Parameterized Complexity of Conflict-Free Matchings and Paths

Akanksha Agrawal, Pallavi Jain, Lawqueen Kanesh, Saket Saurabh

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


An input to a conflict-free variant of a classical problem Γ , called Conflict-FreeΓ , consists of an instance I of Γ coupled with a graph H, called the conflict graph. A solution to Conflict-FreeΓ 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 Maximum Matching (CF-MM) and Conflict-Free Shortest Path (CF-SP), respectively. We show that both CF-MM and CF-SP are W[1]-hard, when parameterized by the solution size. Moreover, W[1]-hardness for CF-MM 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-MM when the conflict graph is chordal. Also, we give FPT algorithms for both CF-MM and CF-SP, when the conflict graph is d-degenerate. Finally, we design FPT algorithms for variants of CF-MM and CF-SP, where the conflicting conditions are given by a (representable) matroid.

Original languageEnglish
Pages (from-to)1939-1965
Number of pages27
Issue number7
StatePublished - 1 Jul 2020


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

ASJC Scopus subject areas

  • Computer Science (all)
  • Computer Science Applications
  • Applied Mathematics


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