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A Complexity Dichotomy for Finding Disjoint Solutions of Vertex Deletion Problems

  • Michael R. Fellows
  • Jiong Guo
  • Hannes Moser
  • Rolf Niedermeier
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5734)

Abstract

We investigate the computational complexity of a general “compression task” centrally occurring in the recently developed technique of iterative compression for exactly solving NP-hard minimization problems. The core issue (particularly but not only motivated by iterative compression) is to determine the computational complexity of, given an already inclusion-minimal solution for an underlying (typically NP-hard) vertex deletion problem in graphs, to find a better disjoint solution. The complexity of this task is so far lacking a systematic study. We consider a large class of vertex deletion problems on undirected graphs and show that, except for few cases which are polynomial-time solvable, the others are NP-complete. This class includes problems such as Vertex Cover (here the corresponding compression task is decidable in polynomial time) or Undirected Feedback Vertex Set (here the corresponding compression task is NP-complete).

Keywords

Vertex Cover Graph Property Complexity Dichotomy Induce Subgraph Vertex Deletion 
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

  • Michael R. Fellows
    • 1
  • Jiong Guo
    • 2
  • Hannes Moser
    • 2
  • Rolf Niedermeier
    • 2
  1. 1.PC Research Unit, Office of DVC (Research)University of NewcastleCallaghanAustralia
  2. 2.Institut für InformatikFriedrich-Schiller-Universität JenaJenaGermany

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