrated on structure-function relationships and evolution of individual components of the Ub-system, a study of the system as a whole is largely lacking.
Results
Using numerous genome-scale datasets, we assemble for the first time a comprehensive reconstruction of the budding yeast Ub-system, revealing static and dynamic properties. We devised two novel representations, the rank plot to understand the functional diversification of different components and the clique-specific point-wise mutual-information network to identify significant interactions in the Ub-system.
Conclusions
Using these representations, evidence is provided for the functional diversification of components such as SUMO-dependent Ub-ligases. We also identify novel components of SCF (Skp1-cullin-F-box)-dependent complexes, receptors in the ERAD (endoplasmic reticulum associated degradation) system and a key role for Sus1 in coordinating multiple Ub-related processes in chromatin dynamics. We present evidence for a major impact of the Ub-system on large parts of the proteome via its interaction with the transcription regulatory network. Furthermore, the dynamics of the Ub-network suggests that Ub and SUMO modifications might function cooperatively with transcription control in regulating cell-cycle-stage-specific complexes and in reinforcing periodicities in gene expression. Combined with evolutionary information, the structure of this network helps in understanding the lineage-specific expansion of SCF complexes with a potential role in pathogen response and the origin of the ERAD and ESCRT systems. Bethesda, MD 20894, USA. venancit@ncbi.nlm.nih.gov
The ubiquitin system (Ub-system) can be defined as the ensemble of components including Ub/ubiquitin-like proteins, their conjugation and deconjugation apparatus, binding partners and the proteasomal system. While several studies have concentrated on structure-function relationships and evolution of individual components of the Ub-system, a study of the system as a whole is largely lacking.
Results
Using numerous genome-scale datasets, we assemble for the first time a comprehensive reconstruction of the budding yeast Ub-system, revealing static and dynamic properties. We devised two novel representations, the rank plot to understand the functional diversification of different components and the clique-specific point-wise mutual-information network to identify significant interactions in the Ub-system.
Conclusions
Using these representations, evidence is provided for the functional diversification of components such as SUMO-dependent Ub-ligases. We also identify novel components of SCF (Skp1-cullin-F-box)-dependent complexes, receptors in the ERAD (endoplasmic reticulum associated degradation) system and a key role for Sus1 in coordinating multiple Ub-related processes in chromatin dynamics. We present evidence for a major impact of the Ub-system on large parts of the proteome via its interaction with the transcription regulatory network. Furthermore, the dynamics of the Ub-network suggests that Ub and SUMO modifications might function cooperatively with transcription control in regulating cell-cycle-stage-specific complexes and in reinforcing periodicities in gene expression. Combined with evolutionary information, the structure of this network helps in understanding the lineage-specific expansion of SCF complexes with a potential role in pathogen response and the origin of the ERAD and ESCRT systems. Bethesda, MD 20894, USA. venancit@ncbi.nlm.nih.gov
@article{VenancioBIA:2009,
author = {Venancio, Thiago M. and Balaji, S. and Iyer, Lakshminarayan M. and Aravind, L.},
title = {Reconstructing the ubiquitin network: cross-talk with other systems and identification of novel functions.},
journal = {Genome Biology},
volume = {10},
number = {3},
pages = {R33},
year = {2009},
doi = {10.1186/gb-2009-10-3-r33},
}Stefan Wuchty, John H. Adams, and Michael T. Ferdig. A comprehensive plasmodium falciparum protein interaction map reveals a distinct architecture of a core interactome. Proteomics, 9(7):1841—9, apr 2009.
We derive a map of protein interactions in the parasite Plasmodium falciparum from conserved interactions in Saccharomyces cerevisiae, Caenorhabditis elegans, Drosophila melanogaster, and Escherichia coli and pool them with experimental interaction data. The application of a clique-percolation algorithm allows us to find overlapping clusters, strongly correlated with yeast specific conserved protein complexes. Such clusters contain core activities that govern gene expression, largely dominated by components of protein production and degradation processes as well as RNA metabolism. A critical role of protein hubs in the interactome of P. falciparum is supported by their appearance in multiple clusters and the tendencies of their interactions to reach into many distinct protein clusters. Parasite proteins with a human ortholog tend to appear in single complexes. Annotating each protein with the stage where it is maximally expressed we observe a high level of cluster integrity in the ring stage. While we find no signal in the trophozoite phase, expression patterns are reversed in the schizont phase, implying a preponderance of parasite specific functions in this late, invasive schizont stage. As such, the inference of potential protein interactions and their analysis contributes to our understanding of the parasite, indicating basic pathways and processes as unique targets for therapeutic intervention. 60201, USA. wuchtys@mail.nih.gov
@article{WuchtyAF:2009,
author = {Wuchty, Stefan and Adams, John H. and Ferdig, Michael T.},
title = {A comprehensive Plasmodium falciparum protein interaction map reveals a distinct architecture of a core interactome.},
journal = {Proteomics},
volume = {9},
number = {7},
pages = {1841-9},
year = {2009},
month = apr,
doi = {10.1002/pmic.200800383},
}Yuanyuan Xiao and Mark R. Segal. Identification of yeast transcriptional regulation networks using multivariate random forests. Plos Computational Biology, 5(6):e1000414, jun 2009.
The recent availability of whole-genome scale data sets that investigate complementary and diverse aspects of transcriptional regulation has spawned an increased need for new and effective computational approaches to analyze and integrate these large scale assays. Here, we propose a novel algorithm, based on random forest methodology, to relate gene expression (as derived from expression microarrays) to sequence features residing in gene promoters (as derived from DNA motif data) and transcription factor binding to gene promoters (as derived from tiling microarrays). We extend the random forest approach to model a multivariate response as represented, for example, by time-course gene expression measures. An analysis of the multivariate random forest output reveals complex regulatory networks, which consist of cohesive, condition-dependent regulatory cliques. Each regulatory clique features homogeneous gene expression profiles and common motifs or synergistic motif groups. We apply our method to several yeast physiological processes: cell cycle, sporulation, and various stress conditions. Our technique displays excellent performance with regard to identifying known regulatory motifs, including high order interactions. In addition, we present evidence of the existence of an alternative MCB-binding pathway, which we confirm using data from two independent cell cycle studies and two other physioloigical processes. Finally, we have uncovered elaborate transcription regulation refinement mechanisms involving PAC and mRRPE motifs that govern essential rRNA processing. These include intriguing instances of differing motif dosages and differing combinatorial motif control that promote regulatory specificity in rRNA metabolism under differing physiological processes. Molecular Biostatistics, University of California, San Francisco, California, USA. Yuanyuan.Xiao@ucsf.edu
@article{XiaoS:2009,
author = {Xiao, Yuanyuan and Segal, Mark R.},
title = {Identification of yeast transcriptional regulation networks using multivariate random forests.},
journal = {Plos Computational Biology},
volume = {5},
number = {6},
pages = {e1000414},
year = {2009},
month = jun,
doi = {10.1371/journal.pcbi.1000414},
}Huanping Zhang, Xiaofeng Song, Huinan Wang, and Xiaobai Zhang. Miclique: An algorithm to identify differentially coexpressed disease gene subset from microarray data. Journal of Biomedicine & Biotechnology, 2009:642524, 2009.
Computational analysis of microarray data has provided an effective way to identify disease-related genes. Traditional disease gene selection methods from microarray data such as statistical test always focus on differentially expressed genes in different samples by individual gene prioritization. These traditional methods might miss differentially coexpressed (DCE) gene subsets because they ignore the interaction between genes. In this paper, MIClique algorithm is proposed to identify DEC gene subsets based on mutual information and clique analysis. Mutual information is used to measure the coexpression relationship between each pair of genes in two different kinds of samples. Clique analysis is a commonly used method in biological network, which generally represents biological module of similar function. By applying the MIClique algorithm to real gene expression data, some DEC gene subsets which correlated under one experimental condition but uncorrelated under another condition are detected from the graph of colon dataset and leukemia dataset. Astronautics, China.
@article{ZhangSWZ:2009,
author = {Zhang, Huanping and Song, Xiaofeng and Wang, Huinan and Zhang, Xiaobai},
title = {MIClique: An algorithm to identify differentially coexpressed disease gene subset from microarray data.},
journal = {Journal of Biomedicine & Biotechnology},
volume = {2009},
pages = {642524},
year = {2009},
doi = {10.1155/2009/642524},
}Michelle Bezanson, Paul A. Garber, John T. Murphy, and L. S. Premo. Patterns of subgrouping and spatial affiliation in a community of mantled howling monkeys (alouatta palliata). American Journal of Primatology, 70(3):282—93, mar 2008.
Studies of social affiliation and social spacing offer important insight into the dynamics of subgroup formation and social strategies in living primates. Among the 11 species in the genus Alouatta, mantled howlers (A. palliata) are the only species to consistently form large, stable social groups composed of several adult males and several adult females. In this study, we examine patterns of subgrouping, activity, and partner preferences in a troop of 26-29 wild mantled howling monkeys (including 12-13 marked individuals) inhabiting Isla de Ometepe, Nicaragua. During two study seasons in 2000 and 2001, we simultaneously monitored the size, composition, and activities of individuals in two to three different subgroups. A half-weight association index was used to calculate partner preferences and patterns of spatial association. Results indicate that our howler study troop fragmented into subgroups of 1-20 with subgroups averaging five and six individuals. Subgroup size and membership reflected individual patterns of social affiliation and social tolerance, and in general remained consistent across activities and from year to year. We also found evidence of cliques or social networks of three to four individuals embedded within larger subgroups. A small number of adult males appeared to play an important social role as the nucleus of clique formation. We argue that the persistence of strong male-male and male-female partner preferences in mantled howlers helps to explain the stability of relatively large multimale-multifemale groups. 95053-1500, USA. mbezanson@scu.edu
@article{BezansonGMP:2008,
author = {Bezanson, Michelle and Garber, Paul A. and Murphy, John T. and Premo, L. S.},
title = {Patterns of subgrouping and spatial affiliation in a community of mantled howling monkeys (Alouatta palliata).},
journal = {American Journal of Primatology},
volume = {70},
number = {3},
pages = {282-93},
year = {2008},
month = mar,
doi = {10.1002/ajp.20486},
}George Jr Chin, Daniel G. Chavarria, Grant C. Nakamura, and Heidi J. Sofia. Biographe: high-performance bionetwork analysis using the biological graph environment. BMC Bioinformatics, 9 Suppl 6:S6, 2008.
Background
Graphs and networks are common analysis representations for biological systems. Many traditional graph algorithms such as k-clique, k-coloring, and subgraph matching have great potential as analysis techniques for newly available data in biology. Yet, as the amount of genomic and bionetwork information rapidly grows, scientists need advanced new computational strategies and tools for dealing with the complexities of the bionetwork analysis and the volume of the data.
Results
We introduce a computational framework for graph analysis called the Biological Graph Environment (BioGraphE), which provides a general, scalable integration platform for connecting graph problems in biology to optimized computational solvers and high-performance systems. This framework enables biology researchers and computational scientists to identify and deploy network analysis applications and to easily connect them to efficient and powerful computational software and hardware that are specifically designed and tuned to solve complex graph problems. In our particular application of BioGraphE to support network analysis in genome biology, we investigate the use of a Boolean satisfiability solver known as Survey Propagation as a core computational solver executing on standard high-performance parallel systems, as well as multi-threaded architectures.
Conclusion
In our application of BioGraphE to conduct bionetwork analysis of homology networks, we found that BioGraphE and a custom, parallel implementation of the Survey Propagation SAT solver were capable of solving very large bionetwork problems at high rates of execution on different high-performance computing platforms. Division, Pacific Northwest National Laboratory, Richland, Washington, USA. george.chin@pnl.gov
Graphs and networks are common analysis representations for biological systems. Many traditional graph algorithms such as k-clique, k-coloring, and subgraph matching have great potential as analysis techniques for newly available data in biology. Yet, as the amount of genomic and bionetwork information rapidly grows, scientists need advanced new computational strategies and tools for dealing with the complexities of the bionetwork analysis and the volume of the data.
Results
We introduce a computational framework for graph analysis called the Biological Graph Environment (BioGraphE), which provides a general, scalable integration platform for connecting graph problems in biology to optimized computational solvers and high-performance systems. This framework enables biology researchers and computational scientists to identify and deploy network analysis applications and to easily connect them to efficient and powerful computational software and hardware that are specifically designed and tuned to solve complex graph problems. In our particular application of BioGraphE to support network analysis in genome biology, we investigate the use of a Boolean satisfiability solver known as Survey Propagation as a core computational solver executing on standard high-performance parallel systems, as well as multi-threaded architectures.
Conclusion
In our application of BioGraphE to conduct bionetwork analysis of homology networks, we found that BioGraphE and a custom, parallel implementation of the Survey Propagation SAT solver were capable of solving very large bionetwork problems at high rates of execution on different high-performance computing platforms. Division, Pacific Northwest National Laboratory, Richland, Washington, USA. george.chin@pnl.gov
@article{ChinCNS:2008,
author = {Chin, George Jr and Chavarria, Daniel G. and Nakamura, Grant C. and Sofia, Heidi J.},
title = {BioGraphE: high-performance bionetwork analysis using the Biological Graph Environment.},
journal = {BMC Bioinformatics},
volume = {9 Suppl 6},
pages = {S6},
year = {2008},
doi = {10.1186/1471-2105-9-S6-S6},
}Guangyu Cui, Yu Chen, De-Shuang Huang, and Kyungsook Han. An algorithm for finding functional modules and protein complexes in protein-protein interaction networks. Journal of Biomedicine & Biotechnology, 2008:860270, 2008.
Biological processes are often performed by a group of proteins rather than by individual proteins, and proteins in a same biological group form a densely connected subgraph in a protein-protein interaction network. Therefore, finding a densely connected subgraph provides useful information to predict the function or protein complex of uncharacterized proteins in the highly connected subgraph. We have developed an efficient algorithm and program for finding cliques and near-cliques in a protein-protein interaction network. Analysis of the interaction network of yeast proteins using the algorithm demonstrates that 59% of the near-cliques identified by our algorithm have at least one function shared by all the proteins within a near-clique, and that 56% of the near-cliques show a good agreement with the experimentally determined protein complexes catalogued in MIPS. South Korea.
@article{CuiCHH:2008,
author = {Cui, Guangyu and Chen, Yu and Huang, De-Shuang and Han, Kyungsook},
title = {An algorithm for finding functional modules and protein complexes in protein-protein interaction networks.},
journal = {Journal of Biomedicine & Biotechnology},
volume = {2008},
pages = {860270},
year = {2008},
doi = {10.1155/2008/860270},
}John C. Cushman, Richard L. Tillett, Joshua A. Wood, Joshua M. Branco, and Karen A. Schlauch. Large-scale mrna expression profiling in the common ice plant, mesembryanthemum crystallinum, performing c3 photosynthesis and crassulacean acid metabolism (cam). Journal of Experimental Botany, 59(7):1875—94, 2008.
The common ice plant (Mesembryanthemum crystallinum L.) has emerged as a useful model for molecular genetic studies of Crassulacean acid metabolism (CAM) because CAM can be induced in this species by water deficit or salinity stress. Non-redundant sequence information from expressed sequence tag data was used to fabricate a custom oligonucleotide microarray to compare large-scale mRNA expression patterns in M. crystallinum plants conducting C(3) photosynthesis versus CAM. Samples were collected every 4 h over a 24 h time period at the start of the subjective second day from plants grown under constant light and temperature conditions in order to capture variation in mRNA expression due to salinity stress and circadian clock control. Of 8455 genes, a total of 2343 genes (approximately 28%) showed a significant change as judged by analysis of variance (ANOVA) in steady-state mRNA abundance at one or more time points over the 24 h period. Of these, 858 (10%) and 599 (7%) exhibited a greater than two-fold ratio (TFR) increase or decrease in mRNA abundance, respectively. Functional categorization of these TFR genes revealed that many genes encoding products that function in CAM-related C(4) acid carboxylation/decarboxylation, glycolysis/gluconeogenesis, polysaccharide, polyol, and starch biosynthesis/degradation, protein degradation, transcriptional activation, signalling, stress response, and transport facilitation, and novel, unclassified proteins exhibited stress-induced increases in mRNA abundance. In contrast, salt stress resulted in a significant decrease in transcript abundance for genes encoding photosynthetic functions, protein synthesis, and cellular biogenesis functions. Many genes with CAM-related functions exhibited phase shifts in their putative circadian expression patterns following CAM induction. This report establishes an extensive catalogue of gene expression patterns for future investigations aimed at understanding the complex, transcriptional hierarchies that govern CAM-specific expression patterns. A novel graph-theoretic approach called ’Max Clique Builder’ is introduced that identifies and organizes sets of coordinately regulated genes, such as those encoding subunits of the vacuolar H(+)-ATPase complex, into tighter functionally related clusters with more similar expression patterns compared with standard hierarchical clustering methods. USA. jcushman@unr.edu
@article{CushmanTWBS:2008,
author = {Cushman, John C. and Tillett, Richard L. and Wood, Joshua A. and Branco, Joshua M. and Schlauch, Karen A.},
title = {Large-scale mRNA expression profiling in the common ice plant, Mesembryanthemum crystallinum, performing C3 photosynthesis and Crassulacean acid metabolism (CAM).},
journal = {Journal of Experimental Botany},
volume = {59},
number = {7},
pages = {1875-94},
year = {2008},
doi = {10.1093/jxb/ern008},
}Amit Ghosh and Saraswathi Vishveshwara. Variations in clique and community patterns in protein structures during allosteric communication: investigation of dynamically equilibrated structures of methionyl trna synthetase complexes. Biochemistry, 47(44):11398—407, nov 2008.
The allosteric concept has played a key role in understanding the biological functions of proteins. The rigidity or plasticity and the conformational population are the two important ideas invoked in explaining the allosteric effect. Although molecular insights have been gained from a large number of structures, a precise assessment of the ligand-induced conformational changes in proteins at different levels, ranging from gross topology to intricate details, remains a challenge. In this study, we have explored the conformational changes in the complexes of methionyl tRNA synthetase (MetRS) through novel network parameters such as cliques and communities, which identify the rigid regions in the protein structure networks (PSNs) constructed from the noncovalent interactions of amino acid side chains. MetRS belongs to the aminoacyl tRNA synthetase (aaRS) family that plays a crucial role in the translation of genetic code. These enzymes are modular with distinct domains from which extensive genetic, kinetic, and structural data are available, highlighting the role of interdomain communication. The network parameters evaluated here on the conformational ensembles of MetRS complexes, generated from molecular dynamics simulations, have enabled us to understand the interdomain communication in detail. Additionally, the characterization of conformational changes in terms of cliques and communities has also become possible, which had eluded conventional analyses. Furthermore, we find that most of the residues participating in cliques and communities are strikingly different from those that take part in long-range communication. The cliques and communities evaluated here for the first time on PSNs have beautifully captured the local geometries in detail within the framework of global topology. Here the allosteric effect is revealed at the residue level via identification of the important residues specific for structural rigidity and functional flexibility in MetRS. This ought to enhance our understanding of the functioning of aaRS in general.
@article{GhoshV:2008,
author = {Ghosh, Amit and Vishveshwara, Saraswathi},
title = {Variations in clique and community patterns in protein structures during allosteric communication: investigation of dynamically equilibrated structures of methionyl tRNA synthetase complexes.},
journal = {Biochemistry},
volume = {47},
number = {44},
pages = {11398-407},
year = {2008},
month = nov,
doi = {10.1021/bi8007559},
}Parthasarathy Guturu and Ram Dantu. An impatient evolutionary algorithm with probabilistic tabu search for unified solution of some np-hard problems in graph and set theory via clique finding. IEEE Transactions On Systems, Man, and Cybernetics. Part B, Cybernetics, 38(3):645—66, jun 2008.
Many graph- and set-theoretic problems, because of their tremendous application potential and theoretical appeal, have been well investigated by the researchers in complexity theory and were found to be NP-hard. Since the combinatorial complexity of these problems does not permit exhaustive searches for optimal solutions, only near-optimal solutions can be explored using either various problem-specific heuristic strategies or metaheuristic global-optimization methods, such as simulated annealing, genetic algorithms, etc. In this paper, we propose a unified evolutionary algorithm (EA) to the problems of maximum clique finding, maximum independent set, minimum vertex cover, subgraph and double subgraph isomorphism, set packing, set partitioning, and set cover. In the proposed approach, we first map these problems onto the maximum clique-finding problem (MCP), which is later solved using an evolutionary strategy. The proposed impatient EA with probabilistic tabu search (IEA-PTS) for the MCP integrates the best features of earlier successful approaches with a number of new heuristics that we developed to yield a performance that advances the state of the art in EAs for the exploration of the maximum cliques in a graph. Results of experimentation with the 37 DIMACS benchmark graphs and comparative analyses with six state-of-the-art algorithms, including two from the smaller EA community and four from the larger metaheuristics community, indicate that the IEA-PTS outperforms the EAs with respect to a Pareto-lexicographic ranking criterion and offers competitive performance on some graph instances when individually compared to the other heuristic algorithms. It has also successfully set a new benchmark on one graph instance. On another benchmark suite called Benchmarks with Hidden Optimal Solutions, IEA-PTS ranks second, after a very recent algorithm called COVER, among its peers that have experimented with this suite. Texas, Denton, TX 76203-1277, USA. e-mail:guturu@unt.edu
@article{GuturuD:2008,
author = {Guturu, Parthasarathy and Dantu, Ram},
title = {An impatient evolutionary algorithm with probabilistic tabu search for unified solution of some NP-hard problems in graph and set theory via clique finding.},
journal = {IEEE Transactions On Systems, Man, and Cybernetics. Part B, Cybernetics},
volume = {38},
number = {3},
pages = {645-66},
year = {2008},
month = jun,
doi = {10.1109/TSMCB.2008.915645},
}Seong-Eui Hong, Inju Park, Hyeseon Cha, Seong-Hwan Rho, Woo Jin Park, Chunghee Cho, and Do Han Kim. Identification of mouse heart transcriptomic network sensitive to various heart diseases. Biotechnology Journal, 3(5):648—58, may 2008.
Exploring biological systems from highly complex datasets is an important task for systems biology. The present study examined co-expression dynamics of mouse heart transcriptome by spectral graph clustering (SGC) to identify a heart transcriptomic network. SGC of microarray data produced 17 classified biological conditions (called condition spectrum, CS) and co-expression patterns by generating bi-clusters. The results showed dynamic co-expression patterns with a modular structure enriched in heart-related CS (CS-1 and -13) containing abundant heart-related microarray data. Consequently, a mouse heart transcriptomic network was constructed by clique analysis from the gene clusters exclusively present in the heart-related CS; 31 cliques were used for constructing the network. The participating genes in the network were closely associated with important cardiac functions (e. g., development, lipid and glycogen metabolisms). Online Mendelian Inheritance in Man (OMIM) database indicates that mutations of the genes in the network induced serious heart diseases. Many of the tested genes in the network showed significantly altered gene expression in an animal model of hypertrophy. The results suggest that the present approach is critical for constructing a heart-related transcriptomic network and for deducing important genes involved in the pathogenesis of various heart diseases. Korea.
@article{HongPCRPCK:2008,
author = {Hong, Seong-Eui and Park, Inju and Cha, Hyeseon and Rho, Seong-Hwan and Park, Woo Jin and Cho, Chunghee and Kim, Do Han},
title = {Identification of mouse heart transcriptomic network sensitive to various heart diseases.},
journal = {Biotechnology Journal},
volume = {3},
number = {5},
pages = {648-58},
year = {2008},
month = may,
doi = {10.1002/biot.200700250},
}Tianyun Liu, Michal Guerquin, and Ram Samudrala. Improving the accuracy of template-based predictions by mixing and matching between initial models. BMC Structural Biology, 8:24, 2008.
Background
Comparative modeling is a technique to predict the three dimensional structure of a given protein sequence based primarily on its alignment to one or more proteins with experimentally determined structures. A major bottleneck of current comparative modeling methods is the lack of methods to accurately refine a starting initial model so that it approaches the resolution of the corresponding experimental structure. We investigate the effectiveness of a graph-theoretic clique finding approach to solve this problem.
Results
Our method takes into account the information presented in multiple templates/alignments at the three-dimensional level by mixing and matching regions between different initial comparative models. This method enables us to obtain an optimized conformation ensemble representing the best combination of secondary structures, resulting in the refined models of higher quality. In addition, the process of mixing and matching accumulates near-native conformations, resulting in discriminating the native-like conformation in a more effective manner. In the seventh Critical Assessment of Structure Prediction (CASP7) experiment, the refined models produced are more accurate than the starting initial models.
Conclusion
This novel approach can be applied without any manual intervention to improve the quality of comparative predictions where multiple template/alignment combinations are available for modeling, producing conformational models of higher quality than the starting initial predictions. Seattle, WA 98195, USA. tianyunl@stanford.edu
Comparative modeling is a technique to predict the three dimensional structure of a given protein sequence based primarily on its alignment to one or more proteins with experimentally determined structures. A major bottleneck of current comparative modeling methods is the lack of methods to accurately refine a starting initial model so that it approaches the resolution of the corresponding experimental structure. We investigate the effectiveness of a graph-theoretic clique finding approach to solve this problem.
Results
Our method takes into account the information presented in multiple templates/alignments at the three-dimensional level by mixing and matching regions between different initial comparative models. This method enables us to obtain an optimized conformation ensemble representing the best combination of secondary structures, resulting in the refined models of higher quality. In addition, the process of mixing and matching accumulates near-native conformations, resulting in discriminating the native-like conformation in a more effective manner. In the seventh Critical Assessment of Structure Prediction (CASP7) experiment, the refined models produced are more accurate than the starting initial models.
Conclusion
This novel approach can be applied without any manual intervention to improve the quality of comparative predictions where multiple template/alignment combinations are available for modeling, producing conformational models of higher quality than the starting initial predictions. Seattle, WA 98195, USA. tianyunl@stanford.edu
@article{LiuGS:2008,
author = {Liu, Tianyun and Guerquin, Michal and Samudrala, Ram},
title = {Improving the accuracy of template-based predictions by mixing and matching between initial models.},
journal = {BMC Structural Biology},
volume = {8},
pages = {24},
year = {2008},
doi = {10.1186/1472-6807-8-24},
}Fan Liu, Anatoliy Kirichenko, Tatiana I. Axenovich, Cornelia M. van Duijn, and Yurii S. Aulchenko. An approach for cutting large and complex pedigrees for linkage analysis. European Journal of Human Genetics, 16(7):854—60, jul 2008.
