%0 Journal Article %T A new upper bound for the maximum weight clique problem %+ COntraintes, ALgorithmes et Applications (COALA) %+ Modélisation, Information et Systèmes - UR UPJV 4290 (MIS) %+ College of Computer Science [Chengdu] %+ University of Colorado [Colorado Springs] (UCCS) %+ Artificial Intelligence Research Institute / Spanish Scientific Research Council (IIIA / CSIC) %+ University of Texas at Austin [Austin] %A Li, Chu-Min %A Liu, Yanli %A Jiang, Hua %A Manya, Felip %A Li, Yu %< avec comité de lecture %@ 0377-2217 %J European Journal of Operational Research %I Elsevier %V 270 %N 1 %P 66-77 %8 2018 %D 2018 %R 10.1016/j.ejor.2018.03.020 %Z Computer Science [cs]Journal articles %X 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. %G English %L hal-03636424 %U https://u-picardie.hal.science/hal-03636424 %~ UNIV-TLN %~ CNRS %~ UNIV-AMU %~ UNIV-PICARDIE %~ LIS-LAB %~ U-PICARDIE %~ MIS %~ UPJV-MIS-GOC