Fixed-Parameter Tractability of Multicut in Directed Acyclic Graphs

  • Stefan Kratsch
  • Marcin Pilipczuk
  • Michał Pilipczuk
  • Magnus Wahlström
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7391)

Abstract

The Multicut problem, given a graph G, a set of terminal pairs \(\ensuremath{\mathcal{T}}=\{(s_i,t_i)\ |\ 1\leq i\leq r\}\) and an integer p, asks whether one can find a cutset consisting of at most p non-terminal vertices that separates all the terminal pairs, i.e., after removing the cutset, t i is not reachable from s i for each 1 ≤ i ≤ r. The fixed-parameter tractability of Multicut in undirected graphs, parameterized by the size of the cutset only, has been recently proven by Marx and Razgon [2] and, independently, by Bousquet et al. [3], after resisting attacks as a long-standing open problem. In this paper we prove that Multicut is fixed-parameter tractable on directed acyclic graphs, when parameterized both by the size of the cutset and the number of terminal pairs. We complement this result by showing that this is implausible for parameterization by the size of the cutset only, as this version of the problem remains W[1]-hard.

Keywords

Directed Acyclic Graph Reduction Rule Degree Reduction Shadow Removal Terminal Pair 
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 2012

Authors and Affiliations

  • Stefan Kratsch
    • 1
  • Marcin Pilipczuk
    • 2
  • Michał Pilipczuk
    • 3
  • Magnus Wahlström
    • 4
  1. 1.Utrecht UniversityUtrechtThe Netherlands
  2. 2.University of WarsawWarsawPoland
  3. 3.University of BergenBergenNorway
  4. 4.Max-Planck-Institute for InformaticsSaarbrückenGermany

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