Utilizing large pedigrees in linkage analysis is a computationally challenging task. The pedigree size limits applicability of the Lander-Green-Kruglyak algorithm for linkage analysis. A common solution is to split large pedigrees into smaller computable subunits. We present a pedigree-splitting method that, within a user supplied bit-size limit, identifies subpedigrees having the maximal number of subjects of interest (eg patients) who share a common ancestor. We compare our method with the maximum clique partitioning method using a large and complex human pedigree consisting of 50 patients with Alzheimer’s disease ascertained from genetically isolated Dutch population. We show that under a bit-size limit our method can assign more patients to subpedigrees than the clique partitioning method, particularly when splitting deep pedigrees where the subjects of interest are scattered in recent generations and are relatively distantly related via multiple genealogic connections. Our pedigree-splitting algorithm and associated software can facilitate genome-wide linkage scans searching for rare mutations in large pedigrees coming from genetically isolated populations. The software package PedCut implementing our approach is available at http://mga.bionet.nsc.ru/soft/index.html. Netherlands.
@article{LiuKAvA:2008,
author = {Liu, Fan and Kirichenko, Anatoliy and Axenovich, Tatiana I. and van Duijn, Cornelia M. and Aulchenko, Yurii S.},
title = {An approach for cutting large and complex pedigrees for linkage analysis.},
journal = {European Journal of Human Genetics},
volume = {16},
number = {7},
pages = {854-60},
year = {2008},
month = jul,
doi = {10.1038/ejhg.2008.24},
}Julian J. McAuley, Tiberio S. Caetano, and Marconi S. Barbosa. Graph rigidity, cyclic belief propagation, and point pattern matching. IEEE Transactions On Pattern Analysis and Machine Intelligence, 30(11):2047—54, nov 2008.
A recent paper [1] proposed a provably optimal polynomial time method for performing near-isometric point pattern matching by means of exact probabilistic inference in a chordal graphical model. Its fundamental result is that the chordal graph in question is shown to be globally rigid, implying that exact inference provides the same matching solution as exact inference in a complete graphical model. This implies that the algorithm is optimal when there is no noise in the point patterns. In this paper, we present a new graph that is also globally rigid but has an advantage over the graph proposed in [1]: Its maximal clique size is smaller, rendering inference significantly more efficient. However, this graph is not chordal, and thus, standard Junction Tree algorithms cannot be directly applied. Nevertheless, we show that loopy belief propagation in such a graph converges to the optimal solution. This allows us to retain the optimality guarantee in the noiseless case, while substantially reducing both memory requirements and processing time. Our experimental results show that the accuracy of the proposed solution is indistinguishable from that in [1] when there is noise in the point patterns. Australia. julian.mcauley@nicta.com.au
@article{McAuleyCB:2008,
author = {McAuley, Julian J. and Caetano, Tiberio S. and Barbosa, Marconi S.},
title = {Graph rigidity, cyclic belief propagation, and point pattern matching.},
journal = {IEEE Transactions On Pattern Analysis and Machine Intelligence},
volume = {30},
number = {11},
pages = {2047-54},
year = {2008},
month = nov,
doi = {10.1109/TPAMI.2008.124},
}Yanjun Qi, Fernanda Balem, Christos Faloutsos, Judith Klein-Seetharaman, and Ziv Bar-Joseph. Protein complex identification by supervised graph local clustering. Bioinformatics, 24(13):i250—8, jul 2008.
Motivation
Protein complexes integrate multiple gene products to coordinate many biological functions. Given a graph representing pairwise protein interaction data one can search for subgraphs representing protein complexes. Previous methods for performing such search relied on the assumption that complexes form a clique in that graph. While this assumption is true for some complexes, it does not hold for many others. New algorithms are required in order to recover complexes with other types of topological structure.
Results
We present an algorithm for inferring protein complexes from weighted interaction graphs. By using graph topological patterns and biological properties as features, we model each complex subgraph by a probabilistic Bayesian network (BN). We use a training set of known complexes to learn the parameters of this BN model. The log-likelihood ratio derived from the BN is then used to score subgraphs in the protein interaction graph and identify new complexes. We applied our method to protein interaction data in yeast. As we show our algorithm achieved a considerable improvement over clique based algorithms in terms of its ability to recover known complexes. We discuss some of the new complexes predicted by our algorithm and determine that they likely represent true complexes.
Availability
Matlab implementation is available on the supporting website: www.cs.cmu.edu/ qyj/SuperComplex. USA.
Protein complexes integrate multiple gene products to coordinate many biological functions. Given a graph representing pairwise protein interaction data one can search for subgraphs representing protein complexes. Previous methods for performing such search relied on the assumption that complexes form a clique in that graph. While this assumption is true for some complexes, it does not hold for many others. New algorithms are required in order to recover complexes with other types of topological structure.
Results
We present an algorithm for inferring protein complexes from weighted interaction graphs. By using graph topological patterns and biological properties as features, we model each complex subgraph by a probabilistic Bayesian network (BN). We use a training set of known complexes to learn the parameters of this BN model. The log-likelihood ratio derived from the BN is then used to score subgraphs in the protein interaction graph and identify new complexes. We applied our method to protein interaction data in yeast. As we show our algorithm achieved a considerable improvement over clique based algorithms in terms of its ability to recover known complexes. We discuss some of the new complexes predicted by our algorithm and determine that they likely represent true complexes.
Availability
Matlab implementation is available on the supporting website: www.cs.cmu.edu/ qyj/SuperComplex. USA.
@article{QiBFKB:2008,
author = {Qi, Yanjun and Balem, Fernanda and Faloutsos, Christos and Klein-Seetharaman, Judith and Bar-Joseph, Ziv},
title = {Protein complex identification by supervised graph local clustering.},
journal = {Bioinformatics},
volume = {24},
number = {13},
pages = {i250-8},
year = {2008},
month = jul,
doi = {10.1093/bioinformatics/btn164},
}Mehmet E. Turanalp and Tolga Can. Discovering functional interaction patterns in protein-protein interaction networks. BMC Bioinformatics, 9:276, 2008.
Background
In recent years, a considerable amount of research effort has been directed to the analysis of biological networks with the availability of genome-scale networks of genes and/or proteins of an increasing number of organisms. A protein-protein interaction (PPI) network is a particular biological network which represents physical interactions between pairs of proteins of an organism. Major research on PPI networks has focused on understanding the topological organization of PPI networks, evolution of PPI networks and identification of conserved subnetworks across different species, discovery of modules of interaction, use of PPI networks for functional annotation of uncharacterized proteins, and improvement of the accuracy of currently available networks.
Results
In this article, we map known functional annotations of proteins onto a PPI network in order to identify frequently occurring interaction patterns in the functional space. We propose a new frequent pattern identification technique, PPISpan, adapted specifically for PPI networks from a well-known frequent subgraph identification method, gSpan. Existing module discovery techniques either look for specific clique-like highly interacting protein clusters or linear paths of interaction. However, our goal is different; instead of single clusters or pathways, we look for recurring functional interaction patterns in arbitrary topologies. We have applied PPISpan on PPI networks of Saccharomyces cerevisiae and identified a number of frequently occurring functional interaction patterns.
Conclusion
With the help of PPISpan, recurring functional interaction patterns in an organism’s PPI network can be identified. Such an analysis offers a new perspective on the modular organization of PPI networks. The complete list of identified functional interaction patterns is available at http://bioserver.ceng.metu.edu.tr/PPISpan/. 42075 Selcuklu, Konya, Turkey. eturanalp@selcuk.edu.tr
In recent years, a considerable amount of research effort has been directed to the analysis of biological networks with the availability of genome-scale networks of genes and/or proteins of an increasing number of organisms. A protein-protein interaction (PPI) network is a particular biological network which represents physical interactions between pairs of proteins of an organism. Major research on PPI networks has focused on understanding the topological organization of PPI networks, evolution of PPI networks and identification of conserved subnetworks across different species, discovery of modules of interaction, use of PPI networks for functional annotation of uncharacterized proteins, and improvement of the accuracy of currently available networks.
Results
In this article, we map known functional annotations of proteins onto a PPI network in order to identify frequently occurring interaction patterns in the functional space. We propose a new frequent pattern identification technique, PPISpan, adapted specifically for PPI networks from a well-known frequent subgraph identification method, gSpan. Existing module discovery techniques either look for specific clique-like highly interacting protein clusters or linear paths of interaction. However, our goal is different; instead of single clusters or pathways, we look for recurring functional interaction patterns in arbitrary topologies. We have applied PPISpan on PPI networks of Saccharomyces cerevisiae and identified a number of frequently occurring functional interaction patterns.
Conclusion
With the help of PPISpan, recurring functional interaction patterns in an organism’s PPI network can be identified. Such an analysis offers a new perspective on the modular organization of PPI networks. The complete list of identified functional interaction patterns is available at http://bioserver.ceng.metu.edu.tr/PPISpan/. 42075 Selcuklu, Konya, Turkey. eturanalp@selcuk.edu.tr
@article{TuranalpC:2008,
author = {Turanalp, Mehmet E. and Can, Tolga},
title = {Discovering functional interaction patterns in protein-protein interaction networks.},
journal = {BMC Bioinformatics},
volume = {9},
pages = {276},
year = {2008},
doi = {10.1186/1471-2105-9-276},
}Jia Zeng and Zhi-Qiang Liu. Markov random field-based statistical character structure modeling for handwritten chinese character recognition. IEEE Transactions On Pattern Analysis and Machine Intelligence, 30(5):767—80, may 2008.
This paper proposes a statistical-structural character modeling method based on Markov random fields (MRFs) for handwritten Chinese character recognition (HCCR). The stroke relationships of a Chinese character reflect its structure, which can be statistically represented by the neighborhood system and clique potentials within the MRF framework. Based on the prior knowledge of character structures, we design the neighborhood system that accounts for the most important stroke relationships. We penalize the structurally mismatched stroke relationships with MRFs using the prior clique potentials, and derive the likelihood clique potentials from Gaussian mixture models, which encode the large variations of stroke relationships statistically. In the proposed HCCR system, we use the single-site likelihood clique potentials to extract many candidate strokes from character images, and use the pairsite clique potentials to determine the best structural match between the input candidate strokes and the MRF-based character models by relaxation labeling. The experiments on the KAIST character database demonstrate that MRFs can statistically model character structures, and work well in the HCCR system. 83, Kowloon Tong, Hong Kong, PR China. j.zeng@ieee.org
@article{ZengL:2008,
author = {Zeng, Jia and Liu, Zhi-Qiang},
title = {Markov random field-based statistical character structure modeling for handwritten Chinese character recognition.},
journal = {IEEE Transactions On Pattern Analysis and Machine Intelligence},
volume = {30},
number = {5},
pages = {767-80},
year = {2008},
month = may,
doi = {10.1109/TPAMI.2007.70734},
}Michael ten Caat, Natasha M. Maurits, and Jos B. T M. Roerdink. Data-driven visualization and group analysis of multichannel eeg coherence with functional units. IEEE Transactions On Visualization and Computer Graphics, 14(4):756—71, jul 2008.
A typical data-driven visualization of electroencephalography (EEG) coherence is a graph layout, with vertices representing electrodes and edges representing significant coherences between electrode signals. A drawback of this layout is its visual clutter for multichannel EEG. To reduce clutter, we define a functional unit (FU) as a data-driven region of interest (ROI). An FU is a spatially connected set of electrodes recording pairwise significantly coherent signals, represented in the coherence graph by a spatially connected clique. Earlier we presented two methods to detect FUs: a maximal clique based (MCB) method (time complexity O(3n/3), with n being the number of vertices) and a more efficient watershed based (WB) method (time complexity O (n2 log n)). To reduce the potential over-segmentation of the WB method, we introduce here an improved WB (IWB) method (time complexity O(n2 log n)). The IWB method merges basins representing FUs during the segmentation if they are spatially connected and if their union is a clique. The WB and IWB methods are both up to a factor of 100,000 faster than the MCB method for a typical multichannel setting with 128 EEG channels, thus making interactive visualization of multichannel EEG coherence possible. Results show that considering the MCB method as the gold standard, the difference between IWB and MCB FU maps is smaller than between WB and MCB FU maps. We also introduce two novel group maps for data-driven group analysis as extensions of the IWB method. First, the group mean coherence map preserves dominant features from a collection of individual FU maps. Second, the group FU size map visualizes the average FU size per electrode across a collection of individual FU maps. Finally, we employ an extensive case study to evaluate the IWB FU map and the two new group maps for data-driven group analysis. Results, in accordance with the conventional findings, indicate differences in EEG coherence between younger and older adults. However, they also suggest that an initial selection of hypothesis-driven ROIs could be extended with additional data-driven ROIs.
@article{tenMR:2008,
author = {ten Caat, Michael and Maurits, Natasha M. and Roerdink, Jos B. T M.},
title = {Data-driven visualization and group analysis of multichannel EEG coherence with functional units.},
journal = {IEEE Transactions On Visualization and Computer Graphics},
volume = {14},
number = {4},
pages = {756-71},
year = {2008},
month = jul,
doi = {10.1109/TVCG.2008.21},
}Carlos M. Carvalho, Hélène Massam, and Mike West. Simulation of hyper-inverse {W}ishart distributions in graphical models. Biometrika, 94(3):647—659, 2007. [graphical models]
We introduce and exemplify an efficient method for direct sampling from hyper-inverse Wishart distributions. The method relies very naturally on the use of standard junction-tree representation of graphs, and couples these with matrix results for inverse Wishart distributions. We describe the theory and resulting computational algorithms for both decomposable and nondecomposable graphical models. An example drawn from financial time series demonstrates application in a context where inferences on a structured covariance model are required. We discuss and investigate questions of scalability of the simulation methods to higher-dimensional distributions. The paper concludes with general comments about the approach, including its use in connection with existing Markov chain Monte Carlo methods that deal with uncertainty about the graphical model structure.
@article{CarvalhoMW:2007,
author = {Carvalho, Carlos M. and Massam, H{\'e}l{\`e}ne and West, Mike},
title = {Simulation of hyper-inverse {W}ishart distributions in graphical models},
journal = {Biometrika},
volume = {94},
number = {3},
pages = {647--659},
year = {2007},
doi = {10.1093/biomet/asm056},
}Antoine Danchin, Gang Fang, and Stanislas Noria. The extant core bacterial proteome is an archive of the origin of life. Proteomics, 7(6):875—89, mar 2007.
Genes consistently present in a clique of genomes, preferring the leading DNA strands are deemed persistent. The persistent bacterial proteome organises around intermediary and RNA metabolism, and RNA-related information transfer, with a significant contribution to compartmentalisation. Despite inevitable losses during evolution, the extant persistent proteome displays functions present early on. Proteins coded by genes staying clustered in a majority of genomes constitute a network of mutual attraction made up of three concentric circles. The outer one, mostly devoted to metabolism, breaks into small pieces and fades away. The second, more continuous, one organises around class I tRNA synthetases. The well-connected inner circle comprises the ribosome and information transfer. This reflects the progressive construction of cells, starting from the metabolism of coenzymes, nucleotides and fatty acids-related molecules. Subsequently, a core set of aminoacyl-tRNA synthetases scaffolded around RNA, connected to cell division machinery and organised metabolism around translation. This remarkable organisation reflects the evolution of life from small molecules metabolism to the RNA world, suggesting that extant microorganisms carry the marks of the ancient processes that created life. Further analysis suggests that RNA degradation, associated to the presence of iron, still plays a role in extant metabolism, including the evolution of genome structures. adanchin@pasteur.fr
@article{DanchinFN:2007,
author = {Danchin, Antoine and Fang, Gang and Noria, Stanislas},
title = {The extant core bacterial proteome is an archive of the origin of life.},
journal = {Proteomics},
volume = {7},
number = {6},
pages = {875-89},
year = {2007},
month = mar,
doi = {10.1002/pmic.200600442},
}Nan Du, Bin Wu, Xin Pei, Bai Wang, and Liutong Xu. Community detection in large-scale social networks. ISBN 978-1-59593-848-0
Recent years have seen that WWW is becoming a flourishing social media which enables individuals to easily share opinions, experiences and expertise at the push of a single button. With the pervasive usage of instant messaging systems and the fundamental shift in the ease of publishing content, social network researchers and graph theory researchers are now concerned with inferring community structures by analyzing the linkage patterns among individuals and web pages. Although the investigation of community structures has motivated many diverse algorithms, most of them are unsuitable for large-scale social networks because of the computational cost. Moreover, in addition to identify the possible community structures, how to define and explain the discovered communities is also significant in many practical scenarios.
In this paper, we present the algorithm ComTector(Community DeTector) which is more efficient for the community detection in large-scale social networks based on the nature of overlapping communities in the real world. This algorithm does not require any priori knowledge about the number or the original division of the communities. Because real networks are often large sparse graphs, its running time is thus \(O(C \times Tri^2)\), where \(C\) is the number of the detected communities and \(Tri\) is the number of the triangles in the given network for the worst case. Then we propose a general naming method by combining the topological information with the entity attributes to define the discovered communities. With respected to practical applications, ComTector is challenged with several real life networks including the Zachary Karate Club, American College Football, Scientific Collaboration, and Telecommunications Call networks. Experimental results show that this algorithm can extract meaningful communities that are agreed with both of the objective facts and our intuitions.
In this paper, we present the algorithm ComTector(Community DeTector) which is more efficient for the community detection in large-scale social networks based on the nature of overlapping communities in the real world. This algorithm does not require any priori knowledge about the number or the original division of the communities. Because real networks are often large sparse graphs, its running time is thus \(O(C \times Tri^2)\), where \(C\) is the number of the detected communities and \(Tri\) is the number of the triangles in the given network for the worst case. Then we propose a general naming method by combining the topological information with the entity attributes to define the discovered communities. With respected to practical applications, ComTector is challenged with several real life networks including the Zachary Karate Club, American College Football, Scientific Collaboration, and Telecommunications Call networks. Experimental results show that this algorithm can extract meaningful communities that are agreed with both of the objective facts and our intuitions.
@inproceedings{DuWPWX:2007,
author = {Du, Nan and Wu, Bin and Pei, Xin and Wang, Bai and Xu, Liutong},
title = {Community detection in large-scale social networks},
booktitle = {Proceedings of the 9th WebKDD and 1st SNA-KDD 2007 workshop on Web mining and social network analysis},
series = {WebKDD/SNA-KDD '07},
pages = {16--25},
publisher = {ACM},
year = {2007},
address = {New York, NY, USA},
doi = {10.1145/1348549.1348552},
}Giacomo Finocchiaro, Francesco Mattia Mancuso, Davide Cittaro, and Heiko Muller. Graph-based identification of cancer signaling pathways from published gene expression signatures using publime. Nucleic Acids Research, 35(7):2343—55, 2007.
Gene expression technology has become a routine application in many laboratories and has provided large amounts of gene expression signatures that have been identified in a variety of cancer types. Interpretation of gene expression signatures would profit from the availability of a procedure capable of assigning differentially regulated genes or entire gene signatures to defined cancer signaling pathways. Here we describe a graph-based approach that identifies cancer signaling pathways from published gene expression signatures. Published gene expression signatures are collected in a database (PubLiME: Published Lists of Microarray Experiments) enabled for cross-platform gene annotation. Significant co-occurrence modules composed of up to 10 genes in different gene expression signatures are identified. Significantly co-occurring genes are linked by an edge in an undirected graph. Edge-betweenness and k-clique clustering combined with graph modularity as a quality measure are used to identify communities in the resulting graph. The identified communities consist of cell cycle, apoptosis, phosphorylation cascade, extra cellular matrix, interferon and immune response regulators as well as communities of unknown function. The genes constituting different communities are characterized by common genomic features and strongly enriched cis-regulatory modules in their upstream regulatory regions that are consistent with pathway assignment of those genes.
@article{FinocchiaroMCM:2007,
author = {Finocchiaro, Giacomo and Mancuso, Francesco Mattia and Cittaro, Davide and Muller, Heiko},
title = {Graph-based identification of cancer signaling pathways from published gene expression signatures using PubLiME.},
journal = {Nucleic Acids Research},
volume = {35},
number = {7},
pages = {2343-55},
year = {2007},
doi = {10.1093/nar/gkm119},
}Marc Garcia-Arnau, Daniel Manrique, Alfonso Rodriguez-Paton, and Petr Sosik. A p system and a constructive membrane-inspired dna algorithm for solving the maximum clique problem. Bio Systems, 90(3):687—97, nov 2007.
We present a P system with replicated rewriting to solve the Maximum Clique Problem for a graph. Strings representing cliques are built gradually. This involves the use of inhibitors that control the space of all generated solutions to the problem. Calculating the maximum clique for a graph is a highly relevant issue not only on purely computational grounds, but also because of its relationship to fundamental problems in genomics. We propose to implement the designed P system by means of a DNA algorithm. This algorithm is then compared with two standard papers that addressed the same problem and its DNA implementation in the past. This comparison is carried out on the basis of a series of computational and physical parameters. Our solution features a significantly lower cost in terms of time, the number and size of strands, as well as the simplicity of the biological implementation. Boadilla del Monte s/n, 28660 Madrid, Spain. mgarciaarnau@alumnos.upm.es
@article{Garcia-ArnauMRS:2007,
author = {Garcia-Arnau, Marc and Manrique, Daniel and Rodriguez-Paton, Alfonso and Sosik, Petr},
title = {A P system and a constructive membrane-inspired DNA algorithm for solving the Maximum Clique Problem.},
journal = {Bio Systems},
volume = {90},
number = {3},
pages = {687-97},
year = {2007},
month = nov,
doi = {10.1016/j.biosystems.2007.02.005},
}Andrew C. Good. Novel dock clique driven 3d similarity database search tools for molecule shape matching and beyond: adding flexibility to the search for ligand kin. Journal of Molecular Graphics & Modelling, 26(3):656—66, oct 2007.
With readily available CPU power and copious disk storage, it is now possible to undertake rapid comparison of 3D properties derived from explicit ligand overlay experiments. With this in mind, shape software tools originally devised in the 1990s are revisited, modified and applied to the problem of ligand database shape comparison. The utility of Connolly surface data is highlighted using the program MAKESITE, which leverages surface normal data to a create ligand shape cast. This cast is applied directly within DOCK, allowing the program to be used unmodified as a shape searching tool. In addition, DOCK has undergone multiple modifications to create a dedicated ligand shape comparison tool KIN. Scoring has been altered to incorporate the original incarnation of Gaussian function derived shape description based on STO-3G atomic electron density. In addition, a tabu-like search refinement has been added to increase search speed by removing redundant starting orientations produced during clique matching. The ability to use exclusion regions, again based on Gaussian shape overlap, has also been integrated into the scoring function. The use of both DOCK with MAKESITE and KIN in database screening mode is illustrated using a published ligand shape virtual screening template. The advantages of using a clique-driven search paradigm are highlighted, including shape optimization within a pharmacophore constrained framework, and easy incorporation of additional scoring function modifications. The potential for further development of such methods is also discussed. andrew.good@bms.com
@article{Good:2007,
author = {Good, Andrew C.},
title = {Novel DOCK clique driven 3D similarity database search tools for molecule shape matching and beyond: adding flexibility to the search for ligand kin.},
journal = {Journal of Molecular Graphics & Modelling},
volume = {26},
number = {3},
pages = {656-66},
year = {2007},
month = oct,
doi = {10.1016/j.jmgm.2007.03.016},
}Radhey S. Gupta and Emily Lorenzini. Phylogeny and molecular signatures (conserved proteins and indels) that are specific for the bacteroidetes and chlorobi species. BMC Evolutionary Biology, 7:71, 2007.
Background
The Bacteroidetes and Chlorobi species constitute two main groups of the Bacteria that are closely related in phylogenetic trees. The Bacteroidetes species are widely distributed and include many important periodontal pathogens. In contrast, all Chlorobi are anoxygenic obligate photoautotrophs. Very few (or no) biochemical or molecular characteristics are known that are distinctive characteristics of these bacteria, or are commonly shared by them.
Results
Systematic blast searches were performed on each open reading frame in the genomes of Porphyromonas gingivalis W83, Bacteroides fragilis YCH46, B. thetaiotaomicron VPI-5482, Gramella forsetii KT0803, Chlorobium luteolum (formerly Pelodictyon luteolum) DSM 273 and Chlorobaculum tepidum (formerly Chlorobium tepidum) TLS to search for proteins that are uniquely present in either all or certain subgroups of Bacteroidetes and Chlorobi. These studies have identified > 600 proteins for which homologues are not found in other organisms. This includes 27 and 51 proteins that are specific for most of the sequenced Bacteroidetes and Chlorobi genomes, respectively; 52 and 38 proteins that are limited to species from the Bacteroidales and Flavobacteriales orders, respectively, and 5 proteins that are common to species from these two orders; 185 proteins that are specific for the Bacteroides genus. Additionally, 6 proteins that are uniquely shared by species from the Bacteroidetes and Chlorobi phyla (one of them also present in the Fibrobacteres) have also been identified. This work also describes two large conserved inserts in DNA polymerase III (DnaE) and alanyl-tRNA synthetase that are distinctive characteristics of the Chlorobi species and a 3 aa deletion in ClpB chaperone that is mainly found in various Bacteroidales, Flavobacteriales and Flexebacteraceae, but generally not found in the homologs from other organisms. Phylogenetic analyses of the Bacteroidetes and Chlorobi species is also reported based on concatenated sequences for 12 conserved proteins by different methods including the character compatibility (or clique) approach. The placement of Salinibacter ruber with other Bacteroidetes species was not resolved by other phylogenetic methods, but this affiliation was strongly supported by the character compatibility approach.
Conclusion
The molecular signatures described here provide novel tools for identifying and circumscribing species from the Bacteroidetes and Chlorobi phyla as well as some of their main groups in clear terms. These results also provide strong evidence that species from these two phyla (and also possibly Fibrobacteres) are specifically related to each other and they form a single superphylum. Functional studies on these proteins and indels should aid in the discovery of novel biochemical and physiological characteristics that are unique to these groups of bacteria. ON, Canada. gupta@mcmaster.ca
The Bacteroidetes and Chlorobi species constitute two main groups of the Bacteria that are closely related in phylogenetic trees. The Bacteroidetes species are widely distributed and include many important periodontal pathogens. In contrast, all Chlorobi are anoxygenic obligate photoautotrophs. Very few (or no) biochemical or molecular characteristics are known that are distinctive characteristics of these bacteria, or are commonly shared by them.
Results
Systematic blast searches were performed on each open reading frame in the genomes of Porphyromonas gingivalis W83, Bacteroides fragilis YCH46, B. thetaiotaomicron VPI-5482, Gramella forsetii KT0803, Chlorobium luteolum (formerly Pelodictyon luteolum) DSM 273 and Chlorobaculum tepidum (formerly Chlorobium tepidum) TLS to search for proteins that are uniquely present in either all or certain subgroups of Bacteroidetes and Chlorobi. These studies have identified > 600 proteins for which homologues are not found in other organisms. This includes 27 and 51 proteins that are specific for most of the sequenced Bacteroidetes and Chlorobi genomes, respectively; 52 and 38 proteins that are limited to species from the Bacteroidales and Flavobacteriales orders, respectively, and 5 proteins that are common to species from these two orders; 185 proteins that are specific for the Bacteroides genus. Additionally, 6 proteins that are uniquely shared by species from the Bacteroidetes and Chlorobi phyla (one of them also present in the Fibrobacteres) have also been identified. This work also describes two large conserved inserts in DNA polymerase III (DnaE) and alanyl-tRNA synthetase that are distinctive characteristics of the Chlorobi species and a 3 aa deletion in ClpB chaperone that is mainly found in various Bacteroidales, Flavobacteriales and Flexebacteraceae, but generally not found in the homologs from other organisms. Phylogenetic analyses of the Bacteroidetes and Chlorobi species is also reported based on concatenated sequences for 12 conserved proteins by different methods including the character compatibility (or clique) approach. The placement of Salinibacter ruber with other Bacteroidetes species was not resolved by other phylogenetic methods, but this affiliation was strongly supported by the character compatibility approach.
