Parameterized complexity of conflict-free matchings and paths

Akanksha Agrawal, Pallavi Jain, Lawqueen Kanesh, Saket Saurabh

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

An input to a conflict-free variant of a classical problem Γ, called Conflict-Free Γ, consists of an instance I of Γ coupled with a graph H, called the conflict graph. A solution to Conflict-Free Γ in (I,H) is a solution to I in Γ, 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.

Original languageEnglish
Title of host publication44th International Symposium on Mathematical Foundations of Computer Science, MFCS 2019
EditorsJoost-Pieter Katoen, Pinar Heggernes, Peter Rossmanith
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771177
DOIs
StatePublished - 1 Aug 2019
Event44th International Symposium on Mathematical Foundations of Computer Science, MFCS 2019 - Aachen, Germany
Duration: 26 Aug 201930 Aug 2019

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume138
ISSN (Print)1868-8969

Conference

Conference44th International Symposium on Mathematical Foundations of Computer Science, MFCS 2019
Country/TerritoryGermany
CityAachen
Period26/08/1930/08/19

Keywords

  • Conflict-free
  • FPT algorithm
  • Matching
  • Matroid
  • Shortest Path
  • W[1]-hard

ASJC Scopus subject areas

  • Software

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