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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Bibliographic Details
Published in:Journal of combinatorial optimization Vol. 49; no. 4; p. 61
Main Author: Tsur, Dekel
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2025
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-025-01300-8