A new branch-and-bound algorithm for the maximum edge-weighted clique problem

Pablo San Segundo, Stefano Coniglio, Fabio Furini and Ivana Ljubić

European Journal of Operational Research, 2019, vol. 278, issue 1, 76-90

Abstract: We study the maximum edge-weighted clique problem, a problem related to the maximum (vertex-weighted) clique problem which asks for finding a complete subgraph (i.e., a clique) of maximum total weight on its edges. The problem appears in a wide range of applications, including bioinformatics, material science, computer vision, robotics, and many more. In this work, we propose a new combinatorial branch-and-bound algorithm for the problem which relies on a novel bounding procedure capable of pruning a very large amount of nodes of the branch-and-bound tree. Extensive computational experiments on random and structured graphs, encompassing standard benchmarks used in the literature as well as recently introduced real-world large-scale graphs, show that our new algorithm outperforms the state-of-the-art by several orders of magnitude on many instances.

Keywords: Combinatorial optimization; Branch-and-bound; Maximum edge-weighted clique problem (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:278:y:2019:i:1:p:76-90

DOI: 10.1016/j.ejor.2019.03.047

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