License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2016.43
URN: urn:nbn:de:0030-drops-57448
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/5744/
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Hols, Eva-Maria C. ; Kratsch, Stefan

A Randomized Polynomial Kernel for Subset Feedback Vertex Set

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Abstract

The SUBSET FEEDBACK VERTEX SET problem generalizes the classical FEEDBACK VERTEX SET problem and asks, for a given undirected graph G=(V,E), a set S subseteq V, and an integer k, whether there exists a set X of at most k vertices such that no cycle in G-X contains a vertex of S. It was independently shown by Cygan et al. (ICALP'11, SIDMA'13) and Kawarabayashi and Kobayashi (JCTB'12) that SUBSET FEEDBACK VERTEX SET is fixed-parameter tractable for parameter k. Cygan et al. asked whether the problem also admits a polynomial kernelization.

We answer the question of Cygan et al. positively by giving a randomized polynomial kernelization for the equivalent version where S is a set of edges. In a first step we show that EDGE SUBSET FEEDBACK VERTEX SET has a randomized polynomial kernel parameterized by |S|+k with O(|S|^2k) vertices. For this we use the matroid-based tools of Kratsch and Wahlstrom (FOCS'12). Next we present a preprocessing that reduces the given instance (G,S,k) to an equivalent instance (G',S',k') where the size of S' is bounded by O(k^4). These two results lead to a polynomial kernel for SUBSET FEEDBACK VERTEX SET with O(k^9) vertices.

BibTeX - Entry

@InProceedings{hols_et_al:LIPIcs:2016:5744,
  author =	{Eva-Maria C. Hols and Stefan Kratsch},
  title =	{{A Randomized Polynomial Kernel for Subset Feedback Vertex Set}},
  booktitle =	{33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
  pages =	{43:1--43:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-001-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{47},
  editor =	{Nicolas Ollinger and Heribert Vollmer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/5744},
  URN =		{urn:nbn:de:0030-drops-57448},
  doi =		{10.4230/LIPIcs.STACS.2016.43},
  annote =	{Keywords: parameterized complexity, kernelization, subset feedback vertex set}
}

Keywords: parameterized complexity, kernelization, subset feedback vertex set
Collection: 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)
Issue Date: 2016
Date of publication: 16.02.2016

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