Journal
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
Volume 278, Issue 1, Pages 76-90Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.ejor.2019.03.047
Keywords
Combinatorial optimization; Branch-and-bound; Maximum edge-weighted clique problem
Funding
- Spanish Ministry of Science, Innovation and Universities through the project COGDRIVE [DPI2017-86915-C3-3-R]
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We study the maximum edge-weighted clique problem, a problem related to the maximum (vertexweighted) 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. (C) 2019 Elsevier B.V. All rights reserved.
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