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Decremental Clique Problem

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Graph-Theoretic Concepts in Computer Science (WG 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3353))

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Abstract

The clique problem consists in determining whether an undirected graph G of order n contains a clique of order ℓ. In this paper we are concerned with the decremental version of clique problem, where the property of containing an ℓ-clique is dynamically checked during deletions of nodes. We provide an improved dynamic algorithm for this problem for every fixed value of ℓ ≥ 3. Our algorithm naturally applies to filtering for the constraint satisfaction problem. In particular, we show how to speed up the filtering based on an important local consistency property: the inverse consistency.

This work has been partially supported by the IST Programme of the EU under contract n. IST-1999-14.186 (ALCOM-FT), by the Italian Ministry of University and Research (Project “ALINWEB: Algorithmics for Internet and the Web”).

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Sistemi e Produzione, Università di Roma “Tor Vergata”, Via del Politecnico 1, 00133, Roma, Italy

    Fabrizio Grandoni & Giuseppe F. Italiano

Authors
  1. Fabrizio Grandoni
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  2. Giuseppe F. Italiano
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Editor information

Editors and Affiliations

  1. Department of Computer Science, ETH Zurich, ETH Zentrum, CH-8022, Zurich, Switzerland

    Juraj Hromkovič

  2. Department of Computer Science, RWTH Aachen, Chair of Computer Science III, Aachen, Germany

    Manfred Nagl

  3. Department of Computer Science III, RWTH Aachen University, Ahornstra{ß}e 55, 52074, Aachen, Germany

    Bernhard Westfechtel

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© 2004 Springer-Verlag Berlin Heidelberg

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Grandoni, F., Italiano, G.F. (2004). Decremental Clique Problem. In: Hromkovič, J., Nagl, M., Westfechtel, B. (eds) Graph-Theoretic Concepts in Computer Science. WG 2004. Lecture Notes in Computer Science, vol 3353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30559-0_12

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  • DOI: https://doi.org/10.1007/978-3-540-30559-0_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24132-4

  • Online ISBN: 978-3-540-30559-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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