On minimization of the number of branches in branch-and-bound algorithms for the maximum clique problem

• DOI: 10.1016/j.cor.2017.02.017
• Publication Date: 2017-02-25T04:02:25Z
• Authors: Chu-Min Li; Hua Jiang; Felip Manyà
• Keywords: Minification; Clique problem; Clique; Branch and bound; Complementarity (molecular biology)

When searching for a maximum clique in a graph G, branch-and-bound algorithms in the literature usually focus on the minimization of the number of branches generated at each search tree node. We call dynamic strategy this minimization without any constraint, because it induces a dynamic vertex ordering in G during the search. In this paper, we introduce a static strategy that minimizes the number of branches subject to the constraint that a static vertex ordering in G must be kept during the search. We analyze the two strategies and show that they are complementary. From this complementarity, we propose a new algorithm, called MoMC, that combines the strengths of the two strategies into a single algorithm. The reported experimental results show that MoMC is generally better than the algorithms implementing a single strategy. ©2017 Elsevier Ltd. All rights reserved.<br/>This work was supported by National Natural Science Foundation of China (Grant No. 61472147, No. 61370184 and No. 61272014) and by the MeCS platform of the University of Picardie Jules Verne. The third author was supported by Mobility Grant PRX16/00215 of the Ministerio de Educación, Cultura y Deporte, the Generalitat de Catalunya grant AGAUR 2014-SGR-118, and the MINECO-FEDER project RASO TIN2015-71799-C2-1-P.<br/>Peer Reviewed<br/>