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Finding Induced Subgraphs via Minimal Triangulations

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Abstract

Potential maximal cliques and minimal separators are combinatorial objects which were introduced and studied in the realm of minimal triangulation problems including Minimum Fill-in and Treewidth. We discover unexpected applications of these notions to the field of moderate exponential algorithms. In particular, we show that given an n-vertex graph G together with its set of potential maximal cliques, and an integer t, it is possible in time the number of potential maximal cliques times $O(n^{O(t)})$ to find a maximum induced subgraph of treewidth t in G and for a given graph F of treewidth t, to decide if G contains an induced subgraph isomorphic to F. Combined with an improved algorithm enumerating all potential maximal cliques in time $O(1.734601^n)$, this yields that both the problems are solvable in time $1.734601^n$ * $n^{O(t)}$.

BibTeX - Entry

@InProceedings{fomin_et_al:LIPIcs:2010:2470,
  author =	{Fedor V. Fomin and Yngve Villanger},
  title =	{{Finding Induced Subgraphs via Minimal Triangulations}},
  booktitle =	{27th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{383--394},
  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/2010/2470},
  URN =		{urn:nbn:de:0030-drops-24708},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.STACS.2010.2470},
  annote =	{Keywords: Bounded treewidth, minimal triangulation, moderately exponential time algorithms}
}

Keywords: Bounded treewidth, minimal triangulation, moderately exponential time algorithms
Seminar: 27th International Symposium on Theoretical Aspects of Computer Science
Issue date: 2010
Date of publication: 2010


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