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Reducing the Branching in a Branch and Bound Algorithm for the Maximum Clique Problem

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Principles and Practice of Constraint Programming (CP 2014)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 8656))

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.

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Author information

Authors and Affiliations

  1. University of Glasgow, Glasgow, UK

    Ciaran McCreesh & Patrick Prosser

Authors
  1. Ciaran McCreesh
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  2. Patrick Prosser
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Editor information

Editors and Affiliations

  1. Insight Centre for Data Analytics, School of Computer Science and IT, University College Cork, Western Road, Cork, Ireland

    Barry O’Sullivan

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McCreesh, C., Prosser, P. (2014). Reducing the Branching in a Branch and Bound Algorithm for the Maximum Clique Problem. In: O’Sullivan, B. (eds) Principles and Practice of Constraint Programming. CP 2014. Lecture Notes in Computer Science, vol 8656. Springer, Cham. https://doi.org/10.1007/978-3-319-10428-7_40

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  • DOI: https://doi.org/10.1007/978-3-319-10428-7_40

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10427-0

  • Online ISBN: 978-3-319-10428-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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