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DOI: 10.4230/LIPIcs.APPROX-RANDOM.2015.284
URN: urn:nbn:de:0030-drops-53085
URL: http://drops.dagstuhl.de/opus/volltexte/2015/5308/
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Guruswami, Venkatesan ; Lee, Euiwoong

Inapproximability of H-Transversal/Packing

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Abstract

Given an undirected graph G=(V,E) and a fixed pattern graph H with k vertices, we consider the H-Transversal and H-Packing problems. The former asks to find the smallest subset S of vertices such that the subgraph induced by V - S does not have H as a subgraph, and the latter asks to find the maximum number of pairwise disjoint k-subsets S1, ..., Sm such that the subgraph induced by each Si has H as a subgraph. We prove that if H is 2-connected, H-Transversal and H-Packing are almost as hard to approximate as general k-Hypergraph Vertex Cover and k-Set Packing, so it is NP-hard to approximate them within a factor of Omega(k) and Omega(k / polylog(k)) respectively. We also show that there is a 1-connected H where H-Transversal admits an O(log k)-approximation algorithm, so that the connectivity requirement cannot be relaxed from 2 to 1. For a special case of H-Transversal where H is a (family of) cycles, we mention the implication of our result to the related Feedback Vertex Set problem, and give a different hardness proof for directed graphs.

BibTeX - Entry

@InProceedings{guruswami_et_al:LIPIcs:2015:5308,
  author =	{Venkatesan Guruswami and Euiwoong Lee},
  title =	{{Inapproximability of H-Transversal/Packing}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)},
  pages =	{284--304},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-89-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{40},
  editor =	{Naveen Garg and Klaus Jansen and Anup Rao and Jos{\'e} D. P. Rolim},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5308},
  URN =		{urn:nbn:de:0030-drops-53085},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2015.284},
  annote =	{Keywords: Constraint Satisfaction Problems, Approximation resistance}
}

Keywords: Constraint Satisfaction Problems, Approximation resistance
Seminar: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)
Issue Date: 2015
Date of publication: 28.07.2015


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