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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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Author Details

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

Funding

  • Agrawal, Akanksha: PBC Program of Fellowships for Outstanding Post-doctoral Researchers from China and India, reference no. 5101479000.
  • Jain, Pallavi: SERB-NPDF fellowship, reference no. PDF/2016/003508, DST, India.
  • Saurabh, Saket: Horizon 2020 Framework program, the European Research Council (ERC) Consolidator Grant LOPPRE reference no. 819416.

Cite AsGet BibTex

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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