Conclusion
The molecular signatures described here provide novel tools for identifying and circumscribing species from the Bacteroidetes and Chlorobi phyla as well as some of their main groups in clear terms. These results also provide strong evidence that species from these two phyla (and also possibly Fibrobacteres) are specifically related to each other and they form a single superphylum. Functional studies on these proteins and indels should aid in the discovery of novel biochemical and physiological characteristics that are unique to these groups of bacteria. ON, Canada. gupta@mcmaster.ca
@article{GuptaL:2007,
author = {Gupta, Radhey S. and Lorenzini, Emily},
title = {Phylogeny and molecular signatures (conserved proteins and indels) that are specific for the Bacteroidetes and Chlorobi species.},
journal = {BMC Evolutionary Biology},
volume = {7},
pages = {71},
year = {2007},
doi = {10.1186/1471-2148-7-71},
}Radhey S. Gupta and Peter H. A. Sneath. Application of the character compatibility approach to generalized molecular sequence data: branching order of the proteobacterial subdivisions. Journal of Molecular Evolution, 64(1):90—100, jan 2007.
The character compatibility approach, which removes all homoplasic characters and involves finding the largest clique of compatible characters in a dataset, in principle, provides a powerful means for obtaining correct topology in difficult to resolve cases. However, the usefulness of this approach to generalized molecular sequence data for phylogeny determination has not been studied in the past. We have used this approach to determine the topology of 23 proteobacterial species (6 each of alpha-, beta- and gamma-, 3 delta-, and 2 epsilon-proteobacteria) using sequence data for 10 conserved proteins (Hsp60, Hsp70, EF-Tu, EF-G, alanyl-tRNA synthetase, RecA, GyrA, GyrB, RpoB and RpoC). All sites in the sequence alignments of these proteins where only two amino acids were found, with each amino acid present in at least two species, were selected. Mutual compatibility determination on these binary state sites was carried out by two means. In one case, all of these sites were combined into a large dataset (Set A; 957 characters) prior to compatibility analysis. In the second case, compatibility analysis was carried out on characters from individual proteins and all compatible sites were combined into a large dataset (Set B; 398 characters) for further studies. Upon compatibility analyses, the largest cliques that were obtained from Sets A and B consisted of 337 and 323 compatible characters, respectively. In these cliques, all proteobacterial subgroups were clearly distinguished and branching orders of most of the species were also resolved. The epsilon-proteobacteria exhibited the earliest branching, whereas the beta- and gamma-subgroups were found to have emerged last. The relative placement of the alpha- and delta-subgroups, however, was not resolved. The topology of these species was also determined based on 16S rRNA sequences and a concatenated dataset of sequences for all 10 proteins by means of neighbor-joining, maximum likelihood, and maximum parsimony methods. In the protein trees, all proteobacterial groups were reliably resolved and they branched in the following order: (epsilon(delta(alpha(beta,gamma)))). However, in the rRNA trees, the gamma- and beta-subgroups exhibited polyphyletic branching and many internal nodes were not resolved. These results indicate that the character compatibility analysis using generalized molecular sequence data provides a powerful means for evolutionary studies. Based on molecular sequences, it should be possible to obtain very large datasets of compatible characters that should prove very helpful in clarifying difficult to resolve phylogenetic relationships. Hamilton, Canada L8N 3Z5. gupta@mcmaster.ca
@article{GuptaS:2007,
author = {Gupta, Radhey S. and Sneath, Peter H. A.},
title = {Application of the character compatibility approach to generalized molecular sequence data: branching order of the proteobacterial subdivisions.},
journal = {Journal of Molecular Evolution},
volume = {64},
number = {1},
pages = {90-100},
year = {2007},
month = jan,
doi = {10.1007/s00239-006-0082-2},
}Delyse M. Hutchinson and Ronald M. Rapee. Do friends share similar body image and eating problems? the role of social networks and peer influences in early adolescence. Behaviour Research and Therapy, 45(7):1557—77, jul 2007.
This study examined the role of friendship networks and peer influences in body image concern, dietary restraint, extreme weight loss behaviours (EWLBs) and binge eating in a large community sample of young adolescent females. Based on girls’ self-reported friendship groups, social network analysis was used to identify 173 friendship cliques. Results indicated that clique members shared similar scores on measures of dieting, EWLB and binge eating, but not body image concern. Average clique scores for dieting, EWLB and binge eating, were also correlated significantly with clique averages on measures of perceived peer influence, body mass index and psychological variables. Multiple regression analyses indicated that perceived peer influences in weight-related attitudes and behaviours were predictive of individual girls’ level of body image concern, dieting, EWLB use and binge eating. Notably, an individual girl’s dieting and EWLB use could be predicted from her friends’ respective dieting and EWLB scores. Findings highlight the significance of the peer environment in body image and eating problems during early adolescence. d.hutchinson@med.unsw.edu.au
@article{HutchinsonR:2007,
author = {Hutchinson, Delyse M. and Rapee, Ronald M.},
title = {Do friends share similar body image and eating problems? The role of social networks and peer influences in early adolescence.},
journal = {Behaviour Research and Therapy},
volume = {45},
number = {7},
pages = {1557-77},
year = {2007},
month = jul,
doi = {10.1016/j.brat.2006.11.007},
}Alan Ironmonger, Benjamin Whittaker, Andrew J. Baron, Blandine Clique, Chris J. Adams, Alison E. Ashcroft, Peter G. Stockley, and Adam Nelson. Scanning conformational space with a library of stereo- and regiochemically diverse aminoglycoside derivatives: the discovery of new ligands for rna hairpin sequences. Organic & Biomolecular Chemistry, 5(7):1081—6, apr 2007.
A library of stereo- and regiochemically diverse aminoglycoside derivatives was screened at 1 microM using surface plasmon resonance (SPR) against RNA hairpin models of the bacterial A-site, and the HIV viral TAR and RRE sequences. In order to double the stereochemical diversity of the library, the compounds were screened against both enantiomers of each of these sequences. Remarkably, this initial screen suggested that the same four aminoglycoside derivatives bound most tightly to all three of the RNAs, suggesting that these compounds were good RNA binders which, nonetheless, discriminated poorly between the RNA sequences. The interactions between selected isomeric aminoglycoside derivatives and the RNA hairpins were then studied in more detail using an SPR assay. Three isomeric tight-binding aminoglycoside derivatives, which had been identified from the initial screen, were found to bind more tightly to the RNA hairpins (with K(D) values in the range 0.23 to 4.7 microM) than a fourth isomeric derivative (which had K(D) values in the range 6.0 to 30 microM). The magnitude of the tightest RNA-aminoglycoside interactions stemmed, in large part, from remarkably slow dissociation of the aminoglycosides from the RNA targets. The three tight-binding aminoglycoside derivatives were found, however, to discriminate rather poorly between alternative RNA sequences with, at best, around a twenty-fold difference in affinity for alternative RNA hairpin sequences. Within the aminoglycoside derivative library studied, high affinity for an RNA target was not accompanied by good discrimination between alternative RNA sequences.
@article{IronmongerWBCAASN:2007,
author = {Ironmonger, Alan and Whittaker, Benjamin and Baron, Andrew J. and Clique, Blandine and Adams, Chris J. and Ashcroft, Alison E. and Stockley, Peter G. and Nelson, Adam},
title = {Scanning conformational space with a library of stereo- and regiochemically diverse aminoglycoside derivatives: the discovery of new ligands for RNA hairpin sequences.},
journal = {Organic & Biomolecular Chemistry},
volume = {5},
number = {7},
pages = {1081-6},
year = {2007},
month = apr,
doi = {10.1039/b618683a},
}Gergely Palla, Albert-Laszlo Barabasi, and Tamas Vicsek. Quantifying social group evolution. Nature, 446(7136):664—7, apr 2007.
The rich set of interactions between individuals in society results in complex community structure, capturing highly connected circles of friends, families or professional cliques in a social network. Thanks to frequent changes in the activity and communication patterns of individuals, the associated social and communication network is subject to constant evolution. Our knowledge of the mechanisms governing the underlying community dynamics is limited, but is essential for a deeper understanding of the development and self-optimization of society as a whole. We have developed an algorithm based on clique percolation that allows us to investigate the time dependence of overlapping communities on a large scale, and thus uncover basic relationships characterizing community evolution. Our focus is on networks capturing the collaboration between scientists and the calls between mobile phone users. We find that large groups persist for longer if they are capable of dynamically altering their membership, suggesting that an ability to change the group composition results in better adaptability. The behaviour of small groups displays the opposite tendency-the condition for stability is that their composition remains unchanged. We also show that knowledge of the time commitment of members to a given community can be used for estimating the community’s lifetime. These findings offer insight into the fundamental differences between the dynamics of small groups and large institutions. 1A, H-1117 Budapest, Hungary.
@article{PallaBV:2007,
author = {Palla, Gergely and Barabasi, Albert-Laszlo and Vicsek, Tamas},
title = {Quantifying social group evolution.},
journal = {Nature},
volume = {446},
number = {7136},
pages = {664-7},
year = {2007},
month = apr,
doi = {10.1038/nature05670},
}Oleg Rokhlenko, Ydo Wexler, and Zohar Yakhini. Similarities and differences of gene expression in yeast stress conditions. Bioinformatics, 23(2):e184—90, jan 2007.
MOTIVATION AND
Methods
All living organisms and the survival of all cells critically depend on their ability to sense and quickly adapt to changes in the environment and to other stress conditions. We study stress response mechanisms in Saccharomyces cerevisiae by identifying genes that, according to very stringent criteria, have persistent co-expression under a variety of stress conditions. This is enabled through a fast clique search method applied to the intersection of several co-expression graphs calculated over the data of Gasch et al. This method exploits the topological characteristics of these graphs.
Results
We observe cliques in the intersection graphs that are much larger than expected under a null model of changing gene identities for different stress conditions but maintaining the co-expression topology within each one. Persistent cliques are analyzed to identify enriched function as well as enriched regulation by a small number of TFs. These TFs, therefore, characterize a universal and persistent reaction to stress response. We further demonstrate that the vertices (genes) of many cliques in the intersection graphs are co-localized in the yeast genome, to a degree far beyond the random expectation. Co-localization can hypothetically contribute to a quick co-ordinated response. We propose the use of persistent cliques in further study of properties of co-regulation. 32000, Israel. olegro@cs.technion.ac.il
Methods
All living organisms and the survival of all cells critically depend on their ability to sense and quickly adapt to changes in the environment and to other stress conditions. We study stress response mechanisms in Saccharomyces cerevisiae by identifying genes that, according to very stringent criteria, have persistent co-expression under a variety of stress conditions. This is enabled through a fast clique search method applied to the intersection of several co-expression graphs calculated over the data of Gasch et al. This method exploits the topological characteristics of these graphs.
Results
We observe cliques in the intersection graphs that are much larger than expected under a null model of changing gene identities for different stress conditions but maintaining the co-expression topology within each one. Persistent cliques are analyzed to identify enriched function as well as enriched regulation by a small number of TFs. These TFs, therefore, characterize a universal and persistent reaction to stress response. We further demonstrate that the vertices (genes) of many cliques in the intersection graphs are co-localized in the yeast genome, to a degree far beyond the random expectation. Co-localization can hypothetically contribute to a quick co-ordinated response. We propose the use of persistent cliques in further study of properties of co-regulation. 32000, Israel. olegro@cs.technion.ac.il
@article{RokhlenkoWY:2007,
author = {Rokhlenko, Oleg and Wexler, Ydo and Yakhini, Zohar},
title = {Similarities and differences of gene expression in yeast stress conditions.},
journal = {Bioinformatics},
volume = {23},
number = {2},
pages = {e184-90},
year = {2007},
month = jan,
doi = {10.1093/bioinformatics/btl308},
}Joe Z. Tsien. Real-time neural coding of memory. Progress in Brain Research, 165:105—22, 2007.
Recent identification of network-level functional coding units, termed neural cliques, in the hippocampus has allowed real-time patterns of memory traces to be mathematically described, intuitively visualized, and dynamically deciphered. Any given episodic event is represented and encoded by the activation of a set of neural clique assemblies that are organized in a categorical and hierarchical manner. This hierarchical feature-encoding pyramid is invariantly composed of the general feature-encoding clique at the bottom, sub-general feature-encoding cliques in the middle, and highly specific feature-encoding cliques at the top. This hierarchical and categorical organization of neural clique assemblies provides the network-level mechanism the capability of not only achieving vast storage capacity, but also generating commonalities from the individual behavioral episodes and converting them to the abstract concepts and generalized knowledge that are essential for intelligence and adaptive behaviors. Furthermore, activation patterns of the neural clique assemblies can be mathematically converted to strings of binary codes that would permit universal categorizations of the brain’s internal representations across individuals and species. Such universal brain codes can also potentially facilitate the unprecedented brain-machine interface communications. Boston, MA 02118, USA. jtsien@bu.edu
@article{Tsien:2007,
author = {Tsien, Joe Z.},
title = {Real-time neural coding of memory.},
journal = {Progress in Brain Research},
volume = {165},
pages = {105-22},
year = {2007},
doi = {10.1016/S0079-6123(06)65007-3},
}Hassan Younies and George O. Wesolowsky. Planar maximal covering location problem under block norm distance measure. Journal of the Operational Research Society, 58(6):740—750, 2007. [planar maximal covering location problem] Clique Partitioning Problem
This paper introduces a new model for the planar maximal covering location problem (PMCLP) under different block norms. The problem involves locating g facilities anywhere on the plane in order to cover the maximum number of n given demand points. The generalization, in this paper, is that the distance measures assigned to facilities are block norms of different types and different proximity measures. First, the PMCLP under different block norms is modelled as a maximum clique partition problem on an equivalent multi-interval graph. Then, the equivalent graph problem is modelled as an unconstrained binary quadratic problem (UQP). Both the maximum clique partition problem and the UQP are NP-hard problems; therefore, we solve the UQP format through a genetic algorithm heuristic. Computational examples are given.
@article{YouniesW:2007,
author = {Younies, Hassan and Wesolowsky, George O.},
title = {Planar maximal covering location problem under block norm distance measure},
journal = {Journal of the Operational Research Society},
volume = {58},
number = {6},
pages = {740-750},
year = {2007},
doi = {10.1057/palgrave.jors.2602172},
}Chunfang Zheng, Qian Zhu, and David Sankoff. Removing noise and ambiguities from comparative maps in rearrangement analysis. IEEE/Acm Transactions On Computational Biology and Bioinformatics / IEEE, Acm, 4(4):515—22, oct 2007.
Comparison of genomic maps is hampered by errors and ambiguities introduced by mapping technology, incorrectly resolved paralogy, small samples of markers and extensive genome rearrangement. We design an analysis to remove or resolve most of these problems and to extract corrected data where markers occur in consecutive strips in both genomes. To do this we introduce the notion of pre-strip, an efficient way of generating these, and a compatibility analysis culminating in a Maximum Weighted Clique (MWC) search. The output can be directly analyzed with genome rearrangement algorithms, allowing the restoration of some of the data not incorporated into the clique solution. We investigate the trade-off between criteria for discarding excessive pre-strips to make MWC feasible, in terms of retaining as many markers as possible in the solution and producing an economical rearrangement analysis. We explore these questions through simulation and through comparison of the rice and sorghum genomes. czhen033@uottawa.ca
@article{ZhengZS:2007,
author = {Zheng, Chunfang and Zhu, Qian and Sankoff, David},
title = {Removing noise and ambiguities from comparative maps in rearrangement analysis.},
journal = {IEEE/Acm Transactions On Computational Biology and Bioinformatics / IEEE, Acm},
volume = {4},
number = {4},
pages = {515-22},
year = {2007},
month = oct,
doi = {10.1109/TCBB.2007.1075},
}Balázs Adamcsek, Gergely Palla, Illés J. Farkas, Imre Derényi, and Tamás Vicsek. Cfinder: locating cliques and overlapping modules in biological networks. Bioinformatics, 22(8):1021—1023, 2006.
Summary: Most cellular tasks are performed not by individual proteins, but by groups of functionally associated proteins, often referred to as modules. In a protein assocation network modules appear as groups of densely interconnected nodes, also called communities or clusters. These modules often overlap with each other and form a network of their own, in which nodes (links) represent the modules (overlaps). We introduce CFinder, a fast program locating and visualizing overlapping, densely interconnected groups of nodes in undirected graphs, and allowing the user to easily navigate between the original graph and the web of these groups. We show that in gene (protein) association networks CFinder can be used to predict the function(s) of a single protein and to discover novel modules. CFinder is also very efficient for locating the cliques of large sparse graphs.
Availability: CFinder (for Windows, Linux and Macintosh) and its manual can be downloaded from http://angel.elte.hu/clustering.
Availability: CFinder (for Windows, Linux and Macintosh) and its manual can be downloaded from http://angel.elte.hu/clustering.
@article{AdamcsekPFDV:2006,
author = {Adamcsek, Bal{\'a}zs and Palla, Gergely and Farkas, Ill{\'e}s J. and Der{\'e}nyi, Imre and Vicsek, Tam{\'a}s},
title = {CFinder: locating cliques and overlapping modules in biological networks},
journal = {Bioinformatics},
volume = {22},
number = {8},
pages = {1021--1023},
publisher = {Oxford University Press},
year = {2006},
doi = {10.1093/bioinformatics/btl039},
}Edward J. Barker, David Buttar, David A. Cosgrove, Eleanor J. Gardiner, Paula Kitts, Peter Willett, and Valerie J. Gillet. Scaffold hopping using clique detection applied to reduced graphs. Journal of Chemical Information and Modeling, 46(2):503—11, mar 2006.
Similarity-based methods for virtual screening are widely used. However, conventional searching using 2D chemical fingerprints or 2D graphs may retrieve only compounds which are structurally very similar to the original target molecule. Of particular current interest then is scaffold hopping, that is, the ability to identify molecules that belong to different chemical series but which could form the same interactions with a receptor. Reduced graphs provide summary representations of chemical structures and, therefore, offer the potential to retrieve compounds that are similar in terms of their gross features rather than at the atom-bond level. Using only a fingerprint representation of such graphs, we have previously shown that actives retrieved were more diverse than those found using Daylight fingerprints. Maximum common substructures give an intuitively reasonable view of the similarity between two molecules. However, their calculation using graph-matching techniques is too time-consuming for use in practical similarity searching in larger data sets. In this work, we exploit the low cardinality of the reduced graph in graph-based similarity searching. We reinterpret the reduced graph as a fully connected graph using the bond-distance information of the original graph. We describe searches, using both the maximum common induced subgraph and maximum common edge subgraph formulations, on the fully connected reduced graphs and compare the results with those obtained using both conventional chemical and reduced graph fingerprints. We show that graph matching using fully connected reduced graphs is an effective retrieval method and that the actives retrieved are likely to be topologically different from those retrieved using conventional 2D methods. University of Sheffield, Western Bank, Sheffield S10 2TN, United Kingdom.
@article{BarkerBCGKWG:2006,
author = {Barker, Edward J. and Buttar, David and Cosgrove, David A. and Gardiner, Eleanor J. and Kitts, Paula and Willett, Peter and Gillet, Valerie J.},
title = {Scaffold hopping using clique detection applied to reduced graphs.},
journal = {Journal of Chemical Information and Modeling},
volume = {46},
number = {2},
pages = {503-11},
year = {2006},
month = mar,
doi = {10.1021/ci050347r},
}Vladimir Boginski, Sergiy Butenko, and Panos M. Pardalos. Mining market data: A network approach. Computers & Operations Research, 33(11):3171—3184, 2006.
We consider anetwork representation of the stock market data referred to as the market graph, which is constructed by calculating cross-correlations between pairs of stocks based on the opening prices data over a certain period of time. We study the evolution of the structural properties of the market graph over time and draw conclusions regarding the dynamics of the stock market development based on the interpretation of the obtained results.
@article{BoginskiBP:2006,
author = {Boginski, Vladimir and Butenko, Sergiy and Pardalos, Panos M.},
title = {Mining market data: A network approach},
journal = {Computers & Operations Research},
volume = {33},
number = {11},
pages = {3171--3184},
publisher = {Elsevier},
year = {2006},
doi = {10.1016/j.cor.2005.01.027},
}Jun Feng, Ashish Sanil, and S. Stanley Young. Pharmid: pharmacophore identification using gibbs sampling. Journal of Chemical Information and Modeling, 46(3):1352—9, may 2006.
The binding of a small molecule to a protein is inherently a 3D matching problem. As crystal structures are not available for most drug targets, there is a need to be able to infer from bioassay data the key binding features of small molecules and their disposition in space, the pharmacophore. Fingerprints of 3D features and a modification of Gibbs sampling to align a set of known flexible ligands, where all compounds are active, are used to discern possible pharmacophores. A clique detection method is used to map the features back onto the binding conformations. The complete algorithm is described in detail, and it is shown that the method can find common superimposition for several test data sets. The method reproduces answers very close to the crystal structure and literature pharmacophores in the examples presented. The basic algorithm is relatively fast and can easily deal with up to 100 compounds and tens of thousands of conformations. The algorithm is also able to handle multiple binding mode problems, which means it can superimpose molecules within the same data set according to two different sets of binding features. We demonstrate the successful use of this algorithm for multiple binding modes for a set of D2 and D4 ligands. Park, North Carolina 27709-4006, USA.
@article{FengSY:2006,
author = {Feng, Jun and Sanil, Ashish and Young, S. Stanley},
title = {PharmID: pharmacophore identification using Gibbs sampling.},
journal = {Journal of Chemical Information and Modeling},
volume = {46},
number = {3},
pages = {1352-9},
year = {2006},
month = may,
doi = {10.1021/ci050427v},
}Kevin Hambly, Joseph Danzer, Steven Muskal, and Derek A. Debe. Interrogating the druggable genome with structural informatics. Molecular Diversity, 10(3):273—81, aug 2006.
Structural genomics projects are producing protein structure data at an unprecedented rate. In this paper, we present the Target Informatics Platform (TIP), a novel structural informatics approach for amplifying the rapidly expanding body of experimental protein structure information to enhance the discovery and optimization of small molecule protein modulators on a genomic scale. In TIP, existing experimental structure information is augmented using a homology modeling approach, and binding sites across multiple target families are compared using a clique detection algorithm. We report here a detailed analysis of the structural coverage for the set of druggable human targets, highlighting drug target families where the level of structural knowledge is currently quite high, as well as those areas where structural knowledge is sparse. Furthermore, we demonstrate the utility of TIP’s intra- and inter-family binding site similarity analysis using a series of retrospective case studies. Our analysis underscores the utility of a structural informatics infrastructure for extracting drug discovery-relevant information from structural data, aiding researchers in the identification of lead discovery and optimization opportunities as well as potential "off-target" liabilities. khambly@eidogen-sertanty.com
@article{HamblyDMD:2006,
author = {Hambly, Kevin and Danzer, Joseph and Muskal, Steven and Debe, Derek A.},
title = {Interrogating the druggable genome with structural informatics.},
journal = {Molecular Diversity},
volume = {10},
number = {3},
pages = {273-81},
year = {2006},
month = aug,
doi = {10.1007/s11030-006-9035-3},
}Xiuzhen Huang, Jing Lai, and Steven F. Jennings. Maximum common subgraph: some upper bound and lower bound results. BMC Bioinformatics, 7 Suppl 4:S6, 2006.
Background
Structure matching plays an important part in understanding the functional role of biological structures. Bioinformatics assists in this effort by reformulating this process into a problem of finding a maximum common subgraph between graphical representations of these structures. Among the many different variants of the maximum common subgraph problem, the maximum common induced subgraph of two graphs is of special interest.
Results
Based on current research in the area of parameterized computation, we derive a new lower bound for the exact algorithms of the maximum common induced subgraph of two graphs which is the best currently known. Then we investigate the upper bound and design techniques for approaching this problem, specifically, reducing it to one of finding a maximum clique in the product graph of the two given graphs. Considering the upper bound result, the derived lower bound result is asymptotically tight.
Conclusion
Parameterized computation is a viable approach with great potential for investigating many applications within bioinformatics, such as the maximum common subgraph problem studied in this paper. With an improved hardness result and the proposed approaches in this paper, future research can be focused on further exploration of efficient approaches for different variants of this problem within the constraints imposed by real applications. Arkansas 72467, USA. xzhuang@csm.astate.edu
Structure matching plays an important part in understanding the functional role of biological structures. Bioinformatics assists in this effort by reformulating this process into a problem of finding a maximum common subgraph between graphical representations of these structures. Among the many different variants of the maximum common subgraph problem, the maximum common induced subgraph of two graphs is of special interest.
Results
Based on current research in the area of parameterized computation, we derive a new lower bound for the exact algorithms of the maximum common induced subgraph of two graphs which is the best currently known. Then we investigate the upper bound and design techniques for approaching this problem, specifically, reducing it to one of finding a maximum clique in the product graph of the two given graphs. Considering the upper bound result, the derived lower bound result is asymptotically tight.
Conclusion
Parameterized computation is a viable approach with great potential for investigating many applications within bioinformatics, such as the maximum common subgraph problem studied in this paper. With an improved hardness result and the proposed approaches in this paper, future research can be focused on further exploration of efficient approaches for different variants of this problem within the constraints imposed by real applications. Arkansas 72467, USA. xzhuang@csm.astate.edu
@article{HuangLJ:2006,
author = {Huang, Xiuzhen and Lai, Jing and Jennings, Steven F.},
title = {Maximum common subgraph: some upper bound and lower bound results.},
journal = {BMC Bioinformatics},
volume = {7 Suppl 4},
pages = {S6},
year = {2006},
doi = {10.1186/1471-2105-7-S4-S6},
}Woochang Hwang, Young-Rae Cho, Aidong Zhang, and Murali Ramanathan. A novel functional module detection algorithm for protein-protein interaction networks. Algorithms for Molecular Biology, 1:24, 2006.
Background
The sparse connectivity of protein-protein interaction data sets makes identification of functional modules challenging. The purpose of this study is to critically evaluate a novel clustering technique for clustering and detecting functional modules in protein-protein interaction networks, termed STM.
Results
STM selects representative proteins for each cluster and iteratively refines clusters based on a combination of the signal transduced and graph topology. STM is found to be effective at detecting clusters with a diverse range of interaction structures that are significant on measures of biological relevance. The STM approach is compared to six competing approaches including the maximum clique, quasi-clique, minimum cut, betweeness cut and Markov Clustering (MCL) algorithms. The clusters obtained by each technique are compared for enrichment of biological function. STM generates larger clusters and the clusters identified have p-values that are approximately 125-fold better than the other methods on biological function. An important strength of STM is that the percentage of proteins that are discarded to create clusters is much lower than the other approaches.
