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International Colloquium on Automata, Languages, and Programming

ICALP 2012: Automata, Languages, and Programming pp 254–265Cite as

Clique Cover and Graph Separation: New Incompressibility Results

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7391))

Abstract

The field of kernelization studies polynomial-time preprocessing routines for hard problems in the framework of parameterized complexity. In this paper we show that, unless \(\textrm{NP} \subseteq \textrm{coNP}/\textrm{poly}\) and the polynomial hierarchy collapses up to its third level, the following parameterized problems do not admit a polynomial-time preprocessing algorithm that reduces the size of an instance to polynomial in the parameter:

  • Edge Clique Cover , parameterized by the number of cliques,

  • Directed Edge/Vertex Multiway Cut , parameterized by the size of the cutset, even in the case of two terminals,

  • Edge/Vertex Multicut , parameterized by the size of the cutset,

  • and k -Way Cut , parameterized by the size of the cutset.

The existence of a polynomial kernelization for Edge Clique Cover was a seasoned veteran in open problem sessions. Furthermore, our results complement very recent developments in designing parameterized algorithms for cut problems by Marx and Razgon [STOC’11], Bousquet et al. [STOC’11], Kawarabayashi and Thorup [FOCS’11] and Chitnis et al. [SODA’12].

The full version of this paper is available online [1].

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Author information

Authors and Affiliations

  1. IDSIA, University of Lugano, Switzerland

    Marek Cygan

  2. Utrecht University, Utrecht, The Netherlands

    Stefan Kratsch

  3. Institute of Informatics, University of Warsaw, Poland

    Marcin Pilipczuk

  4. Department of Informatics, University of Bergen, Norway

    Michał Pilipczuk

  5. Max-Planck-Institute for Informatics, Saarbrücken, Germany

    Magnus Wahlström

Authors
  1. Marek Cygan
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  2. Stefan Kratsch
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  3. Marcin Pilipczuk
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  4. Michał Pilipczuk
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  5. Magnus Wahlström
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Centre for Discrete Mathematics and its Applications, University of Warwick, Warwick, UK

    Artur Czumaj

  2. Max-Planck-Institut für Informatik, Saarbrücken, Germany

    Kurt Mehlhorn

  3. Computer Laboratory, University of Cambridge, UK

    Andrew Pitts

  4. ETH Zurich, Switzerland

    Roger Wattenhofer

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© 2012 Springer-Verlag Berlin Heidelberg

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Cygan, M., Kratsch, S., Pilipczuk, M., Pilipczuk, M., Wahlström, M. (2012). Clique Cover and Graph Separation: New Incompressibility Results. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds) Automata, Languages, and Programming. ICALP 2012. Lecture Notes in Computer Science, vol 7391. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31594-7_22

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  • DOI: https://doi.org/10.1007/978-3-642-31594-7_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31593-0

  • Online ISBN: 978-3-642-31594-7

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