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DOI: 10.4230/LIPIcs.FSTTCS.2016.24
URN: urn:nbn:de:0030-drops-68591
URL: http://drops.dagstuhl.de/opus/volltexte/2016/6859/
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Kumar, Mithilesh ; Lokshtanov, Daniel

Faster Exact and Parameterized Algorithm for Feedback Vertex Set in Bipartite Tournaments

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Abstract

A bipartite tournament is a directed graph T:=(A cup B, E) such that every pair of vertices (a,b), a in A, b in B are connected by an arc, and no arc connects two vertices of A or two vertices of B. A feedback vertex set is a set S of vertices in T such that T - S is acyclic. In this article we consider the Feedback Vertex Set problem in bipartite tournaments. Here the input is a bipartite tournament T on n vertices together with an integer k, and the task is to determine whether T has a feedback vertex set of size at most k. We give a new algorithm for Feedback Vertex Set in Bipartite Tournaments. The running time of our algorithm is upper-bounded by O(1.6181^k + n^{O(1)}), improving over the previously best known algorithm with running time (2^k)k^{O(1)} + n^{O(1)} [Hsiao, ISAAC 2011]. As a by-product, we also obtain the fastest currently known exact exponential-time algorithm for the problem, with running time O(1.3820^n).

BibTeX - Entry

@InProceedings{kumar_et_al:LIPIcs:2016:6859,
  author =	{Mithilesh Kumar and Daniel Lokshtanov},
  title =	{{Faster Exact and Parameterized Algorithm for Feedback Vertex Set in Bipartite Tournaments}},
  booktitle =	{36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)},
  pages =	{24:1--24:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-027-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{65},
  editor =	{Akash Lal and S. Akshay and Saket Saurabh and Sandeep Sen},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6859},
  URN =		{urn:nbn:de:0030-drops-68591},
  doi =		{10.4230/LIPIcs.FSTTCS.2016.24},
  annote =	{Keywords: Parameterized algorithms, Exact algorithms, Feedback vertex set, Tour- naments, Bipartite tournaments}
}

Keywords: Parameterized algorithms, Exact algorithms, Feedback vertex set, Tour- naments, Bipartite tournaments
Seminar: 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)
Issue Date: 2016
Date of publication: 08.12.2016


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