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.IPEC.2017.21
URN: urn:nbn:de:0030-drops-85643
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8564/
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Jaffke, Lars ; Kwon, O-joung ; Telle, Jan Arne

Polynomial-Time Algorithms for the Longest Induced Path and Induced Disjoint Paths Problems on Graphs of Bounded Mim-Width

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Abstract

We give the first polynomial-time algorithms on graphs of bounded maximum induced matching width (mim-width) for problems that are not locally checkable. In particular, we give n^O(w)-time algorithms on graphs of mim-width at most w, when given a decomposition, for the following problems: Longest Induced Path, Induced Disjoint Paths and H-Induced Topological Minor for fixed H. Our results imply that the following graph classes have polynomial-time algorithms for these three problems: Interval and Bi-Interval graphs, Circular Arc, Per- mutation and Circular Permutation graphs, Convex graphs, k-Trapezoid, Circular k-Trapezoid, k-Polygon, Dilworth-k and Co-k-Degenerate graphs for fixed k.

BibTeX - Entry

@InProceedings{jaffke_et_al:LIPIcs:2018:8564,
  author =	{Lars Jaffke and O-joung Kwon and Jan Arne Telle},
  title =	{{Polynomial-Time Algorithms for the Longest Induced Path and Induced Disjoint Paths Problems on Graphs of Bounded Mim-Width}},
  booktitle =	{12th International Symposium on Parameterized and Exact Computation (IPEC 2017)},
  pages =	{21:1--21:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-051-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{89},
  editor =	{Daniel Lokshtanov and Naomi Nishimura},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8564},
  URN =		{urn:nbn:de:0030-drops-85643},
  doi =		{10.4230/LIPIcs.IPEC.2017.21},
  annote =	{Keywords: graph width parameters, dynamic programming, graph classes, induced paths, induced topological minors}
}

Keywords: graph width parameters, dynamic programming, graph classes, induced paths, induced topological minors
Collection: 12th International Symposium on Parameterized and Exact Computation (IPEC 2017)
Issue Date: 2018
Date of publication: 02.03.2018

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