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Parameterized Complexity of Conflict-Free Matchings and Paths

Authors Akanksha Agrawal, Pallavi Jain, Lawqueen Kanesh, Saket Saurabh



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Akanksha Agrawal
  • Ben-Gurion University of the Negev, Beer-Sheva, Israel
Pallavi Jain
  • Institute of Mathematical Sciences, HBNI, Chennai, India
Lawqueen Kanesh
  • Institute of Mathematical Sciences, HBNI, Chennai, India
Saket Saurabh
  • University of Bergen, Bergen, Norway
  • Institute of Mathematical Sciences, HBNI, Chennai, India
  • UMI ReLax

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Akanksha Agrawal, Pallavi Jain, Lawqueen Kanesh, and Saket Saurabh. Parameterized Complexity of Conflict-Free Matchings and Paths. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 35:1-35:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.MFCS.2019.35

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • Conflict-free
  • Matching
  • Shortest Path
  • FPT algorithm
  • W[1]-hard
  • Matroid

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