%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