hal-03636424
https://u-picardie.hal.science/hal-03636424
doi:10.1016/j.ejor.2018.03.020
[UNIV-TLN] Université de Toulon
[CNRS] CNRS - Centre national de la recherche scientifique
[UNIV-AMU] Aix Marseille Université
[UNIV-PICARDIE] Université de Picardie Jules Verne
[LIS-LAB] Laboratoire d'Informatique et Systèmes
[U-PICARDIE] Université de Picardie Jules Verne
[MIS] Modélisation, Information et Systèmes - UR UPJV 4290
[UPJV-MIS-GOC] Equipe Graphes, Optimisation, Contraintes du laboratoire Modélisation, Information & Systèmes (Université de Picardie Jules Verne)
A new upper bound for the maximum weight clique problem
Li, Chu-Min
Liu, Yanli
Jiang, Hua
Manya, Felip
Li, Yu
[INFO] Computer Science [cs]
ART
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
en
European Journal of Operational Research
Elsevier