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Diminishable Parameterized Problems and Strict Polynomial Kernelization

  • Henning Fernau
  • Till Fluschnik
  • Danny Hermelin
  • Andreas Krebs
  • Hendrik Molter
  • Rolf Niedermeier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10936)

Abstract

Kernelization—a mathematical key concept for provably effective polynomial-time preprocessing of NP-hard problems—plays a central role in parameterized complexity and has triggered an extensive line of research. In this paper we consider a restricted yet natural variant of kernelization, namely strict kernelization, where one is not allowed to increase the parameter of the reduced instance (the kernel) by more than an additive constant. Building on earlier work of Chen, Flum, and Müller [CiE 2009, Theory Comput. Syst. 2011], we underline the applicability of their framework by showing that a variety of fixed-parameter tractable problems, including graph problems and Turing machine computation problems, does not admit strict polynomial kernels under the weaker assumption of \( P {}\ne NP {}\). Finally, we study a relaxation of the notion of strict kernels.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Henning Fernau
    • 1
  • Till Fluschnik
    • 2
  • Danny Hermelin
    • 3
  • Andreas Krebs
    • 4
  • Hendrik Molter
    • 2
  • Rolf Niedermeier
    • 2
  1. 1.Fachbereich 4 – Abteilung InformatikUniversität TrierTrierGermany
  2. 2.Institut für Softwaretechnik und Theoretische InformatikTU BerlinBerlinGermany
  3. 3.Ben Gurion University of the NegevBeershebaIsrael
  4. 4.Wilhelm-Schickard-Institut für InformatikUniversität TübingenTübingenGermany

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