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Treewidth Reduction for Constrained Separation and Bipartization Problems

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Abstract

We present a method for reducing the treewidth of a graph while preserving all the minimal $s-t$ separators. This technique turns out to be very useful for establishing the fixed-parameter tractability of constrained separation and bipartization problems. To demonstrate the power of this technique, we prove the fixed-parameter tractability of a number of well-known separation and bipartization problems with various additional restrictions (e.g., the vertices being removed from the graph form an independent set). These results answer a number of open questions in the area of parameterized complexity.

BibTeX - Entry

@InProceedings{marx_et_al:LIPIcs:2010:2485,
  author =	{D{\'a}niel Marx and Barry O'Sullivan and Igor Razgon},
  title =	{{Treewidth Reduction for Constrained Separation and Bipartization Problems}},
  booktitle =	{27th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{561--572},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-16-3},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{5},
  editor =	{Jean-Yves Marion and Thomas Schwentick},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2010/2485},
  URN =		{urn:nbn:de:0030-drops-24850},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.STACS.2010.2485},
  annote =	{Keywords: Fixed-parameter algorithms, graph separation problems, treewidth}
}

Keywords: Fixed-parameter algorithms, graph separation problems, treewidth
Seminar: 27th International Symposium on Theoretical Aspects of Computer Science
Issue date: 2010
Date of publication: 2010


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