TY - GEN
T1 - Parameterized complexity of conflict-free matchings and paths
AU - Agrawal, Akanksha
AU - Jain, Pallavi
AU - Kanesh, Lawqueen
AU - Saurabh, Saket
N1 - Publisher Copyright:
© Akanksha Agrawal, Pallavi Jain, Lawqueen Kanesh, and Saket Saurabh.
PY - 2019/8/1
Y1 - 2019/8/1
N2 - 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.
AB - 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.
KW - Conflict-free
KW - FPT algorithm
KW - Matching
KW - Matroid
KW - Shortest Path
KW - W[1]-hard
UR - https://www.scopus.com/pages/publications/85071744535
U2 - 10.4230/LIPIcs.MFCS.2019.35
DO - 10.4230/LIPIcs.MFCS.2019.35
M3 - Conference contribution
AN - SCOPUS:85071744535
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 44th International Symposium on Mathematical Foundations of Computer Science, MFCS 2019
A2 - Katoen, Joost-Pieter
A2 - Heggernes, Pinar
A2 - Rossmanith, Peter
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 44th International Symposium on Mathematical Foundations of Computer Science, MFCS 2019
Y2 - 26 August 2019 through 30 August 2019
ER -