Author

# Etsuji Tomita

Other affiliations: Tokyo Institute of Technology, Chuo University

Bio: Etsuji Tomita is an academic researcher from University of Electro-Communications. The author has contributed to research in topics: Clique & Clique problem. The author has an hindex of 17, co-authored 81 publications receiving 2131 citations. Previous affiliations of Etsuji Tomita include Tokyo Institute of Technology & Chuo University.

##### Papers published on a yearly basis

##### Papers

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TL;DR: 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, which proves that its worst-case time complexity is O(3n/3) for an n-vertex graph.

Abstract: 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(3n/3) for an n-vertex graph. This is optimal as a function of n, since there exist up to 3n/3 maximal cliques in an n-vertex graph. The algorithm is also demonstrated to run very fast in practice by computational experiments.

748 citations

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TL;DR: An exact and efficient branch-and-bound algorithm MCR for finding a maximum clique in an arbitrary graph that decidedly outperforms other existing algorithms on random graphs and on DIMACS benchmark graphs.

Abstract: We present an exact and efficient branch-and-bound algorithm MCR for finding a maximum clique in an arbitrary graph. The algorithm is not specialized for any particular type of graph. It employs approximate coloring to obtain an upper bound on the size of a maximum clique along with an improved appropriate sorting of vertices. We demonstrate by computational experiments on random graphs with up to 15,000 vertices and on DIMACS benchmark graphs that in general, our algorithm decidedly outperforms other existing algorithms. The algorithm has been successfully applied to interesting problems in bioinformatics, image processing, design of quantum circuits, and design of DNA and RNA sequences for biomolecular computation.

199 citations

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188 citations

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TL;DR: It is demonstrated by computational experiments on random graphs with up to 15,000 vertices and on DIMACS benchmark graphs that the algorithm remarkably outperforms other existing algorithms in general.

Abstract: 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 biomolecular computation.

188 citations

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10 Feb 2010TL;DR: This paper proposes new approximate coloring and other related techniques which markedly improve the run time of the branch-and-bound algorithm MCR, previously shown to be the fastest maximum-clique-finding algorithm for a large number of graphs.

Abstract: This paper proposes new approximate coloring and other related techniques which markedly improve the run time of the branch-and-bound algorithm MCR (J. Global Optim., 37, 95–111, 2007), previously shown to be the fastest maximum-clique-finding algorithm for a large number of graphs. The algorithm obtained by introducing these new techniques in MCR is named MCS. It is shown that MCS is successful in reducing the search space quite efficiently with low overhead. Consequently, it is shown by extensive computational experiments that MCS is remarkably faster than MCR and other existing algorithms. It is faster than the other algorithms by an order of magnitude for several graphs. In particular, it is faster than MCR for difficult graphs of very high density and for very large and sparse graphs, even though MCS is not designed for any particular type of graphs. MCS can be faster than MCR by a factor of more than 100,000 for some extremely dense random graphs.

178 citations

##### Cited by

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TL;DR: A survey of results concerning algorithms, complexity, and applications of the maximum clique problem is presented and enumerative and exact algorithms, heuristics, and a variety of other proposed methods are discussed.

Abstract: The maximum clique problem is a classical problem in combinatorial optimization which finds important applications in different domains. In this paper we try to give a survey of results concerning algorithms, complexity, and applications of this problem, and also provide an updated bibliography. Of course, we build upon precursory works with similar goals [39, 232, 266].

1,065 citations

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01 Mar 2001TL;DR: In this article, it was shown that the complexity of solving k-SAT increases as k increases, and that for k?3, sk is increasing infinitely often assuming ETH.

Abstract: The k-SAT problem is to determine if a given k-CNF has a satisfying assignment It is a celebrated open question as to whether it requires exponential time to solve k-SAT for k?3 Here exponential time means 2?n for some ?>0 In this paper, assuming that, for k?3, k-SAT requires exponential time complexity, we show that the complexity of k-SAT increases as k increases More precisely, for k?3, define sk=inf{?:there exists 2?n algorithm for solving k-SAT} Define ETH (Exponential-Time Hypothesis) for k-SAT as follows: for k?3, sk>0 In this paper, we show that sk is increasing infinitely often assuming ETH for k-SAT Let s∞ be the limit of sk We will in fact show that sk?(1?d/k)s∞ for some constant d>0 We prove this result by bringing together the ideas of critical clauses and the Sparsification Lemma to reduce the satisfiability of a k-CNF to the satisfiability of a disjunction of 2?nk?-CNFs in fewer variables for some k??k and arbitrarily small ?>0 We also show that such a disjunction can be computed in time 2?n for arbitrarily small ?>0

1,018 citations

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TL;DR: 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, which proves that its worst-case time complexity is O(3n/3) for an n-vertex graph.

Abstract: 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(3n/3) for an n-vertex graph. This is optimal as a function of n, since there exist up to 3n/3 maximal cliques in an n-vertex graph. The algorithm is also demonstrated to run very fast in practice by computational experiments.

748 citations

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TL;DR: This bibliography provides a classification of a comprehensive list of 1380 references on the theory and application of metaheuristics that have had widespread successes in attacking a variety of difficult combinatorial optimization problems that arise in many practical areas.

Abstract: Metaheuristics are the most exciting development in approximate optimization techniques of the last two decades. They have had widespread successes in attacking a variety of difficult combinatorial optimization problems that arise in many practical areas. This bibliography provides a classification of a comprehensive list of 1380 references on the theory and application of metaheuristics. Metaheuristics include but are not limited to constraint logic programming; greedy random adaptive search procedures; natural evolutionary computation; neural networks; non-monotonic search strategies; space-search methods; simulated annealing; tabu search; threshold algorithms and their hybrids. References are presented in alphabetical order under a number of subheadings.

646 citations

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TL;DR: FireDock's prediction results are comparable to current state‐of‐the‐art refinement methods while its running time is significantly lower, and its refinement procedure significantly improves the ranking of the rigid‐body PatchDock algorithm for these cases.

Abstract: Here, we present FireDock, an efficient method for the refinement and rescoring of rigid-body docking solutions. The refinement process consists of two main steps: (1) rearrangement of the interface side-chains and (2) adjustment of the relative orientation of the molecules. Our method accounts for the observation that most interface residues that are important in recognition and binding do not change their conformation significantly upon complexation. Allowing full side-chain flexibility, a common procedure in refinement methods, often causes excessive conformational changes. These changes may distort preformed structural signatures, which have been shown to be important for binding recognition. Here, we restrict side-chain movements, and thus manage to reduce the false-positive rate noticeably. In the later stages of our procedure (orientation adjustments and scoring), we smooth the atomic radii. This allows for the minor backbone and side-chain movements and increases the sensitivity of our algorithm. FireDock succeeds in ranking a near-native structure within the top 15 predictions for 83% of the 30 enzyme-inhibitor test cases, and for 78% of the 18 semiunbound antibody-antigen complexes. Our refinement procedure significantly improves the ranking of the rigid-body PatchDock algorithm for these cases. The FireDock program is fully automated. In particular, to our knowledge, FireDock's prediction results are comparable to current state-of-the-art refinement methods while its running time is significantly lower. The method is available at http://bioinfo3d.cs.tau.ac.il/FireDock/.

630 citations