Conclusion
STM outperforms competing approaches and is capable of effectively detecting both densely and sparsely connected, biologically relevant functional modules with fewer discards. Buffalo, USA. whwang2@cse.buffalo.edu
The sparse connectivity of protein-protein interaction data sets makes identification of functional modules challenging. The purpose of this study is to critically evaluate a novel clustering technique for clustering and detecting functional modules in protein-protein interaction networks, termed STM.
Results
STM selects representative proteins for each cluster and iteratively refines clusters based on a combination of the signal transduced and graph topology. STM is found to be effective at detecting clusters with a diverse range of interaction structures that are significant on measures of biological relevance. The STM approach is compared to six competing approaches including the maximum clique, quasi-clique, minimum cut, betweeness cut and Markov Clustering (MCL) algorithms. The clusters obtained by each technique are compared for enrichment of biological function. STM generates larger clusters and the clusters identified have p-values that are approximately 125-fold better than the other methods on biological function. An important strength of STM is that the percentage of proteins that are discarded to create clusters is much lower than the other approaches.
Conclusion
STM outperforms competing approaches and is capable of effectively detecting both densely and sparsely connected, biologically relevant functional modules with fewer discards. Buffalo, USA. whwang2@cse.buffalo.edu
@article{HwangCZR:2006,
author = {Hwang, Woochang and Cho, Young-Rae and Zhang, Aidong and Ramanathan, Murali},
title = {A novel functional module detection algorithm for protein-protein interaction networks.},
journal = {Algorithms for Molecular Biology},
volume = {1},
pages = {24},
year = {2006},
doi = {10.1186/1748-7188-1-24},
}Chih-Hung Jen, Iain W. Manfield, Ioannis Michalopoulos, John W. Pinney, William G. T Willats, Philip M. Gilmartin, and David R. Westhead. The arabidopsis co-expression tool (act): a www-based tool and database for microarray-based gene expression analysis. The Plant Journal, 46(2):336—48, apr 2006.
We present a new WWW-based tool for plant gene analysis, the Arabidopsis Co-Expression Tool (ACT), based on a large Arabidopsis thaliana microarray data set obtained from the Nottingham Arabidopsis Stock Centre. The co-expression analysis tool allows users to identify genes whose expression patterns are correlated across selected experiments or the complete data set. Results are accompanied by estimates of the statistical significance of the correlation relationships, expressed as probability (P) and expectation (E) values. Additionally, highly ranked genes on a correlation list can be examined using the novel clique finder tool to determine the sets of genes most likely to be regulated in a similar manner. In combination, these tools offer three levels of analysis: creation of correlation lists of co-expressed genes, refinement of these lists using two-dimensional scatter plots, and dissection into cliques of co-regulated genes. We illustrate the applications of the software by analysing genes encoding functionally related proteins, as well as pathways involved in plant responses to environmental stimuli. These analyses demonstrate novel biological relationships underlying the observed gene co-expression patterns. To demonstrate the ability of the software to develop testable hypotheses on gene function within a defined biological process we have used the example of cell wall biosynthesis genes. The resource is freely available at http://www.arabidopsis.leeds.ac.uk/ACT/ Yorkshire, LS2 9JT, UK.
@article{JenMMPWGW:2006,
author = {Jen, Chih-Hung and Manfield, Iain W. and Michalopoulos, Ioannis and Pinney, John W. and Willats, William G. T and Gilmartin, Philip M. and Westhead, David R.},
title = {The Arabidopsis co-expression tool (ACT): a WWW-based tool and database for microarray-based gene expression analysis.},
journal = {The Plant Journal},
volume = {46},
number = {2},
pages = {336-48},
year = {2006},
month = apr,
doi = {10.1111/j.1365-313X.2006.02681.x},
}Katharina A. Lehmann, Michael Kaufmann, Stephan Steigele, and Kay Nieselt. On the maximal cliques in c-max-tolerance graphs and their application in clustering molecular sequences. Algorithms for Molecular Biology, 1(1), 2006. [clustering, generation of phylogenetic trees]
Given a set S of n locally aligned sequences, it is a needed prerequisite to partition it into groups of very similar sequences to facilitate subsequent computations, such as the generation of a phylogenetic tree. This article introduces a new method of clustering which partitions S into subsets such that the overlap of each pair of sequences within a subset is at least a given percentage c of the lengths of the two sequences. We show that this problem can be reduced to finding all maximal cliques in a special kind of max-tolerance graph which we call a c-max-tolerance graph. Previously we have shown that finding all maximal cliques in general max-tolerance graphs can be done efficiently in O(n3 + out). Here, using a new kind of sweep-line algorithm, we show that the restriction to c-max-tolerance graphs yields a better runtime of O(n2 log n + out). Furthermore, we present another algorithm which is much easier to implement, and though theoretically slower than the first one, is still running in polynomial time. We then experimentally analyze the number and structure of all maximal cliques in a c-max-tolerance graph, depending on the chosen c-value. We apply our simple algorithm to artificial and biological data and we show that this implementation is much faster than the well-known application Cliquer. By introducing a new heuristic that uses the set of all maximal cliques to partition S, we finally show that the computed partition gives a reasonable clustering for biological data sets.
@article{LehmannKSN:2006,
author = {Lehmann, Katharina A. and Kaufmann, Michael and Steigele, Stephan and Nieselt, Kay},
title = {On the maximal cliques in c-max-tolerance graphs and their application in clustering molecular sequences},
journal = {Algorithms for Molecular Biology},
volume = {1},
number = {1},
year = {2006},
doi = {10.1186/1748-7188-1-9},
}Longnian Lin, Remus Osan, and Joe Z. Tsien. Organizing principles of real-time memory encoding: neural clique assemblies and universal neural codes. Trends in Neurosciences, 29(1):48—57, jan 2006.
Recent identification of network-level coding units, termed neural cliques, in the hippocampus has enabled real-time patterns of memory traces to be mathematically described, directly visualized, and dynamically deciphered. These memory coding units are functionally organized in a categorical and hierarchical manner, suggesting that internal representations of external events in the brain is achieved not by recording exact details of those events, but rather by recreating its own selective pictures based on cognitive importance. This neural-clique-based hierarchical-extraction and parallel-binding process enables the brain to acquire not only large storage capacity but also abstraction and generalization capability. In addition, activation patterns of the neural clique assemblies can be converted to strings of binary codes that would permit universal categorizations of internal brain representations across individuals and species. Engineering, Boston University, Boston, MA 02118, USA.
@article{LinOT:2006,
author = {Lin, Longnian and Osan, Remus and Tsien, Joe Z.},
title = {Organizing principles of real-time memory encoding: neural clique assemblies and universal neural codes.},
journal = {Trends in Neurosciences},
volume = {29},
number = {1},
pages = {48-57},
year = {2006},
month = jan,
doi = {10.1016/j.tins.2005.11.004},
}Iain W. Manfield, Chih-Hung Jen, John W. Pinney, Ioannis Michalopoulos, James R. Bradford, Philip M. Gilmartin, and David R. Westhead. Arabidopsis co-expression tool (act): web server tools for microarray-based gene expression analysis. Nucleic Acids Research, 34(Web Server issue):W504—9, jul 2006. [molecular biology - gene expression networks]
The Arabidopsis Co-expression Tool, ACT, ranks the genes across a large microarray dataset according to how closely their expression follows the expression of a query gene. A database stores pre-calculated co-expression results for approximately 21,800 genes based on data from over 300 arrays. These results can be corroborated by calculation of co-expression results for user-defined sub-sets of arrays or experiments from the NASC/GARNet array dataset. Clique Finder (CF) identifies groups of genes which are consistently co-expressed with each other across a user-defined co-expression list. The parameters can be altered easily to adjust cluster size and the output examined for optimal inclusion of genes with known biological roles. Alternatively, a Scatter Plot tool displays the correlation coefficients for all genes against two user-selected queries on a scatter plot which can be useful for visual identification of clusters of genes with similar r-values. User-input groups of genes can be highlighted on the scatter plots. Inclusion of genes with known biology in sets of genes identified using CF and Scatter Plot tools allows inferences to be made about the roles of the other genes in the set and both tools can therefore be used to generate short lists of genes for further characterization. ACT is freely available at www.Arabidopsis.leeds.ac.uk/ACT.
@article{ManfieldJPMBGW:2006,
author = {Manfield, Iain W. and Jen, Chih-Hung and Pinney, John W. and Michalopoulos, Ioannis and Bradford, James R. and Gilmartin, Philip M. and Westhead, David R.},
title = {Arabidopsis Co-expression Tool (ACT): web server tools for microarray-based gene expression analysis.},
journal = {Nucleic Acids Research},
volume = {34},
number = {Web Server issue},
pages = {W504-9},
year = {2006},
month = jul,
doi = {10.1093/nar/gkl204},
}Amrita Pati, Cecilia Vasquez-Robinet, Lenwood S. Heath, Ruth Grene, and T. M. Murali. Xcisclique: analysis of regulatory bicliques. BMC Bioinformatics, 7:218, 2006. [molecular biology - gene regulatory networks]
Background
Modeling of cis-elements or regulatory motifs in promoter (upstream) regions of genes is a challenging computational problem. In this work, set of regulatory motifs simultaneously present in the promoters of a set of genes is modeled as a biclique in a suitably defined bipartite graph. A biologically meaningful co-occurrence of multiple cis-elements in a gene promoter is assessed by the combined analysis of genomic and gene expression data. Greater statistical significance is associated with a set of genes that shares a common set of regulatory motifs, while simultaneously exhibiting highly correlated gene expression under given experimental conditions.
Methods
XcisClique, the system developed in this work, is a comprehensive infrastructure that associates annotated genome and gene expression data, models known cis-elements as regular expressions, identifies maximal bicliques in a bipartite gene-motif graph; and ranks bicliques based on their computed statistical significance. Significance is a function of the probability of occurrence of those motifs in a biclique (a hypergeometric distribution), and on the new sum of absolute values statistic (SAV) that uses Spearman correlations of gene expression vectors. SAV is a statistic well-suited for this purpose as described in the discussion.
Results
XcisClique identifies new motif and gene combinations that might indicate as yet unidentified involvement of sets of genes in biological functions and processes. It currently supports Arabidopsis thaliana and can be adapted to other organisms, assuming the existence of annotated genomic sequences, suitable gene expression data, and identified regulatory motifs. A subset of Xcis Clique functionalities, including the motif visualization component MotifSee, source code, and supplementary material are available at https://bioinformatics.cs.vt.edu/xcisclique/. University, Blacksburg, VA 24061, USA. apati@vt.edu
Modeling of cis-elements or regulatory motifs in promoter (upstream) regions of genes is a challenging computational problem. In this work, set of regulatory motifs simultaneously present in the promoters of a set of genes is modeled as a biclique in a suitably defined bipartite graph. A biologically meaningful co-occurrence of multiple cis-elements in a gene promoter is assessed by the combined analysis of genomic and gene expression data. Greater statistical significance is associated with a set of genes that shares a common set of regulatory motifs, while simultaneously exhibiting highly correlated gene expression under given experimental conditions.
Methods
XcisClique, the system developed in this work, is a comprehensive infrastructure that associates annotated genome and gene expression data, models known cis-elements as regular expressions, identifies maximal bicliques in a bipartite gene-motif graph; and ranks bicliques based on their computed statistical significance. Significance is a function of the probability of occurrence of those motifs in a biclique (a hypergeometric distribution), and on the new sum of absolute values statistic (SAV) that uses Spearman correlations of gene expression vectors. SAV is a statistic well-suited for this purpose as described in the discussion.
Results
XcisClique identifies new motif and gene combinations that might indicate as yet unidentified involvement of sets of genes in biological functions and processes. It currently supports Arabidopsis thaliana and can be adapted to other organisms, assuming the existence of annotated genomic sequences, suitable gene expression data, and identified regulatory motifs. A subset of Xcis Clique functionalities, including the motif visualization component MotifSee, source code, and supplementary material are available at https://bioinformatics.cs.vt.edu/xcisclique/. University, Blacksburg, VA 24061, USA. apati@vt.edu
@article{PatiVHGM:2006,
author = {Pati, Amrita and Vasquez-Robinet, Cecilia and Heath, Lenwood S. and Grene, Ruth and Murali, T. M.},
title = {XcisClique: analysis of regulatory bicliques.},
journal = {BMC Bioinformatics},
volume = {7},
pages = {218},
year = {2006},
doi = {10.1186/1471-2105-7-218},
}Brynn H. Voy, Jon A. Scharff, Andy D. Perkins, Arnold M. Saxton, Bhavesh Borate, Elissa J. Chesler, Lisa K. Branstetter, and Michael A. Langston. Extracting gene networks for low-dose radiation using graph theoretical algorithms. Plos Computational Biology, 2(7):e89, jul 2006. [molecular biology - gene expression networks]
Genes with common functions often exhibit correlated expression levels, which can be used to identify sets of interacting genes from microarray data. Microarrays typically measure expression across genomic space, creating a massive matrix of co-expression that must be mined to extract only the most relevant gene interactions. We describe a graph theoretical approach to extracting co-expressed sets of genes, based on the computation of cliques. Unlike the results of traditional clustering algorithms, cliques are not disjoint and allow genes to be assigned to multiple sets of interacting partners, consistent with biological reality. A graph is created by thresholding the correlation matrix to include only the correlations most likely to signify functional relationships. Cliques computed from the graph correspond to sets of genes for which significant edges are present between all members of the set, representing potential members of common or interacting pathways. Clique membership can be used to infer function about poorly annotated genes, based on the known functions of better-annotated genes with which they share clique membership (i.e., "guilt-by-association"). We illustrate our method by applying it to microarray data collected from the spleens of mice exposed to low-dose ionizing radiation. Differential analysis is used to identify sets of genes whose interactions are impacted by radiation exposure. The correlation graph is also queried independently of clique to extract edges that are impacted by radiation. We present several examples of multiple gene interactions that are altered by radiation exposure and thus represent potential molecular pathways that mediate the radiation response. voybh@ornl.gov
@article{VoySPSBCBL:2006,
author = {Voy, Brynn H. and Scharff, Jon A. and Perkins, Andy D. and Saxton, Arnold M. and Borate, Bhavesh and Chesler, Elissa J. and Branstetter, Lisa K. and Langston, Michael A.},
title = {Extracting gene networks for low-dose radiation using graph theoretical algorithms.},
journal = {Plos Computational Biology},
volume = {2},
number = {7},
pages = {e89},
year = {2006},
month = jul,
doi = {10.1371/journal.pcbi.0020089},
}Haiyuan Yu, Alberto Paccanaro, Valery Trifonov, and Mark Gerstein. Predicting interactions in protein networks by completing defective cliques. Bioinformatics, 22(7):823—9, apr 2006.
Datasets obtained by large-scale, high-throughput methods for detecting protein-protein interactions typically suffer from a relatively high level of noise. We describe a novel method for improving the quality of these datasets by predicting missed protein-protein interactions, using only the topology of the protein interaction network observed by the large-scale experiment. The central idea of the method is to search the protein interaction network for defective cliques (nearly complete complexes of pairwise interacting proteins), and predict the interactions that complete them. We formulate an algorithm for applying this method to large-scale networks, and show that in practice it is efficient and has good predictive performance. More information can be found on our website http://topnet.gersteinlab.org/clique/
Contact
Mark.Gerstein@yale.edu SUPPLEMENTARY INFORMATION: Supplementary Materials are available at Bioinformatics online. University, PO Box 208114, New Haven, CT 06520-8285, USA.
Contact
Mark.Gerstein@yale.edu SUPPLEMENTARY INFORMATION: Supplementary Materials are available at Bioinformatics online. University, PO Box 208114, New Haven, CT 06520-8285, USA.
@article{YuPTG:2006,
author = {Yu, Haiyuan and Paccanaro, Alberto and Trifonov, Valery and Gerstein, Mark},
title = {Predicting interactions in protein networks by completing defective cliques.},
journal = {Bioinformatics},
volume = {22},
number = {7},
pages = {823-9},
year = {2006},
month = apr,
doi = {10.1093/bioinformatics/btl014},
}Ziding Zhang and Martin G. Grigorov. Similarity networks of protein binding sites. Proteins, 62(2):470—8, feb 2006.
An increasing attention has been dedicated to the characterization of complex networks within the protein world. This work is reporting how we uncovered networked structures that reflected the structural similarities among protein binding sites. First, a 211 binding sites dataset has been compiled by removing the redundant proteins in the Protein Ligand Database (PLD) (http://www-mitchell.ch.cam.ac.uk/pld/). Using a clique detection algorithm we have performed all-against-all binding site comparisons among the 211 available ones. Within the set of nodes representing each binding site an edge was added whenever a pair of binding sites had a similarity higher than a threshold value. The generated similarity networks revealed that many nodes had few links and only few were highly connected, but due to the limited data available it was not possible to definitively prove a scale-free architecture. Within the same dataset, the binding site similarity networks were compared with the networks of sequence and fold similarity networks. In the protein world, indications were found that structure is better conserved than sequence, but on its own, sequence was better conserved than the subset of functional residues forming the binding site. Because a binding site is strongly linked with protein function, the identification of protein binding site similarity networks could accelerate the functional annotation of newly identified genes. In view of this we have discussed several potential applications of binding site similarity networks, such as the construction of novel binding site classification databases, as well as the implications for protein molecular design in general and computational chemogenomics in particular. Switzerland.
@article{ZhangG:2006,
author = {Zhang, Ziding and Grigorov, Martin G.},
title = {Similarity networks of protein binding sites.},
journal = {Proteins},
volume = {62},
number = {2},
pages = {470-8},
year = {2006},
month = feb,
doi = {10.1002/prot.20752},
}Chi Zhang, Song Liu, and Yaoqi Zhou. Fast and accurate method for identifying high-quality protein-interaction modules by clique merging and its application to yeast. Journal of Proteome Research, 5(4):801—7, apr 2006.
Molecular networks in cells are organized into functional modules, where genes in the same module interact densely with each other and participate in the same biological process. Thus, identification of modules from molecular networks is an important step toward a better understanding of how cells function through the molecular networks. Here, we propose a simple, automatic method, called MC(2), to identify functional modules by enumerating and merging cliques in the protein-interaction data from large-scale experiments. Application of MC(2) to the S. cerevisiae protein-interaction data produces 84 modules, whose sizes range from 4 to 69 genes. The majority of the discovered modules are significantly enriched with a highly specific process term (at least 4 levels below root) and a specific cellular component in Gene Ontology (GO) tree. The average fraction of genes with the most enriched GO term for all modules is 82% for specific biological processes and 78% for specific cellular components. In addition, the predicted modules are enriched with coexpressed proteins. These modules are found to be useful for annotating unknown genes and uncovering novel functions of known genes. MC(2) is efficient, and takes only about 5 min to identify modules from the current yeast gene interaction network with a typical PC (Intel Xeon 2.5 GHz CPU and 512 MB memory). The CPU time of MC(2) is affordable (12 h) even when the number of interactions is increased by a factor of 10. MC(2) and its results are publicly available on http://theory.med.buffalo.edu/MC2. of Physiology & Biophysics, State University of New York at Buffalo, 124 Sherman Hall, Buffalo, New York 14214, USA.
@article{ZhangLZ:2006,
author = {Zhang, Chi and Liu, Song and Zhou, Yaoqi},
title = {Fast and accurate method for identifying high-quality protein-interaction modules by clique merging and its application to yeast.},
journal = {Journal of Proteome Research},
volume = {5},
number = {4},
pages = {801-7},
year = {2006},
month = apr,
doi = {10.1021/pr050366g},
}Shihua Zhang, Xuemei Ning, and Xiang-Sun Zhang. Identification of functional modules in a ppi network by clique percolation clustering. Computational Biology and Chemistry, 30(6):445—51, dec 2006.
Large-scale experiments and data integration have provided the opportunity to systematically analyze and comprehensively understand the topology of biological networks and biochemical processes in cells. Modular architecture which encompasses groups of genes/proteins involved in elementary biological functional units is a basic form of the organization of interacting proteins. Here we apply a graph clustering algorithm based on clique percolation clustering to detect overlapping network modules of a protein-protein interaction (PPI) network. Our analysis of the yeast Sacchromyces cerevisiae suggests that most of the detected modules correspond to one or more experimentally functional modules and half of these annotated modules match well with experimentally determined protein complexes. Our method of analysis can of course be applied to protein-protein interaction data for any species and even other biological networks. 100080, China. zsh@amss.ac.cn
@article{ZhangNZ:2006,
author = {Zhang, Shihua and Ning, Xuemei and Zhang, Xiang-Sun},
title = {Identification of functional modules in a PPI network by clique percolation clustering.},
journal = {Computational Biology and Chemistry},
volume = {30},
number = {6},
pages = {445-51},
year = {2006},
month = dec,
doi = {10.1016/j.compbiolchem.2006.10.001},
}Normand Carpentier and Francine Ducharme. Support network transformations in the first stages of the caregiver’s career. Qualitative Health Research, 15(3):289—311, mar 2005.
The purpose of this article is to propose a method to facilitate analysis of the processes involved in the transformation of support networks for caregivers of persons with dementia. The authors are particularly interested in the preliminary phases of the caregiver’s career: the initial period ranging from the first manifestations of dementia to the confirmation of a diagnosis. This method combines the social network approach with narrative analysis. The authors discuss two cases to illustrate the concepts of density and clique to explain the maintenance and dissolution of the caregiver’s supportive relationships. This method shows significant potential, in that it will help researchers explore social mechanisms related to the development of supportive relationships. geriatrie de Montreal, Quebec, Canada.
@article{CarpentierD:2005,
author = {Carpentier, Normand and Ducharme, Francine},
title = {Support network transformations in the first stages of the caregiver's career.},
journal = {Qualitative Health Research},
volume = {15},
number = {3},
pages = {289-311},
year = {2005},
month = mar,
doi = {10.1177/1049732304270813},
}Yu Chen and Gordon M. Crippen. A novel approach to structural alignment using realistic structural and environmental information. Protein Science, 14(12):2935—46, dec 2005.
In the era of structural genomics, it is necessary to generate accurate structural alignments in order to build good templates for homology modeling. Although a great number of structural alignment algorithms have been developed, most of them ignore intermolecular interactions during the alignment procedure. Therefore, structures in different oligomeric states are barely distinguishable, and it is very challenging to find correct alignment in coil regions. Here we present a novel approach to structural alignment using a clique finding algorithm and environmental information (SAUCE). In this approach, we build the alignment based on not only structural coordinate information but also realistic environmental information extracted from biological unit files provided by the Protein Data Bank (PDB). At first, we eliminate all environmentally unfavorable pairings of residues. Then we identify alignments in core regions via a maximal clique finding algorithm. Two extreme value distribution (EVD) form statistics have been developed to evaluate core region alignments. With an optional extension step, global alignment can be derived based on environment-based dynamic programming linking. We show that our method is able to differentiate three-dimensional structures in different oligomeric states, and is able to find flexible alignments between multidomain structures without predetermined hinge regions. The overall performance is also evaluated on a large scale by comparisons to current structural classification databases as well as to other alignment methods. 48109-1065, USA.
@article{ChenC:2005,
author = {Chen, Yu and Crippen, Gordon M.},
title = {A novel approach to structural alignment using realistic structural and environmental information.},
journal = {Protein Science},
volume = {14},
number = {12},
pages = {2935-46},
year = {2005},
month = dec,
doi = {10.1110/ps.051428205},
}Ting Chen and Dimitris Metaxas. A hybrid framework for 3d medical image segmentation. Medical Image Analysis, 9(6):547—65, dec 2005.
In this paper we propose a novel hybrid 3D segmentation framework which combines Gibbs models, marching cubes and deformable models. In the framework, first we construct a new Gibbs model whose energy function is defined on a high order clique system. The new model includes both region and boundary information during segmentation. Next we improve the original marching cubes method to construct 3D meshes from Gibbs models’ output. The 3D mesh serves as the initial geometry of the deformable model. Then we deform the deformable model using external image forces so that the model converges to the object surface. We run the Gibbs model and the deformable model recursively by updating the Gibbs model’s parameters using the region and boundary information in the deformable model segmentation result. In our approach, the hybrid combination of region-based methods and boundary-based methods results in improved segmentations of complex structures. The benefit of the methodology is that it produces high quality segmentations of 3D structures using little prior information and minimal user intervention. The modules in this segmentation methodology are developed within the context of the Insight ToolKit (ITK). We present experimental segmentation results of brain tumors and evaluate our method by comparing experimental results with expert manual segmentations. The evaluation results show that the methodology achieves high quality segmentation results with computational efficiency. We also present segmentation results of other clinical objects to illustrate the strength of the methodology as a generic segmentation framework.
@article{ChenM:2005,
author = {Chen, Ting and Metaxas, Dimitris},
title = {A hybrid framework for 3D medical image segmentation.},
journal = {Medical Image Analysis},
volume = {9},
number = {6},
pages = {547-65},
year = {2005},
month = dec,
doi = {10.1016/j.media.2005.04.004},
}Blandine Clique, Alan Ironmonger, Benjamin Whittaker, Jacqueline Colley, James Titchmarsh, Peter Stockley, and Adam Nelson. Synthesis of a library of stereo- and regiochemically diverse aminoglycoside derivatives. Organic & Biomolecular Chemistry, 3(15):2776—85, aug 2005.
A library of forty modified aminoglycosides was prepared in which the configuration and regiochemistry of two or three rings was widely varied. The library was based around three core ring systems: the 2-deoxystreptamine ring system found in the natural products, and both enantiomers of (1R*,2R*,4R*,5R*)-2,5-diamino-cyclohexane-1,4-diol and (1R*,3R*,4R*,6R*)-4,6-diaminocyclohexane-1,3-diol. In each case, the core was modified by glycosylation with one or two sugar rings. The absolute configuration of the sugar substituents (d or l), the configuration of the anomeric centres (alpha or beta), and the regiochemical arrangement of the amine(s) were varied.
@article{CliqueIWCTSN:2005,
author = {Clique, Blandine and Ironmonger, Alan and Whittaker, Benjamin and Colley, Jacqueline and Titchmarsh, James and Stockley, Peter and Nelson, Adam},
title = {Synthesis of a library of stereo- and regiochemically diverse aminoglycoside derivatives.},
journal = {Organic & Biomolecular Chemistry},
volume = {3},
number = {15},
pages = {2776-85},
year = {2005},
month = aug,
doi = {10.1039/b505865a},
}Imre Derényi, Gergely Palla, and Tamás Vicsek. Clique percolation in random networks. Physical review letters, 94(16):160202, 2005.
The notion of k-clique percolation in random graphs is introduced, where k is the size of the complete subgraphs whose large scale organizations are analytically and numerically investigated. For the Erdős-Rényi graph of N vertices we obtain that the percolation transition of k-cliques takes place when the probability of two vertices being connected by an edge reaches the threshold \(p_c(k)=[(k-1)N]^{-1/(k-1)}\). At the transition point the scaling of the giant component with N is highly nontrivial and depends on k. We discuss why clique percolation is a novel and efficient approach to the identification of overlapping communities in large real networks.
