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A new upper bound for the maximum weight clique problem

Abstract : 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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Soumis le : dimanche 10 avril 2022 - 11:39:20
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Chu-Min Li, Yanli Liu, Hua Jiang, Felip Manya, Yu Li. A new upper bound for the maximum weight clique problem. European Journal of Operational Research, Elsevier, 2018, 270 (1), pp.66-77. ⟨10.1016/j.ejor.2018.03.020⟩. ⟨hal-03636424⟩



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