Journal
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
Volume 270, Issue 1, Pages 66-77Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.ejor.2018.03.020
Keywords
Combinatorial optimization; Branch and bound; Maximum weight clique problem; Upper bound; Weight cover
Funding
- National Natural Science Foundation of China [61272014, 61370183, 61472147, 61370184]
- platforms Matrics of University of Picardie Jules Verne
- HPC of Jianghan Univeristy
- Spanish Ministry of Economy and Competitiveness-FEDER [TIN2015-71799-C2-1-P]
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The maximum weight clique problem (MWCP) for a vertex-weighted graph is to find a complete subgraph in which the sum of vertex weights is maximum. The main goal of this paper is to develop an efficient branch-and-bound algorithm to solve the MWCP. As a crucial aspect of branch-and-bound MWCP algorithms is the incorporation of a tight upper bound, we first define a new upper bound for the MWCP, called UBwc, that is based on a novel notion called weight cover. The idea of a weight cover is to compute a set of independent sets of the graph and define a weight function for each independent set so that the weight of each vertex of the graph is covered by such weight functions. We then propose a new branch-and-bound MWCP algorithm called WC-MWC that uses UBwc to reduce the number of branches of the search space that must be traversed by incrementally constructing a weight cover for the graph. Finally, we present experimental results that show that UBwc reduces the search space much more than previous upper bounds, and the new algorithm WC-MWC outperforms some of the best performing exact and heuristic MWCP algorithms on both small/medium graphs and real-world massive graphs. (C) 2018 Elsevier B.V. All rights reserved.
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