@article{DerenyiPV:2005,
author = {Der{\'e}nyi, Imre and Palla, Gergely and Vicsek, Tam{\'a}s},
title = {Clique percolation in random networks},
journal = {Physical review letters},
volume = {94},
number = {16},
pages = {160202},
publisher = {APS},
year = {2005},
doi = {10.1103/PhysRevLett.94.160202},
}Longnian Lin, Remus Osan, Shy Shoham, Wenjun Jin, Wenqi Zuo, and Joe Z. Tsien. Identification of network-level coding units for real-time representation of episodic experiences in the hippocampus. Proceedings of the National Academy of Sciences of the United States of America, 102(17):6125—30, apr 2005.
To examine the network-level organizing principles by which the brain achieves its real-time encoding of episodic information, we have developed a 96-channel array to simultaneously record the activity patterns of as many as 260 individual neurons in the mouse hippocampus during various startling episodes. We find that the mnemonic startling episodes triggered firing changes in a set of CA1 neurons in both startle-type and environment-dependent manners. Pattern classification methods reveal that these firing changes form distinct ensemble representations in a low-dimensional encoding subspace. Application of a sliding window technique further enabled us to reliably capture not only the temporal dynamics of real-time network encoding but also postevent processing of newly formed ensemble traces. Our analyses revealed that the network-encoding power is derived from a set of functional coding units, termed neural cliques, in the CA1 network. The individual neurons within neural cliques exhibit "collective cospiking" dynamics that allow the neural clique to overcome the response variability of its members and to achieve real-time encoding robustness. Conversion of activation patterns of these coding unit assemblies into a set of real-time digital codes permits concise and universal representation and categorization of discrete behavioral episodes across different individual brains. Engineering, Boston University, Boston, MA 02118, USA.
@article{LinOSJZT:2005,
author = {Lin, Longnian and Osan, Remus and Shoham, Shy and Jin, Wenjun and Zuo, Wenqi and Tsien, Joe Z.},
title = {Identification of network-level coding units for real-time representation of episodic experiences in the hippocampus.},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
volume = {102},
number = {17},
pages = {6125-30},
year = {2005},
month = apr,
doi = {10.1073/pnas.0408233102},
}Heinz Muhlenbein and Robin Hons. The estimation of distributions and the minimum relative entropy principle. Evolutionary Computation, 13(1):1—27, 2005.
Estimation of Distribution Algorithms (EDA) have been proposed as an extension of genetic algorithms. In this paper we explain the relationship of EDA to algorithms developed in statistics, artificial intelligence, and statistical physics. The major design issues are discussed within a general interdisciplinary framework. It is shown that maximum entropy approximations play a crucial role. All proposed algorithms try to minimize the Kullback-Leibler divergence KLD between the unknown distribution p(x) and a class q(x) of approximations. However, the Kullback-Leibler divergence is not symmetric. Approximations which suppose that the function to be optimized is additively decomposed (ADF) minimize KLD(q||p), the methods which learn the approximate model from data minimize KLD(p||q). This minimization is identical to maximizing the log-likelihood. In the paper three classes of algorithms are discussed. FDA uses the ADF to compute an approximate factorization of the unknown distribution. The factors are marginal distributions, whose values are computed from samples. The second class is represented by the Bethe-Kikuchi approach which has recently been rediscovered in statistical physics. Here the values of the marginals are computed from a difficult constrained minimization problem. The third class learns the factorization from the data. We analyze our learning algorithm LFDA in detail. It is shown that learning is faced with two problems: first, to detect the important dependencies between the variables, and second, to create an acyclic Bayesian network of bounded clique size. Germany. heinz.muehlenbein@ais.fraunhofer.de
@article{MuhlenbeinH:2005,
author = {Muhlenbein, Heinz and Hons, Robin},
title = {The estimation of distributions and the minimum relative entropy principle.},
journal = {Evolutionary Computation},
volume = {13},
number = {1},
pages = {1-27},
year = {2005},
doi = {10.1162/1063656053583469},
}David L. Tabb, Melissa R. Thompson, Gurusahai Khalsa-Moyers, Nathan C. VerBerkmoes, and W. Hayes McDonald. Ms2grouper: group assessment and synthetic replacement of duplicate proteomic tandem mass spectra. Journal of the American Society for Mass Spectrometry, 16(8):1250—61, aug 2005.
Shotgun proteomics experiments require the collection of thousands of tandem mass spectra; these sets of data will continue to grow as new instruments become available that can scan at even higher rates. Such data contain substantial amounts of redundancy with spectra from a particular peptide being acquired many times during a single LC-MS/MS experiment. In this article, we present MS2Grouper, an algorithm that detects spectral duplication, assesses groups of related spectra, and replaces these groups with synthetic representative spectra. Errors in detecting spectral similarity are corrected using a paraclique criterion-spectra are only assessed as groups if they are part of a clique of at least three completely interrelated spectra or are subsequently added to such cliques by being similar to all but one of the clique members. A greedy algorithm constructs a representative spectrum for each group by iteratively removing the tallest peaks from the spectral collection and matching to peaks in the other spectra. This strategy is shown to be effective in reducing spectral counts by up to 20% in LC-MS/MS datasets from protein standard mixtures and proteomes, reducing database search times without a concomitant reduction in identified peptides.
@article{TabbTKVM:2005,
author = {Tabb, David L. and Thompson, Melissa R. and Khalsa-Moyers, Gurusahai and VerBerkmoes, Nathan C. and McDonald, W. Hayes},
title = {MS2Grouper: group assessment and synthetic replacement of duplicate proteomic tandem mass spectra.},
journal = {Journal of the American Society for Mass Spectrometry},
volume = {16},
number = {8},
pages = {1250-61},
year = {2005},
month = aug,
doi = {10.1016/j.jasms.2005.04.010},
}James R. Arnold, Keith W. Burdick, Scott C-H Pegg, Samuel Toba, Michelle L. Lamb, and Irwin D. Kuntz. Siteprint: three-dimensional pharmacophore descriptors derived from protein binding sites for family based active site analysis, classification, and drug design. Journal of Chemical Information and Computer Sciences, 44(6):2190—8, nov 2004.
Integrating biological and chemical information is one key task in drug discovery, and one approach to attaining this goal is via three-dimensional pharmacophore descriptors derived from protein binding sites. The SitePrint program generates, aligns, scores, and classifies three-dimensional pharmacophore descriptors, active site grids, and ligand surfaces. The descriptors are formed from molecular fragments that have been docked, minimized, filtered, and clustered in protein active sites. The descriptors have geometric coordinates derived from the fragment positions, and they capture the shape, electrostatics, locations, and angles of entry into pockets of the recognition sites: they also provide a direct link to databases of organic molecules. The descriptors have been shown to be robust with respect to small changes in protein structure observed when multiple compounds are cocrystallized in a protein. Five aligned thrombin cocrystals with an average core alpha-carbon RMSD of 0.7 A gave three-dimensional pharmacophore descriptors with an average RMSD of 1.1 A. On a larger test set, alignment and scoring of the descriptors using clique-based alignment, and a best first search strategy with an adapted forward-looking Ullmann heuristic was able to select the global minimum three-dimensional alignment in twenty-nine out of thirty cases in less than one CPU second on a workstation. A protein family based analysis was then performed to demonstrate the usefulness of the method in producing a correlation of active site pharmacophore descriptors to protein function. Each protein in a test set of thirty was assigned membership to a family based on computed active site similarity to the following families: kinases, nuclear receptors, the aspartyl, cysteine, serine, and metallo proteases. This method of classifying proteins is complementary to approaches based on sequence or fold homology. The values within protein families for correctly assigning membership of a protein to a family ranged from 25% to 80%. California San Francisco, Box 2240, N474-A Genentech Hall, San Francisco, California 94143-2240, USA.
@article{ArnoldBPTLK:2004,
author = {Arnold, James R. and Burdick, Keith W. and Pegg, Scott C-H and Toba, Samuel and Lamb, Michelle L. and Kuntz, Irwin D.},
title = {SitePrint: three-dimensional pharmacophore descriptors derived from protein binding sites for family based active site analysis, classification, and drug design.},
journal = {Journal of Chemical Information and Computer Sciences},
volume = {44},
number = {6},
pages = {2190-8},
year = {2004},
month = nov,
doi = {10.1021/ci049814f},
}Andreas Brakoulias and Richard M. Jackson. Towards a structural classification of phosphate binding sites in protein-nucleotide complexes: an automated all-against-all structural comparison using geometric matching. Proteins, 56(2):250—60, aug 2004.
A method is described for the rapid comparison of protein binding sites using geometric matching to detect similar three-dimensional structure. The geometric matching detects common atomic features through identification of the maximum common sub-graph or clique. These features are not necessarily evident from sequence or from global structural similarity giving additional insight into molecular recognition not evident from current sequence or structural classification schemes. Here we use the method to produce an all-against-all comparison of phosphate binding sites in a number of different nucleotide phosphate-binding proteins. The similarity search is combined with clustering of similar sites to allow a preliminary structural classification. Clustering by site similarity produces a classification of binding sites for the 476 representative local environments producing ten main clusters representing half of the representative environments. The similarities make sense in terms of both structural and functional classification schemes. The ten main clusters represent a very limited number of unique structural binding motifs for phosphate. These are the structural P-loop, di-nucleotide binding motif [FAD/NAD(P)-binding and Rossman-like fold] and FAD-binding motif. Similar classification schemes for nucleotide binding proteins have also been arrived at independently by others using different methods. Street, London, England.
@article{BrakouliasJ:2004,
author = {Brakoulias, Andreas and Jackson, Richard M.},
title = {Towards a structural classification of phosphate binding sites in protein-nucleotide complexes: an automated all-against-all structural comparison using geometric matching.},
journal = {Proteins},
volume = {56},
number = {2},
pages = {250-60},
year = {2004},
month = aug,
doi = {10.1002/prot.20123},
}Mathaus Dejori, Anton Schwaighofer, Volker Tresp, and Martin Stetter. Mining functional modules in genetic networks with decomposable graphical models. Omics, 8(2):176—88, 2004.
In recent years, graphical models have become an increasingly important tool for the structural analysis of genome-wide expression profiles at the systems level. Here we present a new graphical modelling technique, which is based on decomposable graphical models, and apply it to a set of gene expression profiles from acute lymphoblastic leukemia (ALL). The new method explains probabilistic dependencies of expression levels in terms of the concerted action of underlying genetic functional modules, which are represented as so-called "cliques" in the graph. In addition, the method uses continuous-valued (instead of discretized) expression levels, and makes no particular assumption about their probability distribution. We show that the method successfully groups members of known functional modules to cliques. Our method allows the evaluation of the importance of genes for global cellular functions based on both link count and the clique membership count.
@article{DejoriSTS:2004,
author = {Dejori, Mathaus and Schwaighofer, Anton and Tresp, Volker and Stetter, Martin},
title = {Mining functional modules in genetic networks with decomposable graphical models.},
journal = {Omics},
volume = {8},
number = {2},
pages = {176-88},
year = {2004},
doi = {10.1089/1536231041388375},
}Yongmei Ji, Xing Xu, and Gary D. Stormo. A graph theoretical approach for predicting common rna secondary structure motifs including pseudoknots in unaligned sequences. Bioinformatics, 20(10):1591—602, jul 2004.
Motivation
RNA structure motifs contained in mRNAs have been found to play important roles in regulating gene expression. However, identification of novel RNA regulatory motifs using computational methods has not been widely explored. Effective tools for predicting novel RNA regulatory motifs based on genomic sequences are needed.
Results
We present a new method for predicting common RNA secondary structure motifs in a set of functionally or evolutionarily related RNA sequences. This method is based on comparison of stems (palindromic helices) between sequences and is implemented by applying graph-theoretical approaches. It first finds all possible stable stems in each sequence and compares stems pairwise between sequences by some defined features to find stems conserved across any two sequences. Then by applying a maximum clique finding algorithm, it finds all significant stems conserved across at least k sequences. Finally, it assembles in topological order all possible compatible conserved stems shared by at least k sequences and reports a number of the best assembled stem sets as the best candidate common structure motifs. This method does not require prior structural alignment of the sequences and is able to detect pseudoknot structures. We have tested this approach on some RNA sequences with known secondary structures, in which it is capable of detecting the real structures completely or partially correctly and outperforms other existing programs for similar purposes.
Availability
The algorithm has been implemented in C++ in a program called comRNA, which is available at http://ural.wustl.edu/softwares.html 63110, USA.
RNA structure motifs contained in mRNAs have been found to play important roles in regulating gene expression. However, identification of novel RNA regulatory motifs using computational methods has not been widely explored. Effective tools for predicting novel RNA regulatory motifs based on genomic sequences are needed.
Results
We present a new method for predicting common RNA secondary structure motifs in a set of functionally or evolutionarily related RNA sequences. This method is based on comparison of stems (palindromic helices) between sequences and is implemented by applying graph-theoretical approaches. It first finds all possible stable stems in each sequence and compares stems pairwise between sequences by some defined features to find stems conserved across any two sequences. Then by applying a maximum clique finding algorithm, it finds all significant stems conserved across at least k sequences. Finally, it assembles in topological order all possible compatible conserved stems shared by at least k sequences and reports a number of the best assembled stem sets as the best candidate common structure motifs. This method does not require prior structural alignment of the sequences and is able to detect pseudoknot structures. We have tested this approach on some RNA sequences with known secondary structures, in which it is capable of detecting the real structures completely or partially correctly and outperforms other existing programs for similar purposes.
Availability
The algorithm has been implemented in C++ in a program called comRNA, which is available at http://ural.wustl.edu/softwares.html 63110, USA.
@article{JiXS:2004,
author = {Ji, Yongmei and Xu, Xing and Stormo, Gary D.},
title = {A graph theoretical approach for predicting common RNA secondary structure motifs including pseudoknots in unaligned sequences.},
journal = {Bioinformatics},
volume = {20},
number = {10},
pages = {1591-602},
year = {2004},
month = jul,
doi = {10.1093/bioinformatics/bth131},
}Nils Weskamp, Daniel Kuhn, Eyke Hullermeier, and Gerhard Klebe. Efficient similarity search in protein structure databases by k-clique hashing. Bioinformatics, 20(10):1522—6, jul 2004.
Motivation
Graph-based clique-detection techniques are widely used for the recognition of common substructures in proteins. They permit the detection of resemblances that are independent of sequence or fold homologies and are also able to handle conformational flexibility. Their high computational complexity is often a limiting factor and prevents a detailed and fine-grained modeling of the protein structure.
Results
We present an efficient two-step method that significantly speeds up the detection of common substructures, especially when used to screen larger databases. It combines the advantages from both clique-detection and geometric hashing. The method is applied to an established approach for the comparison of protein binding-pockets, and some empirical results are presented.
Availability
Upon request from the authors. Hans-Meerwein-Strasse, 35032 Marburg, Germany.
Graph-based clique-detection techniques are widely used for the recognition of common substructures in proteins. They permit the detection of resemblances that are independent of sequence or fold homologies and are also able to handle conformational flexibility. Their high computational complexity is often a limiting factor and prevents a detailed and fine-grained modeling of the protein structure.
Results
We present an efficient two-step method that significantly speeds up the detection of common substructures, especially when used to screen larger databases. It combines the advantages from both clique-detection and geometric hashing. The method is applied to an established approach for the comparison of protein binding-pockets, and some empirical results are presented.
Availability
Upon request from the authors. Hans-Meerwein-Strasse, 35032 Marburg, Germany.
@article{WeskampKHK:2004,
author = {Weskamp, Nils and Kuhn, Daniel and Hullermeier, Eyke and Klebe, Gerhard},
title = {Efficient similarity search in protein structure databases by k-clique hashing.},
journal = {Bioinformatics},
volume = {20},
number = {10},
pages = {1522-6},
year = {2004},
month = jul,
doi = {10.1093/bioinformatics/bth113},
}Masahiro Hattori, Yasushi Okuno, Susumu Goto, and Minoru Kanehisa. Development of a chemical structure comparison method for integrated analysis of chemical and genomic information in the metabolic pathways. Journal of the American Chemical Society, 125(39):11853—65, oct 2003.
Cellular functions result from intricate networks of molecular interactions, which involve not only proteins and nucleic acids but also small chemical compounds. Here we present an efficient algorithm for comparing two chemical structures of compounds, where the chemical structure is treated as a graph consisting of atoms as nodes and covalent bonds as edges. On the basis of the concept of functional groups, 68 atom types (node types) are defined for carbon, nitrogen, oxygen, and other atomic species with different environments, which has enabled detection of biochemically meaningful features. Maximal common subgraphs of two graphs can be found by searching for maximal cliques in the association graph, and we have introduced heuristics to accelerate the clique finding and to detect optimal local matches (simply connected common subgraphs). Our procedure was applied to the comparison and clustering of 9383 compounds, mostly metabolic compounds, in the KEGG/LIGAND database. The largest clusters of similar compounds were related to carbohydrates, and the clusters corresponded well to the categorization of pathways as represented by the KEGG pathway map numbers. When each pathway map was examined in more detail, finer clusters could be identified corresponding to subpathways or pathway modules containing continuous sets of reaction steps. Furthermore, it was found that the pathway modules identified by similar compound structures sometimes overlap with the pathway modules identified by genomic contexts, namely, by operon structures of enzyme genes. Kyoto 611-0011, Japan.
@article{HattoriOGK:2003,
author = {Hattori, Masahiro and Okuno, Yasushi and Goto, Susumu and Kanehisa, Minoru},
title = {Development of a chemical structure comparison method for integrated analysis of chemical and genomic information in the metabolic pathways.},
journal = {Journal of the American Chemical Society},
volume = {125},
number = {39},
pages = {11853-65},
year = {2003},
month = oct,
doi = {10.1021/ja036030u},
}Kengo Kinoshita and Haruki Nakamura. Identification of protein biochemical functions by similarity search using the molecular surface database ef-site. Protein Science, 12(8):1589—95, aug 2003.
The identification of protein biochemical functions based on their three-dimensional structures is strongly required in the post-genome-sequencing era. We have developed a new method to identify and predict protein biochemical functions using the similarity information of molecular surface geometries and electrostatic potentials on the surfaces. Our prediction system consists of a similarity search method based on a clique search algorithm and the molecular surface database eF-site (electrostatic surface of functional-site in proteins). Using this system, functional sites similar to those of phosphoenoylpyruvate carboxy kinase were detected in several mononucleotide-binding proteins, which have different folds. We also applied our method to a hypothetical protein, MJ0226 from Methanococcus jannaschii, and detected the mononucleotide binding site from the similarity to other proteins having different folds. 230-0045, Japan. kinoshita@tsurumi.yokohama-cu.ac.jp
@article{KinoshitaN:2003,
author = {Kinoshita, Kengo and Nakamura, Haruki},
title = {Identification of protein biochemical functions by similarity search using the molecular surface database eF-site.},
journal = {Protein Science},
volume = {12},
number = {8},
pages = {1589-95},
year = {2003},
month = aug,
doi = {10.1110/ps.0368703},
}Nicholas Rhodes, Peter Willett, Alain Calvet, James B. Dunbar, and Christine Humblet. Clip: similarity searching of 3d databases using clique detection. Journal of Chemical Information and Computer Sciences, 43(2):443—8, mar 2003.
This paper describes a program for 3D similarity searching, called CLIP (for Candidate Ligand Identification Program), that uses the Bron-Kerbosch clique detection algorithm to find those structures in a file that have large structures in common with a target structure. Structures are characterized by the geometric arrangement of pharmacophore points and the similarity between two structures calculated using modifications of the Simpson and Tanimoto association coefficients. This modification takes into account the fact that a distance tolerance is required to ensure that pairs of interatomic distances can be regarded as equivalent during the clique-construction stage of the matching algorithm. Experiments with HIV assay data demonstrate the effectiveness and the efficiency of this approach to virtual screening. University of Sheffield, Western Bank, Sheffield S10 2TN, United Kingdom.
@article{RhodesWCDH:2003,
author = {Rhodes, Nicholas and Willett, Peter and Calvet, Alain and Dunbar, James B. and Humblet, Christine},
title = {CLIP: similarity searching of 3D databases using clique detection.},
journal = {Journal of Chemical Information and Computer Sciences},
volume = {43},
number = {2},
pages = {443-8},
year = {2003},
month = mar,
doi = {10.1021/ci025605o},
}Rong Long Wang, Zheng Tang, and Qi Ping Cao. An efficient approximation algorithm for finding a maximum clique using hopfield network learning. Neural Computation, 15(7):1605—19, jul 2003.
In this article, we present a solution to the maximum clique problem using a gradient-ascent learning algorithm of the Hopfield neural network. This method provides a near-optimum parallel algorithm for finding a maximum clique. To do this, we use the Hopfield neural network to generate a near-maximum clique and then modify weights in a gradient-ascent direction to allow the network to escape from the state of near-maximum clique to maximum clique or better. The proposed parallel algorithm is tested on two types of random graphs and some benchmark graphs from the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS). The simulation results show that the proposed learning algorithm can find good solutions in reasonable computation time. wangrl@hi.iis.toyama-u.ac.jp
@article{WangTC:2003,
author = {Wang, Rong Long and Tang, Zheng and Cao, Qi Ping},
title = {An efficient approximation algorithm for finding a maximum clique using Hopfield network learning.},
journal = {Neural Computation},
volume = {15},
number = {7},
pages = {1605-19},
year = {2003},
month = jul,
doi = {10.1162/089976603321891828},
}D. T Chiu, E. Pezzoli, H. Wu, A. D Stroock, and G. M. Whitesides. Using three-dimensional microfluidic networks for solving computationally hard problems. Proceedings of the National Academy of Sciences of the United States of America, 98(6):2961—6, mar 2001.
This paper describes the design of a parallel algorithm that uses moving fluids in a three-dimensional microfluidic system to solve a nondeterministically polynomial complete problem (the maximal clique problem) in polynomial time. This algorithm relies on (i) parallel fabrication of the microfluidic system, (ii) parallel searching of all potential solutions by using fluid flow, and (iii) parallel optical readout of all solutions. This algorithm was implemented to solve the maximal clique problem for a simple graph with six vertices. The successful implementation of this algorithm to compute solutions for small-size graphs with fluids in microchannels is not useful, per se, but does suggest broader application for microfluidics in computation and control. Street, Cambridge, MA 02138, USA.
@article{ChiuPWSW:2001,
author = {Chiu, D. T and Pezzoli, E. and Wu, H. and Stroock, A. D and Whitesides, G. M.},
title = {Using three-dimensional microfluidic networks for solving computationally hard problems.},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
volume = {98},
number = {6},
pages = {2961-6},
year = {2001},
month = mar,
doi = {10.1073/pnas.061014198},
}Ina Koch. Enumerating all connected maximal common subgraphs in two graphs. Theoretical Computer Science, 250(1-2):1—30, 2001.
Note: Transformation of the problem of finding all connected maximal common subgraphs into cliques. Adaptations of Bron-Kerbosch algorithm with pruning techniques to discard cliques that represent unconnected subgraphs.
We represent a new method for finding all connected maximal common subgraphs in two graphs which is based on the transformation of the problem into the clique problem. We have developed new algorithms for enumerating all cliques that represent connected maximal common subgraphs. These algorithms are based on variants of the Bron-Kerbosch algorithm. In this paper we explain the transformation of the maximal common subgraph problem into the clique problem. We give a short summary of the variants of the Bron-Kerbosch algorithm in order to explain the modification of that algorithm such that the detected cliques represent connected maximal common subgraphs. After introducing and proving several variants of the modified algorithm we discuss the runtimes for all variants by means of random graphs. The results show the drastical reduction of the runtimes for the new algorithms.
@article{Koch:2001,
author = {Ina Koch},
title = {Enumerating all connected maximal common subgraphs in two graphs},
journal = {Theoretical Computer Science},
volume = {250},
number = {1-2},
pages = {1--30},
year = {2001},
doi = {10.1016/S0304-3975(00)00286-3},
}Eleanor J. Gardiner, Peter Willett, and Peter J. Artymiuk. Graph-theoretic techniques for macromolecular docking. Journal of Chemical Information and Computer Sciences, 40(2):273—279, 2000.
We propose a solution to the problem of docking two macromolecules. We represent each of two proteins as a set of potential hydrogen bond donors and acceptors and use a clique-detection algorithm to find maximally complementary sets of donor/acceptor pairs. Preliminary results are presented which demonstrate the feasibility of the method.
@article{GardinerWA:2000,
author = {Gardiner, Eleanor J. and Willett, Peter and Artymiuk, Peter J.},
title = {Graph-theoretic techniques for macromolecular docking},
journal = {Journal of Chemical Information and Computer Sciences},
volume = {40},
number = {2},
pages = {273--279},
publisher = {ACS Publications},
year = {2000},
doi = {10.1021/ci990262o},
}Pavel A. Pevzner and Sing-Hoi Sze. Combinatorial approaches to finding subtle signals in dna sequences. In Russ Altman, Timothy L. Bailey, Philip Bourne, Michael Gribskov, Thomas Lengauer, Ilya N. Shindyalov, Lynn F. Ten Eyck, , and Helge Weissig, editors, Proceedings of the Eighth International Conference on Intelligent Systems for Molecular Biology, volume 8, pages 269—278, 2000.
Signal finding (pattern discovery in unaligned DNA sequences) is a fundamental problem in both computer science and molecular biology with important applications in locating regulatory sites and drug target identification. Despite many studies, this problem is far from being resolved: most signals in DNA sequences are so complicated that we don’t yet have good models or reliable algorithms for their recognition. We complement existing statistical and machine learning approaches to this problem by a combinatorial approach that proved to be successful in identifying very subtle signals.
@inproceedings{PevznerS:2000,
author = {Pevzner, Pavel A. and Sze, Sing-Hoi},
title = {Combinatorial approaches to finding subtle signals in DNA sequences},
volume = {8},
booktitle = {Proceedings of the Eighth International Conference on Intelligent Systems for Molecular Biology},
pages = {269--278},
editor = {Russ Altman and Timothy L. Bailey and Philip Bourne and Michael Gribskov and Thomas Lengauer and Ilya N. Shindyalov and Lynn F. Ten Eyck and and Helge Weissig},
year = {2000},
url = {http://www.aaai.org/Library/ISMB/2000/ismb00-028.php},
}S. Bharitkar, K. Tsuchiya, and Y. Takefuji. Microcode optimization with neural networks. IEEE Transactions On Neural Networks / A Publication of the IEEE Neural Networks Council, 10(3):698—703, 1999.
