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URN: urn:nbn:de:0030-drops-39340
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Computing cutwidth and pathwidth of semi-complete digraphs via degree orderings

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Abstract

The notions of cutwidth and pathwidth of digraphs play a central role in the containment theory for tournaments, or more generally semi-complete digraphs, developed in a recent series of papers by Chudnovsky, Fradkin, Kim, Scott, and Seymour (Maria Chudnovsky, Alexandra Fradkin, and Paul Seymour, 2012; Maria Chudnovsky, Alex Scott, and Paul Seymour, 2011; Maria Chudnovsky and Paul D. Seymour, 2011; Alexandra Fradkin and Paul Seymour, 2010; Alexandra Fradkin and Paul Seymour, 2011; Ilhee Kim and Paul Seymour, 2012). In this work we introduce a new approach to computing these width measures on semi-complete digraphs, via degree orderings. Using the new technique we are able to reprove the main results of (Maria Chudnovsky, Alexandra Fradkin, and Paul Seymour, 2012; Alexandra Fradkin and Paul Seymour, 2011) in a unified and significantly simplified way, as well as obtain new results. First, we present polynomial-time approximation algorithms for both cutwidth and pathwidth, faster and simpler than the previously known ones; the most significant improvement is in case of pathwidth, where instead of previously known O(OPT)-approximation in fixed-parameter tractable time (Fedor V. Fomin and Michal Pilipczuk, 2013) we obtain a constant-factor approximation in polynomial time. Secondly, by exploiting the new set of obstacles for cutwidth and pathwidth, we show that topological containment and immersion in semi-complete digraphs can be tested in single-exponential fixed-parameter tractable time. Finally, we present how the new approach can be used to obtain exact fixed-parameter tractable algorithms for cutwidth and pathwidth, with single-exponential running time dependency on the optimal width.

BibTeX - Entry

@InProceedings{pilipczuk:LIPIcs:2013:3934,
  author =	{Michal Pilipczuk},
  title =	{{Computing cutwidth and pathwidth of semi-complete digraphs via degree orderings}},
  booktitle =	{30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
  pages =	{197--208},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-50-7},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{20},
  editor =	{Natacha Portier and Thomas Wilke},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2013/3934},
  URN =		{urn:nbn:de:0030-drops-39340},
  doi =		{10.4230/LIPIcs.STACS.2013.197},
  annote =	{Keywords: semi-complete digraph, tournament, pathwidth, cutwidth}
}

Keywords: semi-complete digraph, tournament, pathwidth, cutwidth
Seminar: 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)
Issue date: 2013
Date of publication: 2013


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