Win-Win Kernelization for Degree Sequence Completion Problems

  • Vincent Froese
  • André Nichterlein
  • Rolf Niedermeier
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8503)

Abstract

We study the kernelizability of a class of NP-hard graph modification problems based on vertex degree properties. Our main positive results refer to NP-hard graph completion (that is, edge addition) cases while we show that there is no hope to achieve analogous results for the corresponding vertex or edge deletion versions. Our algorithms are based on a method that transforms graph completion problems into efficiently solvable number problems and exploits f-factor computations for translating the results back into the graph setting. Indeed, our core observation is that we encounter a win-win situation in the sense that either the number of edge additions is small (and thus faster to find) or the problem is polynomial-time solvable. This approach helps in answering an open question by Mathieson and Szeider [JCSS 2012].

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Vincent Froese
    • 1
  • André Nichterlein
    • 1
  • Rolf Niedermeier
    • 1
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTU BerlinGermany

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