License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.IPEC.2016.15
URN: urn:nbn:de:0030-drops-69306
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Giannopoulou, Archontia C. ; Pilipczuk, Michal ; Raymond, Jean-Florent ; Thilikos, Dimitrios M. ; Wrochna, Marcin

Cutwidth: Obstructions and Algorithmic Aspects

LIPIcs-IPEC-2016-15.pdf (0.6 MB)


Cutwidth is one of the classic layout parameters for graphs. It measures how well one can order the vertices of a graph in a linear manner, so that the maximum number of edges between any prefix and its complement suffix is minimized. As graphs of cutwidth at most k are closed under taking immersions, the results of Robertson and Seymour imply that there is a finite list of minimal immersion obstructions for admitting a cut layout of width at most k. We prove that every minimal immersion obstruction for cutwidth at most k has size at most 2^O(k^3*log(k)).

As an interesting algorithmic byproduct, we design a new fixed-parameter algorithm for computing the cutwidth of a graph that runs in time 2^O(k^2*log(k))*n, where k is the optimum width and n is the number of vertices. While being slower by a log k-factor in the exponent than the fastest known algorithm, due to Thilikos, Bodlaender, and Serna [J. Algorithms 2005], our algorithm has the advantage of being simpler and self-contained; arguably, it explains better the combinatorics of optimum-width layouts.

BibTeX - Entry

  author =	{Archontia C. Giannopoulou and Michal Pilipczuk and Jean-Florent Raymond and Dimitrios M. Thilikos and Marcin Wrochna},
  title =	{{Cutwidth: Obstructions and Algorithmic Aspects}},
  booktitle =	{11th International Symposium on Parameterized and Exact Computation (IPEC 2016)},
  pages =	{15:1--15:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-023-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{63},
  editor =	{Jiong Guo and Danny Hermelin},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-69306},
  doi =		{10.4230/LIPIcs.IPEC.2016.15},
  annote =	{Keywords: cutwidth, obstructions, immersions, fixed-parameter tractability}

Keywords: cutwidth, obstructions, immersions, fixed-parameter tractability
Collection: 11th International Symposium on Parameterized and Exact Computation (IPEC 2016)
Issue Date: 2017
Date of publication: 09.02.2017

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