Microcode optimization is an NP-complete combinatorial optimization problem. This paper proposes a new method based on the Hopfield neural network for optimizing the wordwidth in the control memory of a microprogrammed digital computer. We present two methodologies, viz., the maximum clique approach, and a cost function based method to minimize an objective function. The maximum clique approach albeit being near O(1) in complexity, is limited in its use for small problem sizes, since it only partitions the data based on the compatibility between the microoperations, and does not minimize the cost function. We thereby use this approach to condition the data initially (to form compatibility classes), and then use the proposed second method to optimize on the cost function. The latter method is then able to discover better solutions than other schemes for the benchmark data set. Los Angeles, CA 90089-2564, USA.
@article{BharitkarTT:1999,
author = {Bharitkar, S. and Tsuchiya, K. and Takefuji, Y.},
title = {Microcode optimization with neural networks.},
journal = {IEEE Transactions On Neural Networks / A Publication of the IEEE Neural Networks Council},
volume = {10},
number = {3},
pages = {698-703},
year = {1999},
doi = {10.1109/72.761728},
}M. D Miller, R. P Sheridan, and S. K. Kearsley. Sq: a program for rapidly producing pharmacophorically relevent molecular superpositions. Journal of Medicinal Chemistry, 42(9):1505—14, may 1999.
A new method SQ has been developed to provide fast, automatic, and objective pairwise three-dimensional molecular alignments. SQ uses an atom-based clique-matching step followed by an alignment scoring function that has been parametrized to recognize pharmacologically relevant atomic properties. Molecular alignments from SQ are consistent with known drug-receptor interactions. We demonstrate this with six pairs of receptor-ligand complexes from the Brookhaven Protein Data Bank. The SQ-generated alignment of one isolated ligand onto another is shown to approximate the alignment of the ligands when the receptors are superimposed. SQ appears to be better than its predecessor SEAL (Kearsley and Smith, Tetrahedron Comput. Methodol. 1990, 3, 615-633) in this regard. SQ has been tailored so that, given one molecule as a probe, it can be used to routinely scan large chemical databases for which precomputed conformations have been stored. The SQ score, a measure of 3D similarity of each candidate molecule to the probe, can be used to rank compounds for the purposes of chemical screening. We demonstrate this with three probes (a thrombin inhibitor, an HIV protease inhibitor, and a model for angiotensin II). In each case SQ can preferentially select from the MDDR database other compounds with the same activity as the probe. We further show, using the angiotensin example, how SQ can identify topologically diverse compounds with the same activity. West Point, Pennsylvania 19486, USA.
@article{MillerSK:1999,
author = {Miller, M. D and Sheridan, R. P and Kearsley, S. K.},
title = {SQ: a program for rapidly producing pharmacophorically relevent molecular superpositions.},
journal = {Journal of Medicinal Chemistry},
volume = {42},
number = {9},
pages = {1505-14},
year = {1999},
month = may,
doi = {10.1021/jm9806143},
}Ram Samudrala and John Moult. A graph-theoretic algorithm for comparative modeling of protein structure1. Journal of molecular biology, 279(1):287—302, 1998.
The interconnected nature of interactions in protein structures appears to be the major hurdle in preventing the construction of accurate comparative models. We present an algorithm that uses graph theory to handle this problem. Each possible conformation of a residue in an amino acid sequence is represented using the notion of a node in a graph. Each node is given a weight based on the degree of the interaction between its side-chain atoms and the local main-chain atoms. Edges are then drawn between pairs of residue conformations/nodes that are consistent with each other (i.e. clash-free and satisfying geometrical constraints). The edges are weighted based on the interactions between the atoms of the two nodes. Once the entire graph is constructed, all the maximal sets of completely connected nodes (cliques) are found using a clique-finding algorithm. The cliques with the best weights represent the optimal combinations of the various main-chain and side-chain possibilities, taking the respective environments into account. The algorithm is used in a comparative modeling scenario to build side-chains, regions of main chain, and mix and match between different homologs in a context-sensitive manner. The predictive power of this method is assessed by applying it to cases where the experimental structure is not known in advance.
@article{SamudralaM:1998,
author = {Samudrala, Ram and Moult, John},
title = {A graph-theoretic algorithm for comparative modeling of protein structure1},
journal = {Journal of molecular biology},
volume = {279},
number = {1},
pages = {287--302},
publisher = {Elsevier},
year = {1998},
doi = {10.1006/jmbi.1998.1689},
}D. Bender and F. Losel. Protective and risk effects of peer relations and social support on antisocial behaviour in adolescents from multi-problem milieus. Journal of Adolescence, 20(6):661—78, dec 1997.
This article addresses the relation between antisocial behaviour and social resources in a 2-year longitudinal study of 100 high-risk adolescents in residential care. Problem behaviour was measured with the Externalizing Scale of the Youth Self Report. Social resources were recorded using semi-structured methods. Hierarchical regression analyses showed interactions suggesting that the same variables can fulfil risk as well as protective functions: clique membership and satisfaction with social support fostered behavioural continuity. In contrast, a lack of social embeddedness had a risk effect for well-adapted adolescents and a protective effect for the deviant ones. Social resources were more influential in girls. Theoretical implications and methodological problems are discussed. Erlangen, D-91054, Germany.
@article{BenderL:1997,
author = {Bender, D. and Losel, F.},
title = {Protective and risk effects of peer relations and social support on antisocial behaviour in adolescents from multi-problem milieus.},
journal = {Journal of Adolescence},
volume = {20},
number = {6},
pages = {661-78},
year = {1997},
month = dec,
doi = {10.1006/jado.1997.0118},
}Eleanor J. Gardiner, Peter J. Artymiuk, and Peter Willett. Clique-detection algorithms for matching three-dimensional molecular structures. Journal of Molecular Graphics and Modelling, 15(4):245—253, 1997.
The representation of chemical and biological molecules by means of graphs permits the use of a maximum common subgraph (MCS) isomorphism algorithm to identify the structural relationships existing between pairs of such molecular graphs. Clique detection provides an efficient way of implementing MCS detection, and this article reports a comparison of several different clique-detection algorithms when used for this purpose. Experiments with both small molecules and proteins demonstrate that the most efficient of these particular applications, which typically involve correspondence graphs with low edge densities, is the algorithm described by Carraghan and Pardalos. This is shown to be two to three times faster than the Bron-Kerbosch algorithm that has been used previously for MCS applications in chemistry and biology. However, the latter algorithm enables all substructures common to a pair of molecules to be identified, and not just the largest ones, as with the other algorithms considered here. The two algorithms can usefully be combined to increase the efficiency of database-searching systems that use the MCS as a measure of structural similarity.
@article{GardinerAW:1997,
author = {Eleanor J. Gardiner and Peter J. Artymiuk and Peter Willett},
title = {Clique-Detection Algorithms for Matching Three-Dimensional Molecular Structures},
journal = {Journal of Molecular Graphics and Modelling},
volume = {15},
number = {4},
pages = {245--253},
year = {1997},
doi = {10.1016/S1093-3263(97)00089-2},
}I. Hussain and T. R. Reed. A bond percolation-based model for image segmentation. IEEE Transactions On Image Processing, 6(12):1698—704, 1997.
This work presents a novel bond percolation-based approach to determine the clique potential parameters of a Gibbs-Markov model as a function of local characteristics of the underlying image. Using the renormalization group transformation, a multiscale description of the clique potential parameters is formed and used to obtain multiresolution image segmentation.
@article{HussainR:1997,
author = {Hussain, I. and Reed, T. R.},
title = {A bond percolation-based model for image segmentation.},
journal = {IEEE Transactions On Image Processing},
volume = {6},
number = {12},
pages = {1698-704},
year = {1997},
doi = {10.1109/83.650123},
}P. D Kaplan, Q. Ouyang, D. S Thaler, and A. Libchaber. Parallel overlap assembly for the construction of computational dna libraries. Journal of Theoretical Biology, 188(3):333—41, oct 1997.
Algorithms for computing with DNA currently require the construction of pools of molecules in which each distinct molecule represents a different starting point for the calculation. We have begun building such pools using the technique of parallel overlap assembly that is already used for the generation of diversity in biologically useful combinatorial search techniques such as gene shuffling. Unlike these applications, a pool in a molecular computer must be complete, containing all possible strands, and ordered, having minimal contamination from incorrectly assembled DNA. We present an experiment in which parallel overlap assembly is used to construct a computational pool and an experiment in which this pool is used to solve the NP-complete maximal-clique problem. kaplanp@sas.upenn.edu
@article{KaplanOTL:1997,
author = {Kaplan, P. D and Ouyang, Q. and Thaler, D. S and Libchaber, A.},
title = {Parallel overlap assembly for the construction of computational DNA libraries.},
journal = {Journal of Theoretical Biology},
volume = {188},
number = {3},
pages = {333-41},
year = {1997},
month = oct,
doi = {10.1006/jtbi.1997.0475},
}Filiberto Pla and John A. Marchant. Matching feature points in image sequences through a region-based method. Computer vision and image understanding, 66(3):271—285, 1997.
In order to achieve reliable matching in image sequences, a hierarchical approach is proposed. First, matching is established between regions of consecutive segmented images. In a second step, feature point matching between features of matched regions is performed. Regions provide a structural representation for features in the same region. To establish matching between features of two corresponding regions, a relational graph is built. Matching features is based on three principles: exclusion, proximity, and rigidity. The use of subgraph matching techniques through maximal clique detection provides a method to cope with partial occlusion and missing features between frames.
@article{PlaM:1997,
author = {Pla, Filiberto and Marchant, John A.},
title = {Matching feature points in image sequences through a region-based method},
journal = {Computer vision and image understanding},
volume = {66},
number = {3},
pages = {271--285},
publisher = {Elsevier},
year = {1997},
doi = {10.1006/cviu.1996.0512},
}Ina Koch, Thomas Lengauer, and Egon Wanke. An algorithm for finding maximal common subtopologies in a set of protein structures. Journal of computational biology, 3(2):289—306, 1996.
For the comparison and analysis of protein structures, it is of interest to find maximal common substructures in a given set of proteins. This question is also relevant for motif definition and structure classification. In this paper we describe first a new suitable representation of the secondary structure topology of a protein by an undirected labeled graph. Based on this representation we developed a new fast algorithm that finds all common subtopologies in a set of protein structures. Our method is based on the algorithm by Bron and Kerbosch (1973), which enumerates all maximal cliques in a graph. The main improvement of our algorithm is to restrict the search process to cliques that represent connected substructures. This restriction reduces the number of cliques to be considered during the search process and the size of the search tree drastically. Thus we are able to handle large proteins. Experiments show the efficiency and superiority of our algorithm in comparison with other existing algorithms basing on graph-theoretical methods.
@article{KochLW:1996,
author = {Koch, Ina and Lengauer, Thomas and Wanke, Egon},
title = {An algorithm for finding maximal common subtopologies in a set of protein structures},
journal = {Journal of computational biology},
volume = {3},
number = {2},
pages = {289--306},
year = {1996},
doi = {10.1089/cmb.1996.3.289},
}Arun Jagota. Approximating maximum clique with a hopfield network. IEEE Transactions On Neural Networks / A Publication of the IEEE Neural Networks Council, 6(3):724—35, 1995.
In a graph, a clique is a set of vertices such that every pair is connected by an edge. MAX-CLIQUE is the optimization problem of finding the largest clique in a given graph and is NP-hard, even to approximate well. Several real-world and theory problems can be modeled as MAX-CLIQUE. In this paper, we efficiently approximate MAX-CLIQUE in a special case of the Hopfield network whose stable states are maximal cliques. We present several energy-descent optimizing dynamics; both discrete (deterministic and stochastic) and continuous. One of these emulates, as special cases, two well-known greedy algorithms for approximating MAX-CLIQUE. We report on detailed empirical comparisons on random graphs and on harder ones. Mean-field annealing, an efficient approximation to simulated annealing, and a stochastic dynamics are the narrow but clear winners. All dynamics approximate much better than one which emulates a "naive" greedy heuristic.
@article{Jagota:1995,
author = {Jagota, Arun},
title = {Approximating maximum clique with a Hopfield network.},
journal = {IEEE Transactions On Neural Networks / A Publication of the IEEE Neural Networks Council},
volume = {6},
number = {3},
pages = {724-35},
year = {1995},
doi = {10.1109/72.377977},
}Helen M. Grindley, Peter J. Artymiuk, David W. Rice, and Peter Willett. Identification of tertiary structure resemblance in proteins using a maximal common subgraph isomorphism algorithm. Journal of Molecular Biology, 229(3):707—721, 1993.
A program called PROTEP is described that permits the rapid comparison of pairs of three-dimensional protein structures to identify the patterns of secondary structure elements that they have in common. The representation of the protein structures as labelled graphs, where the secondary structure elements in a protein and the spatial and angular relationships between them correspond to the nodes and edges of a graph, was developed for use with an earlier program, called POSSUM, which identified subgraph isomorphisms in protein structures. PROTEP takes this representation and uses a different and more flexible approach to locating structural patterns in pairs of proteins, using a maximal common subgraph isomorphism algorithm that is based on a clique detection procedure. A range of searches is described to demonstrate that areas of common structural overlap between protein structures taken from the Protein Data Bank can be identified both effectively and efficiently.
@article{GrindleyARW:1993,
author = {Grindley, Helen M. and Artymiuk, Peter J. and Rice, David W. and Willett, Peter},
title = {Identification of tertiary structure resemblance in proteins using a maximal common subgraph isomorphism algorithm},
journal = {Journal of Molecular Biology},
volume = {229},
number = {3},
pages = {707--721},
publisher = {Elsevier},
year = {1993},
doi = {10.1006/jmbi.1993.1074},
}Radu Horaud and Thomas Skordas. Stereo correspondence through feature grouping and maximal cliques. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 11(11):1168—1180, 1989.
The authors propose a method for solving the stereo correspondence problem. The method consists of extracting local image structures and matching similar such structures between two images. Linear edge segments are extracted from both the left and right images. Each segment is characterized by its position and orientation in the image as well as its relationships with the nearby segments. A relational graph is thus built from each image. For each segment in one image as set of potential assignments is represented as a set of nodes in a correspondence graph. Arcs in the graph represent compatible assignments established on the basis of segment relationships. Stereo matching becomes equivalent to searching for sets of mutually compatible nodes in this graph. Sets are found by looking for maximal cliques. The maximal clique best suited to represent a stereo correspondence is selected using a benefit function. Numerous results obtained with this method are shown
@article{HoraudS:1989,
author = {Horaud, Radu and Skordas, Thomas},
title = {Stereo correspondence through feature grouping and maximal cliques},
journal = {Pattern Analysis and Machine Intelligence, IEEE Transactions on},
volume = {11},
number = {11},
pages = {1168--1180},
publisher = {IEEE},
year = {1989},
doi = {10.1109/34.42855},
}D. Chabardes, M. Gagnan-Brunette, M. Imbert-Teboul, O. Gontcharevskaia, M. Montegut, A. Clique, and F. Morel. Adenylate cyclase responsiveness to hormones in various portions of the human nephron. The Journal of Clinical Investigation, 65(2):439—48, feb 1980.
The action sites for parathyroid hormone (PTH), salmon calcitonin (SCT), and arginine-vasopressin (AVP) were investigated along the human nephron by measuring adenylate cyclase activity, using a single tubule in vitro microassay. Well-localized segments of tubule were isolated by microdissection from five human kidneys unsuitable for transplantation. PTH (10 IU/ml) increased adenylate cyclase activity in the convoluted and the straight proximal tubule, in the medullary and cortical portions of the thick ascending limb, and in the early portion of the distal convoluted tubule (corresponding stimulated:basal activity ratios were 64, 19, 10, 18, and 22, respectively). SCT (10 ng/ml) increased adenylate cyclase activity in the medullary and cortical portions of the thick ascending limb, in the early portion of the distal convoluted tubule, and, to a lesser extent, in the cortical and the medullay collecting tubule (activity ratios were 7, 14, 15, 3, and 3, respectively). AVP (1 microM) stimulated adenylate cyclase activity in the terminal nephron segments only, i.e., the late portion of the distal convoluted tubule, the cortical and medullary portions of the collecting tubule (activity ratios 81, 51, and 97, respectively). As measured in one experiment, nearly one-half maximal responses were obtained with 0.1 IU/ml PTH or 0.3 ng/ml SCT in thick ascending limbs and with 1 nM AVP in collecting tubules, suggesting that enzyme sensitivity to hormones as well preserved under the conditions used in this study.
@article{ChabardesGIGMCM:1980,
author = {Chabardes, D. and Gagnan-Brunette, M. and Imbert-Teboul, M. and Gontcharevskaia, O. and Montegut, M. and Clique, A. and Morel, F.},
title = {Adenylate cyclase responsiveness to hormones in various portions of the human nephron.},
journal = {The Journal of Clinical Investigation},
volume = {65},
number = {2},
pages = {439-48},
year = {1980},
month = feb,
doi = {10.1172/JCI109687},
}J. Gary Augustson and Jack Minker. An analysis of some graph theoretical cluster techniques. Journal of the ACM (JACM), 17(4):571—588, 1970.
Several graph theoretic cluster techniques aimed at the automatic generation of thesauri for information retrieval systems are explored. Experimental cluster analysis is performed on a sample corpus of 2267 documents. A term-term similarity matrix is constructed for the 3950 unique terms used to index the documents. Various threshold values, T, are applied to the similarity matrix to provide a series of binary threshold matrices. The corresponding graph of each binary threshold matrix is used to obtain the term clusters. Three definitions of a cluster are analyzed: (1) the connected components of the threshold matrix; (2) the maximal complete subgraphs of the connected components of the threshold matrix; (3) clusters of the maximal complete subgraphs of the threshold matrix, as described by Gotlieb and Kumar. Algorithms are described and analyzed for obtaining each cluster type. The algorithms are designed to be useful for large document and index collections. Two algorithms have been tested that find maximal complete subgraphs. An algorithm developed by Bierstone offers a significant time improvement over one suggested by Bonner. For threshold levels T \(\ge\) 0.6, basically the same clusters are developed regardless of the cluster definition used. In such situations one need only find the connected components of the graph to develop the clusters.
@article{AugustsonM:1970,
author = {Augustson, J. Gary and Minker, Jack},
title = {An analysis of some graph theoretical cluster techniques},
journal = {Journal of the ACM (JACM)},
volume = {17},
number = {4},
pages = {571--588},
publisher = {ACM},
year = {1970},
doi = {10.1145/321607.321608},
}Frank Harary and Ian C. Ross. A procedure for clique detection using the group matrix. Sociometry, 20(3):205—215, 1957.
@article{HararyR:1957,
author = {Harary, Frank and Ross, Ian C.},
title = {A procedure for clique detection using the group matrix},
journal = {Sociometry},
volume = {20},
number = {3},
pages = {205--215},
publisher = {JSTOR},
year = {1957},
url = {http://www.jstor.org/stable/2785673},
}R. Duncan Luce and Albert D. Perry. A method of matrix analysis of group structure. Psychometrika, 14(1):95—116, 1949.
Matrix methods may be applied to the analysis of experimental data concerning group structure when these data indicate relationships which can be depicted by line diagrams such as sociograms. One may introduce two concepts,n-chain and clique, which have simple relationships to the powers of certain matrices. Using them it is possible to determine the group structure by methods which are both faster and more certain than less systematic methods. This paper describes such a matrix method and applies it to the analysis of practical examples. At several points some unsolved problems in this field are indicated.
@article{LuceP:1949,
author = {Luce, R. Duncan and Perry, Albert D.},
title = {A method of matrix analysis of group structure},
journal = {Psychometrika},
volume = {14},
number = {1},
pages = {95--116},
publisher = {Springer},
year = {1949},
doi = {10.1007/BF02289146},
}1.4 Exact methods
1.4.1 Bron-Kerbosch and variants
David Eppstein and Darren Strash. Listing all maximal cliques in large sparse real-world graphs. In Panos Pardalos and Steffen Rebennack, editors, Experimental Algorithms, volume 6630 of Lecture Notes in Computer Science, pages 364—375. Springer Berlin / Heidelberg, 2011.
Note: Implementation of EppsteinLS:2010 and comparison with TomitaTT:2006 on several benchmarks of real, large, but very sparse graphs with low degenearcy number, or very small DIMACS instances.
We implement a new algorithm for listing all maximal cliques in sparse graphs due to Eppstein, Löffler, and Strash (ISAAC 2010) and analyze its performance on a large corpus of real-world graphs. Our analysis shows that this algorithm is the first to offer a practical solution to listing all maximal cliques in large sparse graphs. All other theoretically-fast algorithms for sparse graphs have been shown to be significantly slower than the algorithm of Tomita et al. (Theoretical Computer Science, 2006) in practice. However, the algorithm of Tomita et al. uses an adjacency matrix, which requires too much space for large sparse graphs. Our new algorithm opens the door for fast analysis of large sparse graphs whose adjacency matrix will not fit into working memory.
@incollection{EppsteinS:2011,
author = {Eppstein, David and Strash, Darren},
title = {Listing All Maximal Cliques in Large Sparse Real-World Graphs},
volume = {6630},
booktitle = {Experimental Algorithms},
series = {Lecture Notes in Computer Science},
pages = {364-375},
editor = {Pardalos, Panos and Rebennack, Steffen},
publisher = {Springer Berlin / Heidelberg},
year = {2011},
doi = {10.1007/978-3-642-20662-7_31},
}David Eppstein, Marteen Löffler, and Darren Strash. Listing all maximal cliques in sparse graphs in near-optimal time. In Otfried Cheong, Kyung-Yong Chwa, and Kunsoo Park, editors, Algorithms and Computation, volume 6506 of Lecture Notes in Computer Science, pages 403—414. Springer Berlin / Heidelberg, 2010.
Note: Variation of BronK:1973 with nodes ordered by degeneracy \(d\), which runs in \(O(dn3^{d/3})\). The algorithm can be applied to large graphs with low degeneracy number (see EppsteinS:2011).
The degeneracy of an n-vertex graph G is the smallest number d such that every subgraph of G contains a vertex of degree at most \(d\). We show that there exists a nearly-optimal fixed-parameter tractable algorithm for enumerating all maximal cliques, parametrized by degeneracy. To achieve this result, we modify the classic Bron-Kerbosch algorithm and show that it runs in time \(O(dn3^{d/3})\). We also provide matching upper and lower bounds showing that the largest possible number of maximal cliques in an n-vertex graph with degeneracy \(d\) (when \(d\) is a multiple of 3 and \(n \ge d + 3\)) is \((n - d)3^{d/3}\). Therefore, our algorithm matches the \(\Theta(d(n - d)3^{d/3})\) worst-case output size of the problem whenever \(n - d = \Omega(n)\).
@incollection{EppsteinLS:2010,
author = {Eppstein, David and L{\"o}ffler, Marteen and Strash, Darren},
title = {Listing All Maximal Cliques in Sparse Graphs in Near-Optimal Time},
volume = {6506},
booktitle = {Algorithms and Computation},
series = {Lecture Notes in Computer Science},
pages = {403--414},
editor = {Cheong, Otfried and Chwa, Kyung-Yong and Park, Kunsoo},
publisher = {Springer Berlin / Heidelberg},
year = {2010},
doi = {10.1007/978-3-642-17517-6_36},
}Coen Bron and Joep Kerbosch. Algorithm 457: finding all cliques of an undirected graph. Communications of ACM, 16(9):575—577, sep 1973.
Note: Exact algorithm very popular in computational chemistry and other application domains. Variants with special pivoting rules are among the best performing exact algorithms for the problem. Being complete, it can be applied only to very small instances or to larger instances with small degeneracy number (see EppsteinS:2011).
@article{BronK:1973,
author = {Bron, Coen and Kerbosch, Joep},
title = {Algorithm 457: finding all cliques of an undirected graph},
journal = {Communications of ACM},
volume = {16},
number = {9},
pages = {575--577},
publisher = {ACM},
year = {1973},
month = sep,
address = {New York, NY, USA},
doi = {10.1145/362342.362367},
}1.4.2 Other exact methods
Chu-Min Li, Zhiwen Fang, and Ke Xu. Combining maxsat reasoning and incremental upper bound for the maximum clique problem. In Tools with Artificial Intelligence (ICTAI), 2013 IEEE 25th International Conference on, pages 939—946, nov 2013.
Recently, MaxSAT reasoning has been shown to be powerful in computing upper bounds for the cardinality of a maximum clique of a graph. However, existing upper bounds based on MaxSAT reasoning have two drawbacks: (1) at every node of the search tree, MaxSAT reasoning has to be performed from scratch to compute an upper bound and is time-consuming, (2) due to the NP-hardness of the MaxSATproblem, MaxSAT reasoning generally cannot be complete at anode of a search tree, and may not give an upper bound tight enough for pruning search space. In this paper, we propose an incremental upper bound and combine it with MaxSATreasoning to remedy the two drawbacks. The new approach is used to develop an efficient branch-and-bound algorithm forMaxClique, called IncMaxCLQ. We conduct experiments to show the complementarity of the incremental upper bound andMaxSAT reasoning and to compare IncMaxCLQ with several state-of-the-art algorithms for MaxClique.
@inproceedings{LiFX:2013,
author = {Li, Chu-Min and Fang, Zhiwen and Xu, Ke},
title = {Combining MaxSAT Reasoning and Incremental Upper Bound for the Maximum Clique Problem},
booktitle = {Tools with Artificial Intelligence (ICTAI), 2013 IEEE 25th International Conference on},
pages = {939--946},
year = {2013},
month = nov,
doi = {10.1109/ICTAI.2013.143},
}Ciaran McCreesh and Patrick Prosser. Multi-threading a state-of-the-art maximum clique algorithm. Algorithms, 6(4):618—635, 2013.
We present a threaded parallel adaptation of a state-of-the-art maximum clique algorithm for dense, computationally challenging graphs. We show that near-linear speedups are achievable in practice and that superlinear speedups are common. We include results for several previously unsolved benchmark problems.
@article{McCreeshP:2013,
author = {Ciaran McCreesh and Patrick Prosser},
title = {Multi-Threading a State-of-the-Art Maximum Clique Algorithm},
journal = {Algorithms},
volume = {6},
number = {4},
pages = {618--635},
publisher = {MDPI, Basel, Switzerland},
year = {2013},
doi = {10.3390/a6040618},
}Jingen Xiang, Cong Guo, and Ashraf Aboulnaga. Scalable maximum clique computation using mapreduce. To appear
We present a scalable and fault-tolerant solution for the maximum clique problem based on the MapReduce framework. The key contribution that enables us to effectively use MapReduce is a recursive partitioning method that partitions the graph into several subgraphs of similar size. After partitioning, the maximum cliques of the different partitions can be computed independently, and the computation is sped up using a branch and bound method. Our experiments show that our approach leads to good scalability, which is unachievable by other partitioning methods since they result in partitions of different sizes and hence lead to load imbalance. Our method is more scalable than an MPI algorithm, and is simpler and more fault tolerant.
