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DOI: 10.4230/LIPIcs.FSTTCS.2009.2305
URN: urn:nbn:de:0030-drops-23055
URL: http://drops.dagstuhl.de/opus/volltexte/2009/2305/
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Bessy, Stéphane ; Fomin, Fedor V. ; Gaspers, Serge ; Paul, Christophe ; Perez, Anthony ; Saurabh, Saket ; Thomassé, Stéphan

Kernels for Feedback Arc Set In Tournaments

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Abstract

A tournament $T = (V,A)$ is a directed graph in which there is exactly one arc between every pair of distinct vertices. Given a digraph on $n$ vertices and an integer parameter $k$, the {\sc Feedback Arc Set} problem asks whether thegiven digraph has a set of $k$ arcs whose removal results in an acyclicdigraph. The {\sc Feedback Arc Set} problem restricted to tournaments is knownas the {\sc $k$-Feedback Arc Set in Tournaments ($k$-FAST)} problem. In thispaper we obtain a linear vertex kernel for \FAST{}. That is, we give apolynomial time algorithm which given an input instance $T$ to \FAST{} obtains an equivalent instance $T'$ on $O(k)$ vertices. In fact, given any fixed $\epsilon > 0$, the kernelized instance has at most $(2 + \epsilon)k$ vertices.Our result improves the previous known bound of $O(k^2)$ on the kernel size for\FAST{}. Our kernelization algorithm solves the problem on a subclass of tournaments in polynomial time and uses a known polynomial time approximation scheme for \FAST.

BibTeX - Entry

@InProceedings{bessy_et_al:LIPIcs:2009:2305,
  author =	{St{\'e}phane Bessy and Fedor V. Fomin and Serge Gaspers and Christophe Paul and Anthony Perez and Saket Saurabh and St{\'e}phan Thomass{\'e}},
  title =	{{Kernels for Feedback Arc Set In Tournaments}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{37--47},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-13-2},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{4},
  editor =	{Ravi Kannan and K. Narayan Kumar},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2009/2305},
  URN =		{urn:nbn:de:0030-drops-23055},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2009.2305},
  annote =	{Keywords: Parameterized complexity, kernels, tournaments}
}

Keywords: Parameterized complexity, kernels, tournaments
Seminar: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science
Issue Date: 2009
Date of publication: 14.12.2009


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