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Clique Cover and Graph Separation: New Incompressibility Results

  • Marek Cygan
  • Stefan Kratsch
  • Marcin Pilipczuk
  • Michał Pilipczuk
  • Magnus Wahlström
Part of the Lecture Notes in Computer Science book series (LNCS, 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].

Keywords

Input Graph Polynomial Kernel Full Version Input Instance Graph Separation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Marek Cygan
    • 1
  • Stefan Kratsch
    • 2
  • Marcin Pilipczuk
    • 3
  • Michał Pilipczuk
    • 4
  • Magnus Wahlström
    • 5
  1. 1.IDSIAUniversity of LuganoSwitzerland
  2. 2.Utrecht UniversityUtrechtThe Netherlands
  3. 3.Institute of InformaticsUniversity of WarsawPoland
  4. 4.Department of InformaticsUniversity of BergenNorway
  5. 5.Max-Planck-Institute for InformaticsSaarbrückenGermany

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