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Linear-Time Enumeration of Isolated Cliques

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Algorithms – ESA 2005 (ESA 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3669))

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Abstract

For a given graph G of n vertices and m edges, a clique S of size k is said to be c-isolated if there are at most ck outgoing edges from S. It is shown that this parameter c is an interesting measure which governs the complexity of finding cliques. In particular, if c is a constant, then we can enumerate all c-isolated maximal cliques in linear time, and if c = O(log n), then we can enumerate all c-isolated maximal cliques in polynomial time. Note that there is a graph which has a superlinear number of c-isolated cliques if c is not a constant, and there is a graph which has a superpolynomial number of c-isolated cliques if c = ω(log n). In this sense our algorithm is optimal for the linear-time and polynomial-time enumeration of c-isolated cliques.

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Author information

Authors and Affiliations

  1. Department of Communications and Computer Engineering, School of Informatics, Kyoto University, Kyoto, 606-8501, Japan

    Hiro Ito, Kazuo Iwama & Tsuyoshi Osumi

Authors
  1. Hiro Ito
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  2. Kazuo Iwama
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  3. Tsuyoshi Osumi
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Editor information

Editors and Affiliations

  1. BRICS, MADALGO, Department of Computer Science, University of Aarhus, Denmark

    Gerth Stølting Brodal

  2. University of Rome “La Sapienza”, Rome, Italy

    Stefano Leonardi

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© 2005 Springer-Verlag Berlin Heidelberg

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Ito, H., Iwama, K., Osumi, T. (2005). Linear-Time Enumeration of Isolated Cliques. In: Brodal, G.S., Leonardi, S. (eds) Algorithms – ESA 2005. ESA 2005. Lecture Notes in Computer Science, vol 3669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11561071_13

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  • DOI: https://doi.org/10.1007/11561071_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29118-3

  • Online ISBN: 978-3-540-31951-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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