Finding the largest clique in a given graph is one of the fundamental NP-hard problems. We take a widely used branch and bound algorithm for the maximum clique problem, and discuss an alternative way of understanding the algorithm which closely resembles a constraint model. By using this view, and by taking measurements inside search, we provide a new explanation for the success of the algorithm: one of the intermediate steps, by coincidence, often approximates a "smallest domain first" heuristic. We show that replacing this step with a genuine "smallest domain first" heuristic leads to a reduced branching factor and a smaller search space, but longer runtimes. We then introduce a "domains of size two first" heuristic, which integrates cleanly into the algorithm, and which both reduces the size of the search space and gives a reduction in runtimes. © 2014 Springer International Publishing Switzerland.
CITATION STYLE
McCreesh, C., & Prosser, P. (2014). Reducing the branching in a branch and bound algorithm for the maximum clique problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8656 LNCS, pp. 549–563). Springer Verlag. https://doi.org/10.1007/978-3-319-10428-7_40
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