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Kernel Bounds for Disjoint Cycles and Disjoint Paths

  • Hans L. Bodlaender
  • Stéphan Thomassé
  • Anders Yeo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5757)

Abstract

In this paper, we give evidence for the problems Disjoint Cycles and Disjoint Paths that they cannot be preprocessed in polynomial time such that resulting instances always have a size bounded by a polynomial in a specified parameter (or, in short: do not have a polynomial kernel); these results are assuming the validity of certain complexity theoretic assumptions. We build upon recent results by Bodlaender et al. [3] and Fortnow and Santhanam [13], that show that NP-complete problems that are or-compositional do not have polynomial kernels, unless NP ⊆ coNP/poly. To this machinery, we add a notion of transformation, and thus obtain that Disjoint Cycles and Disjoint Paths do not have polynomial kernels, unless NP ⊆ coNP/poly. We also show that the related Disjoint Cycles Packing problem has a kernel of size O(k logk).

Keywords

Polynomial Time Planar Graph Parameterised Problem Parameter Transformation Polynomial Kernel 
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 2009

Authors and Affiliations

  • Hans L. Bodlaender
    • 1
  • Stéphan Thomassé
    • 2
  • Anders Yeo
    • 3
  1. 1.Institute of Information and Computing SciencesUtrecht UniversityUtrechtthe Netherlands
  2. 2.LIRMM-Université Montpellier IIMontpellier CedexFrance
  3. 3.Departmente of Computer ScienceRoyal Holloway University of LondonEghamUnited Kingdom

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