@inproceedings{XiangGA:2013,
author = {Xiang, Jingen and Guo, Cong and Aboulnaga, Ashraf},
title = {Scalable Maximum Clique Computation Using MapReduce},
booktitle = {Proceedings of the IEEE International Conference on Data Engineering (ICDE '13)},
pages = {--},
publisher = {IEEE Computer Society},
year = {2013},
note = {To appear.},
}Chu-Min Li and Zhe Quan. An efficient branch-and-bound algorithm based on maxsat for the maximum clique problem. In Maria Fox and David Poole, editors, Proceedings of the Twenty-Fourth AAAI Conference on Artificial Intelligence, AAAI 2010, Atlanta, Georgia, USA, July 11-15, 2010. AAAI Press, 2010.
State-of-the-art branch-and-bound algorithms for the maximum clique problem (Maxclique) frequently use an upper bound based on a partition P of a graph into independent sets for a maximum clique of the graph, which cannot be very tight for imperfect graphs. In this paper we propose a new encoding from Maxclique into MaxSAT and use MaxSAT technology to improve the upper bound based on the partition P. In this way, the strength of specific algorithms for Maxclique in partitioning a graph and the strength of MaxSAT technology in propositional reasoning are naturally combined to solve Maxclique. Experimental results show that the approach is very effective on hard random graphs and on DIMACS Maxclique benchmarks, and allows to close an open DIMACS problem.
@inproceedings{LiQ:2010,
author = {Li, Chu-Min and Quan, Zhe},
title = {An Efficient Branch-and-Bound Algorithm Based on MaxSAT for the Maximum Clique Problem},
booktitle = {Proceedings of the Twenty-Fourth AAAI Conference on Artificial Intelligence, AAAI 2010, Atlanta, Georgia, USA, July 11-15, 2010},
editor = {Maria Fox and David Poole},
publisher = {AAAI Press},
year = {2010},
url = {http://www.aaai.org/ocs/index.php/AAAI/AAAI10/paper/view/1611},
}Chu-Min Li and Zhe Quan. Combining graph structure exploitation and propositional reasoning for the maximum clique problem. In 22nd IEEE International Conference on Tools with Artificial Intelligence (ICTAI), volume 1, pages 344—351. IEEE Computer Society, 2010.
State-of-the-art branch-and-bound algorithms for the maximum clique problem (Maxclique) generally exploit the structural information of a graph G to partition G into independent sets, in order to derive an upper bound for the cardinality of a maximum clique of G, which cannot be very tight for imperfect graphs. On the other hand, while Maxclique can be easily encoded into MaxSAT to be solved using a MaxSAT solver, general-purpose MaxSAT solvers are not competitive for solving Maxclique, because they do not exploit the structural information of the graph. Recently, we have shown that propositional reasoning developed for the MaxSAT solvers can be used to improve the upper bound based on the partition. In this paper, we propose and study several improvements to this approach by better combining graph structure exploitation and propositional reasoning to solve Maxclique. Experimental results show that the improvements are very effective on hard random graphs and on DIMACS Maxclique benchmarks which are widely used to evaluate branch-and-bound algorithms for Maxclique.
@inproceedings{LiQ:2010b,
author = {Chu-Min Li and Zhe Quan},
title = {Combining Graph Structure Exploitation and Propositional Reasoning for the Maximum Clique Problem},
volume = {1},
booktitle = {22nd IEEE International Conference on Tools with Artificial Intelligence (ICTAI)},
pages = {344--351},
publisher = {IEEE Computer Society},
year = {2010},
doi = {10.1109/ICTAI.2010.57},
}Etsuji Tomita, Akira Tanaka, and Haruhisa Takahashi. The worst-case time complexity for generating all maximal cliques and computational experiments. Theoretical Computer Science, 363(1):28—42, 2006.
Note: Theoretical work on worst case complexity of generating all maximal cliques with a depth-first search algorithm. The exact algorithm has a pruning methods that are similar to the Bron-Kerbosh algorithm (BronK:1973), and a different, more compact, representation of the enumerated maximal cliques. The algorithm has \(O(3^{n/3})\) worst-case time complexity for enumerating all maximal cliques (which is optimal).
We present a depth-first search algorithm for generating all maximal cliques of an undirected graph, in which pruning methods are employed as in the Bron-Kerbosch algorithm. All the maximal cliques generated are output in a tree-like form. Subsequently, we prove that its worst-case time complexity is \(O(3^{n/3})\) for an n-vertex graph. This is optimal as a function of n, since there exist up to \(3^{n/3}\) maximal cliques in an n-vertex graph. The algorithm is also demonstrated to run very fast in practice by computational experiments.
@article{TomitaTT:2006,
author = {Tomita, Etsuji and Tanaka, Akira and Takahashi, Haruhisa},
title = {The worst-case time complexity for generating all maximal cliques and computational experiments},
journal = {Theoretical Computer Science},
volume = {363},
number = {1},
pages = {28--42},
publisher = {Elsevier},
year = {2006},
doi = {10.1016/j.tcs.2006.06.015},
}Etsuji Tomita and Tomokazu Seki. An efficient branch-and-bound algorithm for finding a maximum clique. In Cristian Calude, Michael Dinneen, and Vincent Vajnovszki, editors, Discrete Mathematics and Theoretical Computer Science, volume 2731 of Lecture Notes in Computer Science, pages 278—289. Springer Berlin / Heidelberg, 2003.
We present an exact and efficient branch-and-bound algorithm for finding a maximum clique in an arbitrary graph. The algorithm is not specialized for any particular kind of graph. It employs approximate coloring and appropriate sorting of vertices to get an upper bound on the size of a maximum clique. We demonstrate by computational experiments on random graphs with up to 15,000 vertices and on DIMACS benchmark graphs that our algorithm remarkably outperforms other existing algorithms in general. It has been successfully applied to interesting problems in bioinformatics, image processing, the design of quantum circuits, and the design of DNA and RNA sequences for bio-molecular computation.
@incollection{TomitaS:2003,
author = {Tomita, Etsuji and Seki, Tomokazu},
title = {An Efficient Branch-and-Bound Algorithm for Finding a Maximum Clique},
volume = {2731},
booktitle = {Discrete Mathematics and Theoretical Computer Science},
series = {Lecture Notes in Computer Science},
pages = {278--289},
editor = {Calude, Cristian and Dinneen, Michael and Vajnovszki, Vincent},
publisher = {Springer Berlin / Heidelberg},
year = {2003},
doi = {10.1007/3-540-45066-1_22},
}Torsten Fahle. Simple and fast: Improving a branch-and-bound algorithm for maximum clique. In Rolf Möhring and Rajeev Raman, editors, Algorithms — ESA 2002, volume 2461 of Lecture Notes in Computer Science, pages 47—86. Springer Berlin / Heidelberg, 2002.
We consider a branch-and-bound algorithm for maximum clique problems. We introduce cost based filtering techniques for the socalled candidate set (i.e. a set of nodes that can possibly extend the clique in the current choice point).
Additionally, we present a taxonomy of upper bounds for maximum clique. Analytical results show that our cost based filtering is in a sense as tight as most of these well-known bounds for the maximum clique problem.
Experiments demonstrate that the combination of cost based filtering and vertex coloring bounds outperforms the old approach as well as approaches that only apply either of these techniques. Furthermore, the new algorithm is competitive with other recent algorithms for maximum clique.
Additionally, we present a taxonomy of upper bounds for maximum clique. Analytical results show that our cost based filtering is in a sense as tight as most of these well-known bounds for the maximum clique problem.
Experiments demonstrate that the combination of cost based filtering and vertex coloring bounds outperforms the old approach as well as approaches that only apply either of these techniques. Furthermore, the new algorithm is competitive with other recent algorithms for maximum clique.
@incollection{Fahle:2002,
author = {Fahle, Torsten},
title = {Simple and Fast: Improving a Branch-And-Bound Algorithm for Maximum Clique},
volume = {2461},
booktitle = {Algorithms -- ESA 2002},
series = {Lecture Notes in Computer Science},
pages = {47--86},
editor = {M{\"o}hring, Rolf and Raman, Rajeev},
publisher = {Springer Berlin / Heidelberg},
year = {2002},
doi = {10.1007/3-540-45749-6_44},
}Patric R.J. Östergård. A fast algorithm for the maximum clique problem. Discrete Applied Mathematics, 120(1):197—207, 2002.
Given a graph, in the maximum clique problem, one desires to find the largest number of vertices, any two of which are adjacent. A branch-and-bound algorithm for the maximum clique problem—which is computationally equivalent to the maximum independent (stable) set problem—is presented with the vertex order taken from a coloring of the vertices and with a new pruning strategy. The algorithm performs successfully for many instances when applied to random graphs and DIMACS benchmark graphs.
@article{Ostergard:2002,
author = {{\"O}sterg{\aa}rd, Patric R.J.},
title = {A fast algorithm for the maximum clique problem},
journal = {Discrete Applied Mathematics},
volume = {120},
number = {1},
pages = {197--207},
publisher = {Elsevier},
year = {2002},
doi = {10.1016/S0166-218X(01)00290-6},
}Yuji Shinano, Tetsuya Fujie, Yoshiko Ikebe, and Ryuichi Hirabayashi. Solving the maximum clique problem using pubb. In Parallel Processing Symposium, 1998. IPPS/SPDP 1998. Proceedings of the First Merged International… and Symposium on Parallel and Distributed Processing 1998, pages 326—332. IEEE, 1998.
Given an (undirected) graph G=(V, E), a clique of G is a subset of vertices in which every pair is connected by an edge. The problem of finding a clique of maximum size is a classical NP-hard problem, and many algorithms, both heuristic and exact, have been proposed. While the philosophy behind the heuristic algorithms varies greatly, almost all of the exact algorithms are designed in the branch-and-bound framework. As is well known, branch-and-bound is well suited to parallelization, and PUBB is a software utility which implements a generic version of it. The authors show effectiveness of parallelization of branch-and-bound for the maximum clique problem. Especially, by using PUBB with good heuristics and branching techniques, they were able to solve five previously unsolved DIMACS benchmark problems to optimality
@inproceedings{ShinanoFIH:1998,
author = {Shinano, Yuji and Fujie, Tetsuya and Ikebe, Yoshiko and Hirabayashi, Ryuichi},
title = {Solving the maximum clique problem using PUBB},
booktitle = {Parallel Processing Symposium, 1998. IPPS/SPDP 1998. Proceedings of the First Merged International... and Symposium on Parallel and Distributed Processing 1998},
pages = {326--332},
year = {1998},
doi = {10.1109/IPPS.1998.669935},
}David R. Wood. An algorithm for finding a maximum clique in a graph. Operations Research Letters, 21(5):211—217, 1997.
This paper introduces a branch-and-bound algorithm for the maximumclique problem which applies existing cliquefinding and vertex coloring heuristics to determine lower and upper bounds for the size of amaximumclique. Computational results on a variety of graphs indicate the proposed procedure in most instances outperforms leading algorithms.
@article{Wood:1997,
author = {Wood, David R.},
title = {An algorithm for finding a maximum clique in a graph},
journal = {Operations Research Letters},
volume = {21},
number = {5},
pages = {211--217},
publisher = {Elsevier},
year = {1997},
doi = {10.1016/S0167-6377(97)00054-0},
}Randy Carraghan and Panos M. Pardalos. An exact algorithm for the maximum clique problem. Operations Research Letters, 9(6):375—382, 1990.
A partially enumerative algorithm is presented for the maximum clique problem which is very simple to implement. Computational results for an efficient implementation on an IBM 3090 computer are provided for randomly generated graphs with up to 3000 vertices and over one million edges. Also provided are exact specifications for test problems to facilitate future comparisons. In addition, the Fortran 77 code of the proposed algorithm is given.
@article{CarraghanP:1990,
author = {Randy Carraghan and Panos M. Pardalos},
title = {An exact algorithm for the maximum clique problem},
journal = {Operations Research Letters},
volume = {9},
number = {6},
pages = {375--382},
year = {1990},
doi = {10.1016/0167-6377(90)90057-C},
}C. Friden, A. Hertz, and D. De Werra. Tabaris: an exact algorithm based on tabu search for finding a maximum independent set in a graph. Computers & Operations Research, 17(5):437—445, 1990. [Maximum Independent Set]
A technique for finding in a graph an independent set with maximum cardinality is presented. It consists of an implicit enumeration procedure; the procedure uses at various stages bounds on the independence number of a subgraph. These are obtained by applying an adaptation of Tabu Search. Computational results are given which show that with Tabu Search a competitive algorithm is obtained; the case of randomly generated graphs having up to 450 or 500 nodes (with edge density 0.5) can be handled by this approach.
@article{FridenHW:1990,
author = {Friden, C. and Hertz, A. and De Werra, D.},
title = {TABARIS: an exact algorithm based on Tabu Search for finding a maximum independent set in a graph},
journal = {Computers & Operations Research},
volume = {17},
number = {5},
pages = {437--445},
publisher = {Elsevier},
year = {1990},
doi = {10.1016/0305-0548(90)90048-C},
}Egon Balas and Chang Sung Yu. Finding a maximum clique in an arbitrary graph. SIAM Journal on Computing, 15:1054, 1986.
We describe a new type of branch and bound procedure for finding a maximum clique in an arbitrary graph \(G = (V,E)\). The two main ingredients, both of \(O(|V| + |E|)\) time complexity, are (i) an algorithm for finding a maximal triangulated induced subgraph of \(G\); and (ii) an algorithm for finding a maximal \(k\)-chromatic induced subgraph of \(G\). We discuss computational experience on randomly generated graphs with up to 400 vertices and 30,000 edges.
@article{BalasY:1986,
author = {Balas, Egon and Yu, Chang Sung},
title = {Finding a maximum clique in an arbitrary graph},
journal = {SIAM Journal on Computing},
volume = {15},
pages = {1054},
year = {1986},
doi = {10.1137/0215075},
}1.5 Continuous formulations
Yuejian Peng and Cheng Zhao. A motzkin-straus type result for 3-uniform hypergraphs. Graphs and Combinatorics, pages 1—14, 2012.
Motzkin and Straus established a remarkable connection between the maximum clique and the Lagrangian of a graph in [ 8 ]. They showed that if G is a 2-graph in which a largest clique has order l then \({\lambda(G)=\lambda(K^{(2)}_l),}\) where λ( G ) denotes the Lagrangian of G . It is interesting to study a generalization of the Motzkin-Straus Theorem to hypergraphs. In this note, we give a Motzkin-Straus type result. We show that if m and l are positive integers satisfying \({{l-1 \choose 3} \le m \le {l-1 \choose 3} + {l-2 \choose 2}}\) and G is a 3-uniform graph with m edges and G contains a \({K_{l-1}^{(3)}}\), a clique of order l -1, then \({\lambda(G) = \lambda(K_{l-1}^{(3)})}\). Furthermore, the upper bound \({{l-1 \choose 3} + {l-2 \choose 2}}\) is the best possible.
@article{PengZ:2012,
author = {Peng, Yuejian and Zhao, Cheng},
title = {A Motzkin-Straus Type Result for 3-Uniform Hypergraphs},
journal = {Graphs and Combinatorics},
pages = {1-14},
publisher = {Springer Japan},
year = {2012},
}Marcello Pelillo and Andrea Torsello. Payoff-monotonic game dynamics and the maximum clique problem. Neural Computation, 18(5):1215—58, may 2006.
Evolutionary game-theoretic models and, in particular, the so-called replicator equations have recently proven to be remarkably effective at approximately solving the maximum clique and related problems. The approach is centered around a classic result from graph theory that formulates the maximum clique problem as a standard (continuous) quadratic program and exploits the dynamical properties of these models, which, under a certain symmetry assumption, possess a Lyapunov function. In this letter, we generalize previous work along these lines in several respects. We introduce a wide family of game-dynamic equations known as payoff-monotonic dynamics, of which replicator dynamics are a special instance, and show that they enjoy precisely the same dynamical properties as standard replicator equations. These properties make any member of this family a potential heuristic for solving standard quadratic programs and, in particular, the maximum clique problem. Extensive simulations, performed on random as well as DIMACS benchmark graphs, show that this class contains dynamics that are considerably faster than and at least as accurate as replicator equations. One problem associated with these models, however, relates to their inability to escape from poor local solutions. To overcome this drawback, we focus on a particular subclass of payoff-monotonic dynamics used to model the evolution of behavior via imitation processes and study the stability of their equilibria when a regularization parameter is allowed to take on negative values. A detailed analysis of these properties suggests a whole class of annealed imitation heuristics for the maximum clique problem, which are based on the idea of varying the parameter during the imitation optimization process in a principled way, so as to avoid unwanted inefficient solutions. Experiments show that the proposed annealing procedure does help to avoid poor local optima by initially driving the dynamics toward promising regions in state space. Furthermore, the models outperform state-of-the-art neural network algorithms for maximum clique, such as mean field annealing, and compare well with powerful continuous-based heuristics. Mestre, Italy. pelillo@dsi.unive.it
@article{PelilloT:2006,
author = {Pelillo, Marcello and Torsello, Andrea},
title = {Payoff-monotonic game dynamics and the maximum clique problem.},
journal = {Neural Computation},
volume = {18},
number = {5},
pages = {1215-58},
year = {2006},
month = may,
doi = {10.1162/089976606776241011},
}Immanuel M. Bomze, Marco Budinich, Marcello Pelillo, and Claudio Rossi. Annealed replication: a new heuristic for the maximum clique problem. Discrete Applied Mathematics, 121(1-3):27—49, 2002.
We propose a new heuristic for approximating the maximum clique problem based on a detailed analysis of a class of continuous optimization models which provide a complete characterization of solutions to this NP-hard combinatorial problem. We start from a known continuous formulation of the maximum clique, and tackle the search for local solutions with replicator dynamics, a class of dynamical systems developed in various branches of mathematical biology. Hereby, we add to the objective used in previous works a regularization term that controls the global shape of the energy landscape, that is the function actually maximized by the dynamics. The parameter controlling the regularization is changed during the evolution of the dynamical system to render inefficient local solutions (which formerly were stable) unstable, thus conducting the system to escape from sub-optimal points, and so to improve the final results. The role of this parameter is thus superficially similar to that of temperature in simulated annealing in the sense that its variation allows to find better solutions for the problem at hand. We demonstrate several theoretical results on the regularization term and we further support the validity of this approach, reporting on its performances when applied to selected DIMACS benchmark graphs.
@article{BomzeBPR:2002,
author = {Immanuel M. Bomze and Marco Budinich and Marcello Pelillo and Claudio Rossi},
title = {Annealed replication: a new heuristic for the maximum clique problem},
journal = {Discrete Applied Mathematics},
volume = {121},
number = {1-3},
pages = {27--49},
publisher = {Elsevier},
year = {2002},
doi = {10.1016/S0166-218X(01)00233-5},
}Samuel Burer, Renato D.C. Monteiro, and Yin Zhang. Maximum stable set formulations and heuristics based on continuous optimization. Mathematical Programming, 94(1):137—166, 2002. [Maximum Independent Set]
The stability number α(G) for a given graph G is the size of a maximum stable set in G . The Lovász theta number provides an upper bound on α(G) and can be computed in polynomial time as the optimal value of the Lovász semidefinite program. In this paper, we show that restricting the matrix variable in the Lovász semidefinite program to be rank-one and rank-two, respectively, yields a pair of continuous, nonlinear optimization problems each having the global optimal value α(G) . We propose heuristics for obtaining large stable sets in G based on these new formulations and present computational results indicating the effectiveness of the heuristics.
@article{BurerMZ:2002,
author = {Burer, Samuel and Monteiro, Renato D.C. and Zhang, Yin},
title = {Maximum stable set formulations and heuristics based on continuous optimization},
journal = {Mathematical Programming},
volume = {94},
number = {1},
pages = {137--166},
publisher = {Springer},
year = {2002},
doi = {10.1007/s10107-002-0356-4},
}Immanuel M. Bomze, Marcello Pelillo, and Robert Giacomini. Evolutionary approach to the maximum clique problem: Empirical evidence on a larger scale. In Immanuel M. Bomze, Tibor Csendes, Reiner Horst, and Panos M. Pardalos, editors, Developments in global optimization, volume 18, pages 95—108. Dordrecht, The Netherlands: Kluwer, 1997.
An algorithm for finding a maximum clique in a graph is presented which uses the Comtet regularization of the Motzkin/Straus continuous problem formulation: maximize an indefinite quadratic form over the standard simplex. We shortly review some surprising connection of the problem with dynamic principles of evolutionary game theory, and give a detailed report our numerical experiences with the method proposed.
@incollection{BomzePG:1997,
author = {Bomze, Immanuel M. and Pelillo, Marcello and Giacomini, Robert},
title = {Evolutionary approach to the maximum clique problem: Empirical evidence on a larger scale},
volume = {18},
booktitle = {Developments in global optimization},
pages = {95--108},
editor = {Bomze, Immanuel M. and Csendes, Tibor and Horst, Reiner and Pardalos, Panos M.},
publisher = {Dordrecht, The Netherlands: Kluwer},
year = {1997},
}Luana E. Gibbons, Donald W. Hearn, Panos M. Pardalos, and Motakuri V. Ramana. Continuous characterizations of the maximum clique problem. Mathematics of Operations Research, 22(3):pp. 754—768, 1997.
Given a graph G whose adjacency matrix is A, the Motzkin-Strauss formulation of the Maximum-Clique Problem is the quadratic program max \(\{x^{T}Ax|x^{T}e=1,\ x\geq 0\}\). It is well known that the global optimum value of this QP is \((1 - 1/\omega(G))\), where \(\omega(G)\) is the clique number of G. Here, we characterize the following properties pertaining to the above QP: (1) first order optimality, (2) second order optimality, (3) local optimality, (4) strict local optimality. These characterizations reveal interesting underlying discrete structures, and are polynomial time verifiable. A parametrization of the Motzkin-Strauss QP is then introduced and its properties are investigated. Finally, an extension of the Motzkin-Strauss formulation is provided for the weighted clique number of a graph.
@article{GibbonsJPR:1997,
author = {Gibbons, Luana E. and Hearn, Donald W. and Pardalos, Panos M. and Ramana, Motakuri V.},
title = {Continuous Characterizations of the Maximum Clique Problem},
journal = {Mathematics of Operations Research},
volume = {22},
number = {3},
pages = {pp. 754--768},
publisher = {INFORMS},
year = {1997},
url = {http://www.jstor.org/stable/3690403},
}Luana E. Gibbons, Donald W. Hearn, and Panos M. Pardalos. A continuous based heuristic for the maximum clique problem. Cliques Coloring and Satisfiability Second DIMACS Implementation Challenge, 26:103—124, 1996.
@article{GibbonsJP:1996,
author = {Gibbons, Luana E. and Hearn, Donald W. and Pardalos, Panos M.},
title = {A continuous based heuristic for the maximum clique problem},
journal = {Cliques Coloring and Satisfiability Second DIMACS Implementation Challenge},
volume = {26},
series = {DIMACS Series},
pages = {103--124},
publisher = {American Mathematical Society},
year = {1996},
}Marcello Pelillo. Relaxation labeling networks for the maximum clique problem. Journal of Artificial Neural Networks, 2(4):313—328, 1995.
Relaxation labeling networks are a class of parallel distributed computational models extremely popular in computer vision and pattern recognition. Despite their original heuristic derivation, they possess in fact interesting dynamical properties and learning abilities, and exhibit also a certain biological plausibility. In this paper, it is shown how to take advantage of the properties of these models to solve the maximum clique problem, a well-known intractable optimization problem which has practical applications in various fields. The approach is based on a result by Motzkin and Straus which naturally leads to formulate the problem in a manner that is readily mapped onto a relaxation labeling network. Extensive simulations have practically demonstrated the validity of the proposed model.
@article{Pelillo:1995,
author = {Pelillo, Marcello},
title = {Relaxation labeling networks for the maximum clique problem},
journal = {Journal of Artificial Neural Networks},
volume = {2},
number = {4},
pages = {313--328},
year = {1995},
doi = {10.1049/cp:19950548},
}Panos M. Pardalos and Andrew T. Phillips. A global optimization approach for solving the maximum clique problem. International Journal of Computer Mathematics, 33(3-4):209—216, 1990.
The problem of finding a maximum clique of an undirected graph is formulated and solved as a linearly constrained indefinite quadratic global optimization problem. Theoretical upper and lower bounds on the size k of the maximum clique are derived from the global optimization formulation, and a relationship between the set of distinct global maxima of the optimization problem and the set of distinct maximum cliques of the graph is discussed. In addition, some preliminary computational results are also presented.
@article{PardalosP:1990,
author = {Pardalos, Panos M. and Phillips, Andrew T.},
title = {A global optimization approach for solving the maximum clique problem},
journal = {International Journal of Computer Mathematics},
volume = {33},
number = {3-4},
pages = {209--216},
publisher = {Taylor & Francis},
year = {1990},
doi = {10.1080/00207169008803851},
}1.6 Instances
1.6.1DIMACS
Mark Brockington and Joseph C. Culberson. Camouflaging independent sets in quasi-random graphs. Cliques Coloring and Satisfiability Second DIMACS Implementation Challenge, 26:75—88, 1996.
In this paper, we look at the problem of how one might try to hide a large independent set in a graph in which all other independent sets are significantly smaller.
We observe that the most common methods of generating graphs with known maximum independent sets are subject to attack using simple techniques that are regularly successful on graphs of practical size. We present an improved random graph generation system, DELTA, which increases the range of maximum independent sets that can be hidden from these techniques.
We observe that the most common methods of generating graphs with known maximum independent sets are subject to attack using simple techniques that are regularly successful on graphs of practical size. We present an improved random graph generation system, DELTA, which increases the range of maximum independent sets that can be hidden from these techniques.
@article{BrockingtonC:1996,
author = {Brockington, Mark and Culberson, Joseph C.},
title = {Camouflaging Independent Sets in Quasi-Random Graphs},
journal = {Cliques Coloring and Satisfiability Second DIMACS Implementation Challenge},
volume = {26},
series = {DIMACS Series},
pages = {75--88},
publisher = {American Mathematical Society},
year = {1996},
}Jeffrey C. Lagarias and Peter W. Shor. Keller’s cube-tiling conjecture is false in high dimensions. BAMS: Bulletin of the American Mathematical Society, 27(2):279—283, 1992.
O. H. Keller conjectured in 1930 that in any tiling of \(\mathbb{R}^n\) by unit \(n\)-cubes there exist two of them having a complete facet in common. O. Perron proved this conjecture for \(n \lt 6\). We show that for all \(n \gt 10\) there exists a tiling of \(\mathbb{R}^n\) by unit \(n\)-cubes such that no two n-cubes have a complete facet in common.
@article{LagariasS:1992,
author = {Lagarias, Jeffrey C. and Shor, Peter W.},
title = {Keller's Cube-Tiling Conjecture Is False in High Dimensions},
journal = {BAMS: Bulletin of the American Mathematical Society},
volume = {27},
number = {2},
pages = {279--283},
year = {1992},
doi = {10.1090/S0273-0979-1992-00318-X},
}David S. Johnson, Cecilia R. Aragon, Lyle A. McGeoch, and Catherine Schevon. Optimization by simulated annealing: an experimental evaluation; part {II}, graph coloring and number partitioning. Operations Research, 39(3):378—406, may 1991.
