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A Complexity Dichotomy for Finding Disjoint Solutions of Vertex Deletion Problems

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Mathematical Foundations of Computer Science 2009 (MFCS 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,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).

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Author information

Authors and Affiliations

  1. PC Research Unit, Office of DVC (Research), University of Newcastle, Callaghan, NSW, 2308, Australia

    Michael R. Fellows

  2. Institut für Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, D-07743, Jena, Germany

    Jiong Guo, Hannes Moser & Rolf Niedermeier

Authors
  1. Michael R. Fellows
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  2. Jiong Guo
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  3. Hannes Moser
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  4. Rolf Niedermeier
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Faculty of Mathematics, Physics and Informatics, Comenius University, Research partially funded by grant APVV 0433-06, Bratislava, Slovakia

    Rastislav Královič

  2. Members of EACSL Jury for the Ackermann Award, Poland

    Damian Niwiński

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© 2009 Springer-Verlag Berlin Heidelberg

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Fellows, M.R., Guo, J., Moser, H., Niedermeier, R. (2009). A Complexity Dichotomy for Finding Disjoint Solutions of Vertex Deletion Problems. In: Královič, R., Niwiński, D. (eds) Mathematical Foundations of Computer Science 2009. MFCS 2009. Lecture Notes in Computer Science, vol 5734. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03816-7_28

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  • DOI: https://doi.org/10.1007/978-3-642-03816-7_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03815-0

  • Online ISBN: 978-3-642-03816-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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