A new upper bound for the maximum weight clique problem

Chu-Min Li, Yanli Liu, Hua Jiang, Felip Manyà and Yu Li

European Journal of Operational Research, 2018, vol. 270, issue 1, 66-77

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.

Keywords: Combinatorial optimization; Branch and bound; Maximum weight clique problem; Upper bound; Weight cover (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:270:y:2018:i:1:p:66-77

DOI: 10.1016/j.ejor.2018.03.020

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