Faster parameterized algorithms for variants of 3-Hitting Set

IF 0.9 4区数学 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Combinatorial Optimization Pub Date : 2025-05-07 DOI:10.1007/s10878-025-01300-8

Dekel Tsur

引用次数: 0

Abstract

In the A-Multi3-Hitting Set problem (A-M3HS), where \(A \subseteq \{1,2,3\}\), 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 \(|S \cap e| \in A\) 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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3命中集变异体的更快参数化算法

在a - multi3命中集问题（a -M3HS）中，其中\(A \subseteq \{1,2,3\}\)，输入是一个超图G，其中超边的大小最多为3和整数k，目标是确定是否存在一个最多包含k个顶点的集合S，使得\(|S \cap e| \in A\)对于每个超边e。在本文中我们给出了\(\{1\}\) -M3HS和\(\{1,3\}\) -M3HS的\(O^*(2.027^k)\)时间算法，以及\(\{2\}\) -M3HS的\(O^*(1.381^k)\)时间算法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Combinatorial Optimization 数学-计算机：跨学科应用

CiteScore

2.00

自引率

10.00%

发文量

审稿时长

6 months

期刊介绍： The objective of Journal of Combinatorial Optimization is to advance and promote the theory and applications of combinatorial optimization, which is an area of research at the intersection of applied mathematics, computer science, and operations research and which overlaps with many other areas such as computation complexity, computational biology, VLSI design, communication networks, and management science. It includes complexity analysis and algorithm design for combinatorial optimization problems, numerical experiments and problem discovery with applications in science and engineering. The Journal of Combinatorial Optimization publishes refereed papers dealing with all theoretical, computational and applied aspects of combinatorial optimization. It also publishes reviews of appropriate books and special issues of journals.