Faster parameterized algorithms for variants of 3-Hitting Set

In the A -Multi 3 -Hitting Set problem ( A -M3HS), where A ⊆ { 1 , 2 , 3 } , the input is a hypergraph G in which the hyperedges have sizes at most 3 and an integer k , and the goal is to decide if there is a set S of at most k vertices such that | S ∩ e | ∈ A for every hyperedge e . In this paper w...

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Veröffentlicht in:	Journal of combinatorial optimization Jg. 49; H. 4; S. 61
1. Verfasser:	Tsur, Dekel
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York Springer US 01.05.2025 Springer Nature B.V
Schlagworte:	Algorithms Apexes Combinatorics Convex and Discrete Geometry Graphs Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Theory of Computation Parameterized complexity Branching algorithms Graph algorithms
ISSN:	1382-6905, 1573-2886
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Abstract	In the A -Multi 3 -Hitting Set problem ( A -M3HS), where A ⊆ { 1 , 2 , 3 } , the input is a hypergraph G in which the hyperedges have sizes at most 3 and an integer k , and the goal is to decide if there is a set S of at most k vertices such that \| S ∩ e \| ∈ A for every hyperedge e . In this paper we give O ∗ ( 2 . 027 k ) -time algorithms for { 1 } -M3HS and { 1 , 3 } -M3HS, and an O ∗ ( 1 . 381 k ) -time algorithm for { 2 } -M3HS.
AbstractList	In the A -Multi 3 -Hitting Set problem ( A -M3HS), where A ⊆ { 1 , 2 , 3 } , the input is a hypergraph G in which the hyperedges have sizes at most 3 and an integer k , and the goal is to decide if there is a set S of at most k vertices such that \| S ∩ e \| ∈ A for every hyperedge e . In this paper we give O ∗ ( 2 . 027 k ) -time algorithms for { 1 } -M3HS and { 1 , 3 } -M3HS, and an O ∗ ( 1 . 381 k ) -time algorithm for { 2 } -M3HS. In the A-Multi3-Hitting Set problem (A-M3HS), where A⊆{1,2,3}, the input is a hypergraph G in which the hyperedges have sizes at most 3 and an integer k, and the goal is to decide if there is a set S of at most k vertices such that \|S∩e\|∈A for every hyperedge e. In this paper we give O∗(2.027k)-time algorithms for {1}-M3HS and {1,3}-M3HS, and an O∗(1.381k)-time algorithm for {2}-M3HS. In the A -Multi 3 -Hitting Set problem ( A -M3HS), where $$A \subseteq \{1,2,3\}$$ A ⊆ { 1 , 2 , 3 } , the input is a hypergraph G in which the hyperedges have sizes at most 3 and an integer k , and the goal is to decide if there is a set S of at most k vertices such that $$\|S \cap e\| \in A$$ \| S ∩ e \| ∈ A for every hyperedge e . In this paper we give $$O^(2.027^k)$$ O ∗ ( 2 . 027 k ) -time algorithms for $$\{1\}$$ { 1 } -M3HS and $$\{1,3\}$$ { 1 , 3 } -M3HS, and an $$O^(1.381^k)$$ O ∗ ( 1 . 381 k ) -time algorithm for $$\{2\}$$ { 2 } -M3HS.
ArticleNumber	61
Author	Tsur, Dekel
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Snippet	In the A -Multi 3 -Hitting Set problem ( A -M3HS), where A ⊆ { 1 , 2 , 3 } , the input is a hypergraph G in which the hyperedges have sizes at most 3 and an... In the A -Multi 3 -Hitting Set problem ( A -M3HS), where $$A \subseteq \{1,2,3\}$$ A ⊆ { 1 , 2 , 3 } , the input is a hypergraph G in which the hyperedges have... In the A-Multi3-Hitting Set problem (A-M3HS), where A⊆{1,2,3}, the input is a hypergraph G in which the hyperedges have sizes at most 3 and an integer k, and...
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SubjectTerms	Algorithms Apexes Combinatorics Convex and Discrete Geometry Graphs Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Theory of Computation
Title	Faster parameterized algorithms for variants of 3-Hitting Set
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