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DOI: 10.4230/LIPIcs.MFCS.2019.35
URN: urn:nbn:de:0030-drops-109798
URL: http://drops.dagstuhl.de/opus/volltexte/2019/10979/
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Agrawal, Akanksha ; Jain, Pallavi ; Kanesh, Lawqueen ; Saurabh, Saket

Parameterized Complexity of Conflict-Free Matchings and Paths

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Abstract

An input to a conflict-free variant of a classical problem Gamma, called Conflict-Free Gamma, consists of an instance I of Gamma coupled with a graph H, called the conflict graph. A solution to Conflict-Free Gamma in (I,H) is a solution to I in Gamma, which is also an independent set in H. In this paper, we study conflict-free variants of Maximum Matching and Shortest Path, which we call Conflict-Free Matching (CF-Matching) and Conflict-Free Shortest Path (CF-SP), respectively. We show that both CF-Matching and CF-SP are W[1]-hard, when parameterized by the solution size. Moreover, W[1]-hardness for CF-Matching holds even when the input graph where we want to find a matching is itself a matching, and W[1]-hardness for CF-SP holds for conflict graph being a unit-interval graph. Next, we study these problems with restriction on the conflict graphs. We give FPT algorithms for CF-Matching when the conflict graph is chordal. Also, we give FPT algorithms for both CF-Matching and CF-SP, when the conflict graph is d-degenerate. Finally, we design FPT algorithms for variants of CF-Matching and CF-SP, where the conflicting conditions are given by a (representable) matroid.

BibTeX - Entry

@InProceedings{agrawal_et_al:LIPIcs:2019:10979,
  author =	{Akanksha Agrawal and Pallavi Jain and Lawqueen Kanesh and Saket Saurabh},
  title =	{{Parameterized Complexity of Conflict-Free Matchings and Paths}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{35:1--35:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Peter Rossmanith and Pinar Heggernes and Joost-Pieter Katoen},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10979},
  URN =		{urn:nbn:de:0030-drops-109798},
  doi =		{10.4230/LIPIcs.MFCS.2019.35},
  annote =	{Keywords: Conflict-free, Matching, Shortest Path, FPT algorithm, W[1]-hard, Matroid}
}

Keywords: Conflict-free, Matching, Shortest Path, FPT algorithm, W[1]-hard, Matroid
Seminar: 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)
Issue Date: 2019
Date of publication: 23.08.2019


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