Improvements to MCS algorithm for the maximum clique problem

In this paper we present improvements to one of the most recent and fastest branch-and-bound algorithm for the maximum clique problem—MCS algorithm by Tomita et al. (Proceedings of the 4th international conference on Algorithms and Computation, WALCOM’10, pp. 191–203, 2010 ). The suggested improveme...

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Bibliographic Details
Published inJournal of combinatorial optimization Vol. 27; no. 2; pp. 397 - 416
Main Authors Batsyn, Mikhail, Goldengorin, Boris, Maslov, Evgeny, Pardalos, Panos M.
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.02.2014
Subjects
Combinatorics
Convex and Discrete Geometry
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Theory of Computation
Graph colouring
Heuristic solution
Maximum clique problem
Branch-and-bound algorithm
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Summary:In this paper we present improvements to one of the most recent and fastest branch-and-bound algorithm for the maximum clique problem—MCS algorithm by Tomita et al. (Proceedings of the 4th international conference on Algorithms and Computation, WALCOM’10, pp. 191–203, 2010 ). The suggested improvements include: incorporating of an efficient heuristic returning a high-quality initial solution, fast detection of clique vertices in a set of candidates, better initial colouring, and avoiding dynamic memory allocation. Our computational study shows some impressive results, mainly we have solved p_hat1000-3 benchmark instance which is intractable for MCS algorithm and got speedups of 7, 3000, and 13000 times for gen400_p0.9_55, gen400_p0.9_65, and gen400_p0.9_75 instances correspondingly.
ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-012-9592-6