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URN: urn:nbn:de:0030-drops-12333
URL: http://drops.dagstuhl.de/opus/volltexte/2007/1233/

Chen, Jianer ; Liu, Yang ; Lu, Songiian

Directed Feedback Vertex Set Problem is FPT

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Abstract

To decide if the {sc parameterized feedback vertex set} problem in directed graph is fixed-parameter tractable is a long standing open problem. In this paper, we prove that the {sc parameterized feedback vertex set} in directed graph is fixed-parameter tractable and give the first FPT algorithm of running time $O((1.48k)^kn^{O(1)})$ for it. As the {sc feedback arc set} problem in directed graph can be transformed to a {sc feedback vertex set} problem in directed graph, hence we also show that the {sc parameterized feedback arc set} problem can be solved in time of $O((1.48k)^kn^{O(1)})$.

BibTeX - Entry

@InProceedings{chen_et_al:DSP:2007:1233,
  author =	{Jianer Chen and Yang Liu and Songiian Lu},
  title =	{Directed Feedback Vertex Set Problem is FPT},
  booktitle =	{Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs},
  year =	{2007},
  editor =	{Erik Demaine and Gregory Z. Gutin and Daniel Marx and Ulrike Stege},
  number =	{07281},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2007/1233},
  annote =	{Keywords: Directed feedback vertex set problem, parameterized algorithm,}
}

Keywords: Directed feedback vertex set problem, parameterized algorithm,
Seminar: 07281 - Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs
Issue date: 2007
Date of publication: 28.11.2007


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