Reducing the branching in a branch and bound algorithm for the maximum clique problem

McCreesh, C. and Prosser, P. (2014) Reducing the branching in a branch and bound algorithm for the maximum clique problem. In: 20th International Conference, CP 2014, Lyon, France, 8-12 Sep 2014, pp. 549-563. ISBN 9783319104270 (doi:10.1007/978-3-319-10428-7_40)

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Abstract

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.

Item Type:Conference Proceedings
Additional Information:Lecture Notes in Computer Science: 8656
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Prosser, Dr Patrick and Mccreesh, Dr Ciaran
Authors: McCreesh, C., and Prosser, P.
College/School:College of Science and Engineering > School of Computing Science
ISSN:0302-9743
ISBN:9783319104270
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