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DOI: 10.4230/LIPIcs.FSTTCS.2012.400
URN: urn:nbn:de:0030-drops-38765
URL: http://drops.dagstuhl.de/opus/volltexte/2012/3876/
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Crowston, Robert ; Gutin, Gregory ; Jones, Mark

Directed Acyclic Subgraph Problem Parameterized above the Poljak-Turzik Bound

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Abstract

An oriented graph is a directed graph without directed 2-cycles. Poljak and Turzik (1986) proved that every connected oriented graph G on n vertices and m arcs contains an acyclic subgraph with at least m/2+(n-1)/4 arcs. Raman and Saurabh (2006) gave another proof of this result and left it as an open question to establish the parameterized complexity of the following problem: does G have an acyclic subgraph with least m/2 + (n-1)/4 + k arcs, where k is the parameter? We answer this question by showing that the problem can be solved by an algorithm of runtime (12k)!n^{O(1)}. Thus, the problem is fixed-parameter tractable. We also prove that there is a polynomial time algorithm that either establishes that the input instance of the problem is a Yes-instance or reduces the input instance to an equivalent one of size O(k^2).

BibTeX - Entry

@InProceedings{crowston_et_al:LIPIcs:2012:3876,
  author =	{Robert Crowston and Gregory Gutin and Mark Jones},
  title =	{{Directed Acyclic Subgraph Problem Parameterized above the Poljak-Turzik Bound}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012) },
  pages =	{400--411},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-47-7},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{18},
  editor =	{Deepak D'Souza and Telikepalli Kavitha and Jaikumar Radhakrishnan},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2012/3876},
  URN =		{urn:nbn:de:0030-drops-38765},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2012.400},
  annote =	{Keywords: Acyclic Subgraph, Fixed-parameter tractable, Polynomial Kernel}
}

Keywords: Acyclic Subgraph, Fixed-parameter tractable, Polynomial Kernel
Seminar: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)
Issue Date: 2012
Date of publication: 10.12.2012


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