HAL CCSD
A new upper bound for the maximum weight clique problem
Li, Chu-Min
Liu, Yanli
Jiang, Hua
Manya, Felip
Li, Yu
COntraintes, ALgorithmes et Applications (COALA) ; Laboratoire d'Informatique et Systèmes (LIS) ; Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)
Modélisation, Information et Systèmes - UR UPJV 4290 (MIS) ; Université de Picardie Jules Verne (UPJV)
College of Computer Science [Chengdu] ; Sichuan University [Chengdu] (SCU)
University of Colorado [Colorado Springs] (UCCS)
Artificial Intelligence Research Institute / Spanish Scientific Research Council (IIIA / CSIC) ; Universitat Autònoma de Barcelona (UAB)
University of Texas at Austin [Austin]
International audience
ISSN: 0377-2217
EISSN: 1872-6860
European Journal of Operational Research
Elsevier
hal-03636424
https://u-picardie.hal.science/hal-03636424
https://u-picardie.hal.science/hal-03636424
European Journal of Operational Research, 2018, 270 (1), pp.66-77. ⟨10.1016/j.ejor.2018.03.020⟩
DOI: 10.1016/j.ejor.2018.03.020
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.ejor.2018.03.020
en
[INFO]Computer Science [cs]
info:eu-repo/semantics/article
Journal articles
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.
2018