License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.MFCS.2018.67
URN: urn:nbn:de:0030-drops-96490
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9649/
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Belmonte, Rémy ; Hanaka, Tesshu ; Katsikarelis, Ioannis ; Kim, Eun Jung ; Lampis, Michael

New Results on Directed Edge Dominating Set

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LIPIcs-MFCS-2018-67.pdf (0.5 MB)

Abstract

We study a family of generalizations of Edge Dominating Set on directed graphs called Directed (p,q)-Edge Dominating Set. In this problem an arc (u,v) is said to dominate itself, as well as all arcs which are at distance at most q from v, or at distance at most p to u.
First, we give significantly improved FPT algorithms for the two most important cases of the problem, (0,1)-dEDS and (1,1)-dEDS (that correspond to versions of Dominating Set on line graphs), as well as polynomial kernels. We also improve the best-known approximation for these cases from logarithmic to constant. In addition, we show that (p,q)-dEDS is FPT parameterized by p+q+tw, but W-hard parameterized just by tw, where tw is the treewidth of the underlying graph of the input.
We then go on to focus on the complexity of the problem on tournaments. Here, we provide a complete classification for every possible fixed value of p,q, which shows that the problem exhibits a surprising behavior, including cases which are in P; cases which are solvable in quasi-polynomial time but not in P; and a single case (p=q=1) which is NP-hard (under randomized reductions) and cannot be solved in sub-exponential time, under standard assumptions.

BibTeX - Entry

@InProceedings{belmonte_et_al:LIPIcs:2018:9649,
  author =	{R{\'e}my Belmonte and Tesshu Hanaka and Ioannis Katsikarelis and Eun Jung Kim and Michael Lampis},
  title =	{{New Results on Directed Edge Dominating Set}},
  booktitle =	{43rd International Symposium on Mathematical Foundations  of Computer Science (MFCS 2018)},
  pages =	{67:1--67:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Igor Potapov and Paul Spirakis and James Worrell},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9649},
  URN =		{urn:nbn:de:0030-drops-96490},
  doi =		{10.4230/LIPIcs.MFCS.2018.67},
  annote =	{Keywords: Edge Dominating Set, Tournaments, Treewidth}
}

Keywords: Edge Dominating Set, Tournaments, Treewidth
Collection: 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)
Issue Date: 2018
Date of publication: 27.08.2018

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