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DOI: 10.4230/LIPIcs.STACS.2011.189
URN: urn:nbn:de:0030-drops-30103
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Fomin, Fedor V. ; Lokshtanov, Daniel ; Misra, Neeldhara ; Philip, Geevarghese ; Saurabh, Saket

Hitting forbidden minors: Approximation and Kernelization

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We study a general class of problems called F-Deletion problems. In an F-Deletion problem, we are asked whether a subset of at most k
vertices can be deleted from a graph G such that the resulting graph does not contain as a minor any graph from the family F of forbidden minors. We obtain a number of algorithmic results on the F-Deletion problem when F contains a planar graph. We give

- a linear vertex kernel on graphs excluding t-claw K_(1,t), the star with t leaves, as an induced subgraph, where t is a fixed integer.
- an approximation algorithm achieving an approximation ratio of O(log^(3/2) OPT), where $OPT$ is the size of an optimal solution on general undirected graphs.

Finally, we obtain polynomial kernels for the case when F only contains graph theta_c as a minor for a fixed integer c. The graph theta_c consists of two vertices connected by $c$ parallel edges. Even though this may appear to be a very restricted class of problems it already encompasses well-studied problems such as Vertex Cover, Feedback Vertex Set and Diamond Hitting Set. The generic kernelization algorithm is based on a non-trivial application of protrusion techniques, previously used only for problems on topological graph classes.

BibTeX - Entry

  author =	{Fedor V. Fomin and Daniel Lokshtanov and Neeldhara Misra and Geevarghese Philip and Saket Saurabh},
  title =	{{Hitting forbidden minors: Approximation and Kernelization}},
  booktitle =	{28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011) },
  pages =	{189--200},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-25-5},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{9},
  editor =	{Thomas Schwentick and Christoph D{\"u}rr},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-30103},
  doi =		{10.4230/LIPIcs.STACS.2011.189},
  annote =	{Keywords: kernelization}

Keywords: kernelization
Collection: 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)
Issue Date: 2011
Date of publication: 11.03.2011

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