Parameterized Complexity of Conflict-Free Matchings and Paths

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...

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Veröffentlicht in:Algorithmica Jg. 82; H. 7; S. 1939 - 1965
Hauptverfasser: Agrawal, Akanksha, Jain, Pallavi, Kanesh, Lawqueen, Saurabh, Saket
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.07.2020
Springer Nature B.V
Schlagworte:
Algorithm Analysis and Problem Complexity
Algorithms
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Hardness
Matching
Mathematics of Computing
Parameterization
Shortest-path problems
Theory of Computation
Matching
Shortest path
W-hard
FPT algorithm
Matroid
Conflict-free
ISSN:0178-4617, 1432-0541
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Zusammenfassung: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 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.
Bibliographie:ObjectType-Article-1
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-020-00681-y