Faster parameterized algorithms for variants of 3-Hitting Set

Dekel Tsur

doi:10.1007/s10878-025-01300-8

Faster parameterized algorithms for variants of 3-Hitting Set

Dekel Tsur

Department of Computer Science

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	American English
Article number	61
Journal	Journal of Combinatorial Optimization
Volume	49
Issue number	4
DOIs	https://doi.org/10.1007/s10878-025-01300-8
State	Published - 1 May 2025

Keywords

Branching algorithms
Graph algorithms
Parameterized complexity

All Science Journal Classification (ASJC) codes

Computer Science Applications
Discrete Mathematics and Combinatorics
Control and Optimization
Computational Theory and Mathematics
Applied Mathematics

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10.1007/s10878-025-01300-8

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abstract = "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.",

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N2 - 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.

AB - 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.

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JF - Journal of Combinatorial Optimization

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ER -

Faster parameterized algorithms for variants of 3-Hitting Set

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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