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.FSTTCS.2018.35
URN: urn:nbn:de:0030-drops-99341
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9934/
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Misra, Pranabendu ; Saurabh, Saket ; Sharma, Roohani ; Zehavi, Meirav

Sub-Exponential Time Parameterized Algorithms for Graph Layout Problems on Digraphs with Bounded Independence Number

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Abstract

Fradkin and Seymour [Journal of Combinatorial Graph Theory, Series B, 2015] defined the class of digraphs of bounded independence number as a generalization of the class of tournaments. They argued that the class of digraphs of bounded independence number is structured enough to be exploited algorithmically. In this paper, we further strengthen this belief by showing that several cut problems that admit sub-exponential time parameterized algorithms (a trait uncommon to parameterized algorithms) on tournaments, including Directed Feedback Arc Set, Directed Cutwidth and Optimal Linear Arrangement, also admit such algorithms on digraphs of bounded independence number. Towards this, we rely on the generic approach of Fomin and Pilipczuk [ESA, 2013], where to get the desired algorithms, it is enough to bound the number of k-cuts in digraphs of bounded independence number by a sub-exponential FPT function (Fomin and Pilipczuk bounded the number of k-cuts in transitive tournaments). Specifically, our main technical contribution is that the yes-instances of the problems above have a sub-exponential number of k-cuts. We prove this bound by using a combination of chromatic coding, an inductive argument and structural properties of the digraphs.

BibTeX - Entry

@InProceedings{misra_et_al:LIPIcs:2018:9934,
  author =	{Pranabendu Misra and Saket Saurabh and Roohani Sharma and Meirav Zehavi},
  title =	{{Sub-Exponential Time Parameterized Algorithms for Graph Layout Problems on Digraphs with Bounded Independence Number}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software  Technology and Theoretical Computer Science (FSTTCS 2018)},
  pages =	{35:1--35:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-093-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{122},
  editor =	{Sumit Ganguly and Paritosh Pandya},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9934},
  URN =		{urn:nbn:de:0030-drops-99341},
  doi =		{10.4230/LIPIcs.FSTTCS.2018.35},
  annote =	{Keywords: sub-exponential fixed-parameter tractable algorithms, directed feedback arc set, directed cutwidth, optimal linear arrangement, bounded independence n}
}

Keywords: sub-exponential fixed-parameter tractable algorithms, directed feedback arc set, directed cutwidth, optimal linear arrangement, bounded independence n
Collection: 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)
Issue Date: 2018
Date of publication: 05.12.2018

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