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European Symposium on Algorithms

ESA 2002: Algorithms — ESA 2002 pp 485–498Cite as

Simple and Fast: Improving a Branch-And-Bound Algorithm for Maximum Clique

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2461))

Abstract

We consider a branch-and-bound algorithm for maximum clique problems. We introduce cost based filtering techniques for the socalled candidate set (i.e. a set of nodes that can possibly extend the clique in the current choice point).

Additionally, we present a taxonomy of upper bounds for maximum clique. Analytical results show that our cost based filtering is in a sense as tight as most of these well-known bounds for the maximum clique problem.

Experiments demonstrate that the combination of cost based filtering and vertex coloring bounds outperforms the old approach as well as approaches that only apply either of these techniques. Furthermore, the new algorithm is competitive with other recent algorithms for maximum clique.

Partially supported by the Future and Emerging Technologies programme of the EU under contract number IST-1999-14186 (ALCOM-FT).

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Paderborn, Fürstenallee 11, D-33102, Paderborn, Germany

    Torsten Fahle

Authors
  1. Torsten Fahle
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Editor information

Editors and Affiliations

  1. Fakultät II: Mathematik und Naturwissenschaften, Technische Universität Berlin, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Rolf Möhring

  2. Department of Mathematics and Computer Science, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Rajeev Raman

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© 2002 Springer-Verlag Berlin Heidelberg

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Fahle, T. (2002). Simple and Fast: Improving a Branch-And-Bound Algorithm for Maximum Clique. In: Möhring, R., Raman, R. (eds) Algorithms — ESA 2002. ESA 2002. Lecture Notes in Computer Science, vol 2461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45749-6_44

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  • DOI: https://doi.org/10.1007/3-540-45749-6_44

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44180-9

  • Online ISBN: 978-3-540-45749-7

  • eBook Packages: Springer Book Archive

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