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.ICALP.2017.70
URN: urn:nbn:de:0030-drops-74537
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7453/
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Barbero, Florian ; Paul, Christophe ; Pilipczuk, Michal

Exploring the Complexity of Layout Parameters in Tournaments and Semi-Complete Digraphs

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Abstract

A simple digraph is semi-complete if for any two of its vertices u and v, at least one of the arcs (u,v) and (v,u) is present. We study the complexity of computing two layout parameters of semi-complete digraphs: cutwidth and optimal linear arrangement (OLA). We prove that:
-Both parameters are NP-hard to compute and the known exact and parameterized algorithms for them have essentially optimal running times, assuming the Exponential Time Hypothesis.
- The cutwidth parameter admits a quadratic Turing kernel, whereas it does not admit any polynomial kernel unless coNP/poly contains NP. By contrast, OLA admits a linear kernel.

These results essentially complete the complexity analysis of computing cutwidth and OLA on semi-complete digraphs. Our techniques can be also used to analyze the sizes of minimal obstructions for having small cutwidth under the induced subdigraph relation.

BibTeX - Entry

@InProceedings{barbero_et_al:LIPIcs:2017:7453,
  author =	{Florian Barbero and Christophe Paul and Michal Pilipczuk},
  title =	{{Exploring the Complexity of Layout Parameters in Tournaments and Semi-Complete Digraphs}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{70:1--70:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Ioannis Chatzigiannakis and Piotr Indyk and Fabian Kuhn and Anca Muscholl},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7453},
  URN =		{urn:nbn:de:0030-drops-74537},
  doi =		{10.4230/LIPIcs.ICALP.2017.70},
  annote =	{Keywords: cutwidth, OLA, tournament, semi-complete digraph}
}

Keywords: cutwidth, OLA, tournament, semi-complete digraph
Collection: 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)
Issue Date: 2017
Date of publication: 07.07.2017

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