This is the second in a series of three papers that empirically examine the competitiveness of simulated annealing in certain well-studied domains of combinatorial optimization. Simulated annealing is a randomized technique proposed by S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi for improving local optimization algorithms. Here we report on experiments at adapting simulated annealing to graph coloring and number partitioning, two problems for which local optimization had not previously been thought suitable. For graph coloring, we report on three simulated annealing schemes, all of which can dominate traditional techniques for certain types of graphs, at least when large amounts of computing time are available. For number partitioning, simulated annealing is not competitive with the differencing algorithm of N. Karmarkar and R. M. Karp, except on relatively small instances. Moreover, if running time is taken into account, natural annealing schemes cannot even outperform multiple random runs of the local optimization algorithms on which they are based, in sharp contrast to the observed performance of annealing on other problems.
@article{JohnsonAMS:1991,
author = {Johnson, David S. and Aragon, Cecilia R. and McGeoch, Lyle A. and Schevon, Catherine},
title = {Optimization by simulated annealing: an experimental evaluation; part {II}, graph coloring and number partitioning},
journal = {Operations Research},
volume = {39},
number = {3},
pages = {378--406},
publisher = {INFORMS},
year = {1991},
month = may,
address = {Institute for Operations Research and the Management Sciences (INFORMS), Linthicum, Maryland, USA},
doi = {10.1287/opre.39.3.378},
}K. Corrádi and S. Szabó. A combinatorial approach for keller’s conjecture. Periodica Mathematica Hungarica, 21(2):95—100, 1990.
The statement, that in a tiling by translates of an \(n\)-dimensional cube there are two cubes having common (n-1)-dimensional faces, is known as Keller’s conjecture. We shall prove that there is a counterexample for this conjecture if and only if the following graphs \(\Gamma_n\) has a \(2^n\) size clique. The \(4^n\) vertices of \(\Gamma_n\) are \(n\)-tuples of integers 0, 1, 2, and 3. A pair of these \(n\)-tuples are adjacent if there is a position at which the difference of the corresponding components is 2 modulo 4 and if there is a further position at which the corresponding components are different. We will give the size of the maximal cliques of \(\Gamma_n\) for \(n \lt 5\).
@article{CorradiS:1990,
author = {Corr{\'a}di, K. and Szab{\'o}, S.},
title = {A combinatorial approach for Keller's conjecture},
journal = {Periodica Mathematica Hungarica},
volume = {21},
number = {2},
pages = {95-100},
publisher = {Akad{\'e}miai Kiad{\'o}, co-published with Springer Science+Business Media B.V., Formerly Kluwer Academic Publishers B.V.},
year = {1990},
doi = {10.1007/BF01946848},
}2 Generalisations
2.1 Quasi-Cliques
2.1.1 Stochastic Local Search algorithms
Sanghamitra Bandyopadhyay and Malay Bhattacharyya. A neuro-ga approach for the maximum fuzzy clique problem. 5506:605—612, 2009
The maximum clique problem, into which many problems have been mapped effectively, is of great importance in graph theory. A natural extension to this problem, emerging very recently in many real-life networks, is its fuzzification. The problem of finding the maximum clique in a fuzzy graph has been addressed in this paper. It has been shown here, that this problem reduces to an unconstrained quadratic 0-1 programming problem. Using a maximum neural network, along with, chaotic mutation capability of genetic algorithms, the reduced problem has been solved. Empirical studies have been done by applying the method on a gene co-expression network and on some benchmark graphs.
@article{BandyopadhyayB:2009,
author = {Bandyopadhyay, Sanghamitra and Bhattacharyya, Malay},
title = {A Neuro-GA approach for the maximum fuzzy clique problem},
volume = {5506},
booktitle = {Advances in Neuro-Information Processing},
series = {Lecture Notes in Computer Science},
pages = {605-612},
editor = {K{\"o}ppen, Mario and Kasabov, Nikola and Coghill, George},
publisher = {Springer Berlin / Heidelberg},
year = {2009},
doi = {10.1007/978-3-642-02490-0_74},
}Mauro Brunato, Holger H. Hoos, and Roberto Battiti. On effectively finding maximal quasi-cliques in graphs. In Vittorio Maniezzo, Roberto Battiti, and Jean-Paul Watson, editors, Learning and Intelligent Optimization, Lecture Notes in Computer Science, pages 41—55. Springer-Verlag, Berlin, Heidelberg, 2008.
Note: New unifying formulation of quasi-cliques and adaptation of a reactive tabu search (BattitiM:2010) and a dynamic local search (PullanH:2006) for the problem.
The problem of finding a maximum clique in a graph is prototypical for many clustering and similarity problems; however, in many real-world scenarios, the classical problem of finding a complete subgraph needs to be relaxed to finding an almost complete subgraph, a so-called quasi-clique. In this work, we demonstrate how two previously existing definitions of quasi-cliques can be unified and how the resulting, more general quasi-clique finding problem can be solved by extending two state-of-the-art stochastic local search algorithms for the classical maximum clique problem. Preliminary results for these algorithms applied to both, artificial and real-world problem instances demonstrate the usefulness of the new quasi-clique definition and the effectiveness of our algorithms.
@incollection{BrunatoHB:2008,
author = {Brunato, Mauro and Hoos, Holger H. and Battiti, Roberto},
title = {On Effectively Finding Maximal Quasi-cliques in Graphs},
booktitle = {Learning and Intelligent Optimization},
series = {Lecture Notes in Computer Science},
pages = {41--55},
editor = {Maniezzo, Vittorio and Battiti, Roberto and Watson, Jean-Paul},
publisher = {Springer-Verlag},
year = {2008},
address = {Berlin, Heidelberg},
doi = {10.1007/978-3-540-92695-5_4},
}2.1.2 Applications
Gaël Varoquaux, Alexandre Gramfort, Jean-Baptiste Poline, and Bertrand Thirion. Markov models for fmri correlation structure: Is brain functional connectivity small world, or decomposable into networks. In press [neuroscience - brain networks]
Correlations in the signal observed via functional Magnetic Resonance Imaging (fMRI), are expected to reveal the interactions in the underlying neural populations through hemodynamic response. In particular, they highlight distributed set of mutually correlated regions that correspond to brain networks related to different cognitive functions. Yet graph-theoretical studies of neural connections give a different picture: that of a highly integrated system with small-world properties: local clustering but with short pathways across the complete structure. We examine the conditional independence properties of the fMRI signal, i.e. its Markov structure, to find realistic assumptions on the connectivity structure that are required to explain the observed functional connectivity. In particular we seek a decomposition of the Markov structure into segregated functional networks using decomposable graphs: a set of strongly-connected and partially overlapping cliques. We introduce a new method to efficiently extract such cliques on a large, strongly-connected graph. We compare methods learning different graph structures from functional connectivity by testing the goodness of fit of the model they learn on new data. We find that summarizing the structure as strongly-connected networks can give a good description only for very large and overlapping networks. These results highlight that Markov models are good tools to identify the structure of brain connectivity from fMRI signals, but for this purpose they must reflect the small-world properties of the underlying neural systems.
@article{VaroquauxGPT:2012,
author = {Ga{\"e}l Varoquaux and Alexandre Gramfort and Jean-Baptiste Poline and Bertrand Thirion},
title = {Markov models for fMRI correlation structure: Is brain functional connectivity small world, or decomposable into networks?},
journal = {Journal of Physiology-Paris},
year = {2012},
note = {In press.},
doi = {10.1016/j.jphysparis.2012.01.001},
}2.2 Weighted Maximum Clique
2.2.1 Surveys / Theory
Andreas Brandstädt and Vassilis Giakoumakis. Maximum weight independent sets in hole- and co-chair-free graphs. Information Processing Letters, 112(3):67—71, 2012. [Maximum Independent Set] Restriction to graph class having special properties.
The Maximum Weight Independent Set (MWIS) problem on graphs with vertex weights asks for a set of pairwise nonadjacent vertices of maximum total weight. Being one of the most investigated and most important problems on graphs, it is well known to be NP-complete and hard to approximate. The complexity of MWIS is open for hole-free graphs (i.e., graphs without induced subgraphs isomorphic to a chordless cycle of length at least five). By applying a combination of clique separator and modular decomposition, we obtain a polynomial time solution of MWIS for hole- and co-chair-free graphs (the co-chair consists of five vertices four of which form a clique minus one edge - a diamond - and the fifth has degree one and is adjacent to one of the degree two vertices of the diamond).
@article{BrandstadtG:2012,
author = {Brandst{\"a}dt, Andreas and Giakoumakis, Vassilis},
title = {Maximum Weight Independent Sets in hole- and co-chair-free graphs},
journal = {Information Processing Letters},
volume = {112},
number = {3},
pages = {67-71},
year = {2012},
doi = {10.1016/j.ipl.2011.09.015},
}Pedro Martins. Cliques with maximum/minimum edge neighborhood and neighborhood density. Computers and Operations Research, 39(3):594—608, 2012.
Given a graph \(G=(V,E)\) and a clique \(C\) of \(G\), the edge neighborhood of \(C\) can be defined as the total number of edges running between \(C\) and \(V \setminus C\), being denoted by \(N(C)\). The density of the edge neighborhood \(N(C)\) can be set as the ratio \((|N(C)|/(|C|\cdot|V/C|))\). This paper addresses maximum/minimum edge neighborhood and neighborhood density cliques in G. Two versions will be undertaken, by fixing, or not, the size of the cliques. From an optimization point of view these problems do not bring much novelty, as they can be seen as particular or special versions of weighted clique problems. However, from a practical point of view, they concentrate on certain kinds of properties of cliques, rather than their size, revealing clique’s engagement in the graph. In fact, a maximum edge neighborhood clique should be strongly embraced in the graph, while a minimum edge neighborhood clique should reveal an almost isolated strong component. In particular, special versions of the new problems allow to distinguish among cliques of the same size, namely among possible tied maximum cliques in the graph. We propose node based formulations for these edge based clique related problems. Using these models, we present computational results and suggest applications where the new problems can bring additional insights.
@article{Martins:2012,
author = {Martins, Pedro},
title = {Cliques with maximum/minimum edge neighborhood and neighborhood density},
journal = {Computers and Operations Research},
volume = {39},
number = {3},
pages = {594-608},
year = {2012},
doi = {10.1016/j.cor.2011.04.016},
}Nicolas Trotignon and Kristina Vušković. Combinatorial optimization with 2-joins. Journal of Combinatorial Theory. Series B, 102(1):153—185, 2012. Restriction to graph class having special properties.
A 2-join is an edge cutset that naturally appears in decomposition of several classes of graphs closed under taking induced subgraphs, such as perfect graphs and claw-free graphs. In this paper we construct combinatorial polynomial time algorithms for finding a maximum weighted clique, a maximum weighted stable set and an optimal coloring for a class of perfect graphs decomposable by 2-joins: the class of perfect graphs that do not have a balanced skew partition, a 2-join in the complement, nor a homogeneous pair. The techniques we develop are general enough to be easily applied to finding a maximum weighted stable set for another class of graphs known to be decomposable by 2-joins, namely the class of even-hole-free graphs that do not have a star cutset. We also give a simple class of graphs decomposable by 2-joins into bipartite graphs and line graphs, and for which finding a maximum stable set is NP-hard. This shows that having holes all of the same parity gives essential properties for the use of 2-joins in computing stable sets.
@article{TrotignonV:2012,
author = {Trotignon, Nicolas and Vu{\vs}kovi{\'c}, Kristina},
title = {Combinatorial optimization with 2-joins},
journal = {Journal of Combinatorial Theory. Series B},
volume = {102},
number = {1},
pages = {153-185},
year = {2012},
doi = {10.1016/j.jctb.2011.06.002},
}2.2.2 Stochastic Local Search algorithms
Qinghua Wu, Jin-Kao Hao, and Fred Glover. Multi-neighborhood tabu search for the maximum weight clique problem. Annals of Operations Research, 196(1):611—634, 2012.
Given an undirected graph \(G =( V , E )\) with vertex set \(V ={1, \dots, n}\) and edge set \(E \subseteq V \times V\). Let \(w : V \to Z^+\) be a weighting function that assigns to each vertex \(i \in V\) a positive integer. The maximum weight clique problem (MWCP) is to determine a clique of maximum weight. This paper introduces a tabu search heuristic whose key features include a combined neighborhood and a dedicated tabu mechanism using a randomized restart strategy for diversification. The proposed algorithm is evaluated on a total of 136 benchmark instances from different sources (DIMACS, BHOSLIB and set packing). Computational results disclose that our new tabu search algorithm outperforms the leading algorithm for the maximum weight clique problem, and in addition rivals the performance of the best methods for the unweighted version of the problem without being specialized to exploit this problem class.
@article{WuHG:2012,
author = {Wu, Qinghua and Hao, Jin-Kao and Glover, Fred},
title = {Multi-neighborhood tabu search for the maximum weight clique problem},
journal = {Annals of Operations Research},
volume = {196},
number = {1},
pages = {611-634},
publisher = {Springer Netherlands},
year = {2012},
doi = {10.1007/s10479-012-1124-3},
}Wayne Pullan. Approximating the maximum vertex/edge weighted clique using local search. Journal of Heuristics, 14(2):117—134, 2007.
This paper extends the recently introduced Phased Local Search (PLS) algorithm to more difficult maximum clique problems and also adapts the algorithm to handle maximum vertex/edge weighted clique instances. PLS is a stochastic reactive dynamic local search algorithm that interleaves sub-algorithms which alternate between sequences of iterative improvement, during which suitable vertices are added to the current sub-graph, and plateau search, where vertices of the current sub-graph are swapped with vertices not contained in the current sub-graph. These sub-algorithms differ in firstly their vertex selection techniques in that selection can be solely based on randomly selecting a vertex, randomly selecting within highest vertex degree, or random selecting within vertex penalties that are dynamically adjusted during the search. Secondly, the perturbation mechanism used to overcome search stagnation differs between the sub-algorithms. PLS has no problem instance dependent parameters and achieves state-of-the-art performance for maximum clique and maximum vertex/edge weighted clique problems over a large range of the commonly used DIMACS benchmark instances.
@article{Pullan:2007,
author = {Pullan, Wayne},
title = {Approximating the maximum vertex/edge weighted clique using local search},
journal = {Journal of Heuristics},
volume = {14},
number = {2},
pages = {117--134},
year = {2007},
doi = {10.1007/s10732-007-9026-2},
}2.2.3 Applications
Xavier Delorme, Alexandre Dolgui, and Mikhail Y. Kovalyov. Combinatorial design of a minimum cost transfer line. Omega, 40(1):31—41, 2012. [assemply lines optimisation]
The problem of equipment selection for a production line is considered. Each piece of equipment, also called unit or block, performs a set of operations. All necessary operations of the line and all available blocks with their costs are known. The difficulty is to choose the most appropriate blocks and group them into (work)stations. There are some constraints that restrict the assignment of different blocks to the same station. Two combinatorial approaches for solving this problem are suggested. Both are based on a novel concept of locally feasible stations. The first approach combinatorially enumerates all feasible solutions, and the second reduces the problem to search for a maximum weight clique. A boolean linear program based on a set packing formulation is presented. Computer experiments with benchmark data are described. Their results show that the set packing model is competitive and can be used to solve real-life problems.
@article{DelormeDK:2012,
author = {Delorme, Xavier and Dolgui, Alexandre and Kovalyov, Mikhail Y.},
title = {Combinatorial design of a minimum cost transfer line},
journal = {Omega},
volume = {40},
number = {1},
pages = {31-41},
year = {2012},
doi = {10.1016/j.omega.2011.03.004},
}Franco Mascia, Elisa Cilia, Mauro Brunato, and Andrea Passerini. Predicting structural and functional sites in proteins by searching for maximum-weight cliques. In Maria Fox and David Poole, editors, Proceedings of the Twenty-Fourth AAAI Conference on Artificial Intelligence, AAAI 2010, Atlanta, Georgia, USA, July 11-15, 2010. AAAI Press, 2010. [bioinformatics - proteomics - metal-binding site discovery - active site prediction - supervised clustering]
Note: Novel supervised clustering technique based on weighted maximum cliques, for collectively predicting all the residues belonging to the same protein functional site.
Fully characterizing structural and functional sites in proteins is a fundamental step in understanding their roles in the cell. This extremely challenging combinatorial problem requires determining the number of sites in the protein and the set of residues involved in each of them. We formulate it as a distance-based supervised clustering task, where training proteins are employed to learn a proper distance function between residues. A partial clustering is then returned by searching for maximum-weight cliques in the resulting weighted graph representation of proteins. A novel stochastic local search algorithm is proposed to efficiently generate approximate solutions. Our method achieves substantial improvements over a previous structured-output approach for metal binding site prediction. Significant improvements over the current state-of-the-art are also achieved in predicting catalytic sites from 3D structure in enzymes.
@inproceedings{MasciaCBP:2010,
author = {Mascia, Franco and Cilia, Elisa and Brunato, Mauro and Passerini, Andrea},
title = {Predicting Structural and Functional Sites in Proteins by Searching for Maximum-weight Cliques},
booktitle = {Proceedings of the Twenty-Fourth AAAI Conference on Artificial Intelligence, AAAI 2010, Atlanta, Georgia, USA, July 11-15, 2010},
editor = {Maria Fox and David Poole},
publisher = {AAAI Press},
year = {2010},
url = {http://www.aaai.org/ocs/index.php/AAAI/AAAI10/paper/view/1833},
}Massimiliano Pavan and Marcello Pelillo. Dominant sets and pairwise clustering. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 29(1):167—172, 2007. [clustering - computer vision - image segmentation]
We develop a new graph-theoretic approach for pairwise data clustering which is motivated by the analogies between the intuitive concept of a cluster and that of a dominant set of vertices, a notion introduced here which generalizes that of a maximal complete subgraph to edge-weighted graphs. We establish a correspondence between dominant sets and the extrema of a quadratic form over the standard simplex, thereby allowing the use of straightforward and easily implementable continuous optimization techniques from evolutionary game theory. Numerical examples on various point-set and image segmentation problems confirm the potential of the proposed approach.
@article{PavanP:2007,
author = {Pavan, Massimiliano and Pelillo, Marcello},
title = {Dominant sets and pairwise clustering},
journal = {Pattern Analysis and Machine Intelligence, IEEE Transactions on},
volume = {29},
number = {1},
pages = {167--172},
publisher = {IEEE},
year = {2007},
doi = {10.1109/TPAMI.2007.250608},
}Shidong Wang, Li Zheng, and Zhihai Zhang. Study on plan of track lines in marshalling station. In IEEM 2007: 2007 IEEE International Conference on Industrial Engineering and Engineering Management, pages 852—856, 2007. [planning of track lines, train schedules]
The plan of track lines is an important factor which influences the efficiency of marshaling station. When a train reaches the station, schedulers need to decide which track will be occupied by train and how long the train will stay at the track. The problem is NP-complete when the number of track and train are unfixed. After the mathematical model is analyzed, the schedule of single track can be transformed into a weighted clique problem, and a polynomial algorithm is designed. For solving the schedule problem of multi-track, two heuristic algorithms are introduced, and genetic algorithm is also adopted. Moreover, some benchmarks which data are generated randomly are used to validate the rational efficiency and computation burden of foregoing algorithms.
@inproceedings{WangZZ:2007,
author = {Wang, Shidong and Zheng, Li and Zhang, Zhihai},
title = {Study on plan of track lines in marshalling station},
booktitle = {IEEM 2007: 2007 IEEE International Conference on Industrial Engineering and Engineering Management},
pages = {852-856},
year = {2007},
doi = {10.1109/IEEM.2007.4419311},
}2.2.4 Exact methods
Egon Balas and J. Xue. Minimum weighted coloring of triangulated graphs, with application to maximum weight vertex packing and clique finding in arbitrary graphs. SIAM Journal on Computing, 20:209, 1991.
Efficient algorithms are known for finding a maximum weight stable set, a minimum weighted clique covering, and a maximum weight clique of a vertex-weighted triangulated graph. However, there is no comparably efficient algorithm in the literature for finding a minimum weighted vertex coloring of such a graph. This paper gives an \(O(|V|^2 )\) procedure for the problem (Algorithm 1). It then extends the procedure to the problem of finding in an arbitrary graph \(G = (V,E)\) a maximal induced subgraph \(G(W)\) color-equivalent (as defined in § 3) to a maximal triangulated subgraph \(G(T)\) (Algorithm 2). Finally, it uses this latter algorithm as the main ingredient of a branch-and-bound procedure for the maximum weight clique problem in an arbitrary graph. Computational experience is presented on arbitrary random graphs with up to 2,000 vertices.
@article{BalasX:1991,
author = {Balas, Egon and Xue, J.},
title = {Minimum weighted coloring of triangulated graphs, with application to maximum weight vertex packing and clique finding in arbitrary graphs},
journal = {SIAM Journal on Computing},
volume = {20},
pages = {209},
year = {1991},
doi = {10.1137/0220012},
}2.2.5 Continuous formulations
Massimiliano Pavan and Marcello Pelillo. Dominant sets and pairwise clustering. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 29(1):167—172, 2007.
We develop a new graph-theoretic approach for pairwise data clustering which is motivated by the analogies between the intuitive concept of a cluster and that of a dominant set of vertices, a notion introduced here which generalizes that of a maximal complete subgraph to edge-weighted graphs. We establish a correspondence between dominant sets and the extrema of a quadratic form over the standard simplex, thereby allowing the use of straightforward and easily implementable continuous optimization techniques from evolutionary game theory. Numerical examples on various point-set and image segmentation problems confirm the potential of the proposed approach.
@article{PavanP:2007,
author = {Pavan, Massimiliano and Pelillo, Marcello},
title = {Dominant sets and pairwise clustering},
journal = {Pattern Analysis and Machine Intelligence, IEEE Transactions on},
volume = {29},
number = {1},
pages = {167--172},
publisher = {IEEE},
year = {2007},
doi = {10.1109/TPAMI.2007.250608},
}Stanislav Busygin. A new trust region technique for the maximum weight clique problem. Discrete Applied Mathematics, 154(15):2080—2096, 2006.
Anew simple generalization of the Motzkin-Straus theorem for the maximum weight clique problem is formulated and directly proved. Within this framework a trust region heuristic is developed. In contrast to usual trust region methods, it regards not only the global optimum of a quadratic objective over a sphere, but also a set of other stationary points of the program. We formulate and prove a condition when a Motzkin-Straus optimum coincides with such a point. The developed method has complexity \(O(n^3)\), where n is the number of vertices of the graph. It was implemented in a publicly available software package QUALEX-MS.
Computational experiments indicate that the algorithm is exact on small graphs and very efficient on the DIMACS benchmark graphs and various random maximum weight clique problem instances.
Computational experiments indicate that the algorithm is exact on small graphs and very efficient on the DIMACS benchmark graphs and various random maximum weight clique problem instances.
@article{Busygin:2006,
author = {Busygin, Stanislav},
title = {A new trust region technique for the maximum weight clique problem},
journal = {Discrete Applied Mathematics},
volume = {154},
number = {15},
pages = {2080--2096},
publisher = {Elsevier},
year = {2006},
doi = {10.1016/j.dam.2005.04.010},
}Alessio Massaro, Marcello Pelillo, and Immanuel M. Bomze. A complementary pivoting approach to the maximum weight clique problem. SIAM Journal on Optimization, 12(4):928—948, 2002.
Given an undirected graph with positive weights on the vertices, the maximum weight clique problem (MWCP) is to find a subset of mutually adjacent vertices (i.e., a clique) having largest total weight. The problem is known to be N P-hard, even to approximate. Motivated by a recent quadratic programming formulation, which generalizes an earlier remarkable result of Motzkin and Straus, in this paper we propose a new framework for the MWCP based on the corresponding linear complementarity problem (LCP). We show that, generically, all stationary points of the MWCP quadratic program exhibit strict complementarity. Despite this regularity result, however, the LCP turns out to be inherently degenerate, and we find that Lemke’s well-known pivoting method, equipped with standard degeneracy resolution strategies, yields unsatisfactory experimental results. We exploit the degeneracy inherent in the problem to develop a variant of Lemke’s algorithm which incorporates a new and effective ‘‘look-ahead” pivot rule. The resulting algorithm is tested extensively on various instances of random as well as DIMACS benchmark graphs, and the results obtained show the effectiveness of our method.
@article{MassaroPB:2002,
author = {Massaro, Alessio and Pelillo, Marcello and Bomze, Immanuel M.},
title = {A complementary pivoting approach to the maximum weight clique problem},
journal = {SIAM Journal on Optimization},
volume = {12},
number = {4},
pages = {928--948},
publisher = {Philadelphia, Pa.: The Society, c1991-},
year = {2002},
doi = {10.1137/S1052623400381413},
}Immanuel M. Bomze, Marcello Pelillo, and Volker Stix. Approximating the maximum weight clique using replicator dynamics. IEEE Transactions On Neural Networks / A Publication of the IEEE Neural Networks Council, 11(6):1228—41, 2000.
Given an undirected graph with weights on the vertices, the maximum weight clique problem (MWCP) is to find a subset of mutually adjacent vertices (i.e., a clique) having the largest total weight. This is a generalization of the classical problem of finding the maximum cardinality clique of an unweighted graph, which arises as a special case of the MWCP when all the weights associated to the vertices are equal. The problem is known to be NP-hard for arbitrary graphs and, according to recent theoretical results, so is the problem of approximating it within a constant factor. Although there has recently been much interest around neural-network algorithms for the unweighted maximum clique problem, no effort has been directed so far toward its weighted counterpart. In this paper, we present a parallel, distributed heuristic for approximating the MWCP based on dynamics principles developed and studied in various branches of mathematical biology. The proposed framework centers around a recently introduced continuous characterization of the MWCP which generalizes an earlier remarkable result by Motzkin and Straus. This allows us to formulate the MWCP (a purely combinatorial problem) in terms of a continuous quadratic programming problem. One drawback associated with this formulation, however, is the presence of "spurious" solutions, and we present characterizations of these solutions. To avoid them we introduce a new regularized continuous formulation of the MWCP inspired by previous works on the unweighted problem, and show how this approach completely solves the problem. The continuous formulation of the MWCP naturally maps onto a parallel, distributed computational network whose dynamical behavior is governed by the so-called replicator equations. These are dynamical systems introduced in evolutionary game theory and population genetics to model evolutionary processes on a macroscopic scale.We present theoretical results which guarantee that the solutions provided by our clique finding replicator network are actually the ones being sought. Extensive experiments on both randomly generated and standard benchmark graphs have been conducted, and the results obtained confirm the effectiveness of the proposed approach. Universitatsstrasse 5, A-1010 Wien, Austria.
@article{BomzePS:2000,
author = {Bomze, Immanuel M. and Pelillo, Marcello and Stix, Volker},
title = {Approximating the maximum weight clique using replicator dynamics.},
journal = {IEEE Transactions On Neural Networks / A Publication of the IEEE Neural Networks Council},
volume = {11},
number = {6},
pages = {1228-41},
year = {2000},
doi = {10.1109/72.883403},
}last update, 26 Oct 2015