单位磁盘图中的完全（受约束）支配

IF 0.8 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Information and Computation Pub Date : 2024-08-02 DOI:10.1016/j.ic.2024.105210

Yu Yang , Cai-Xia Wang , Shou-Jun Xu

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引用次数: 0

摘要

最小总支配问题和最小总约束支配问题是经典的组合优化问题。在本文中，我们首先证明了最小总支配问题和最小总约束支配问题的决策版本对于网格图（单位盘图的一个子类）都是 NP-完全的，从而加强了 Jena 等人（2021 年）建立的单位盘图中总支配决策问题的结果。然后，我们针对单位盘图中的最小总支配问题提出了一种线性时间为 6.387 的近似算法，比 Jena 等人（2021 年）之前的算法提高了 8 倍。最后，我们提出了单位盘图中最小总约束支配问题的线性时间 10.387 近似算法和 PTAS。

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Total (restrained) domination in unit disk graphs

The minimum total domination problem and the minimum total restrained domination problem are classical combinatorial optimization problems. In this paper, we first show that the decision versions of both the minimum total domination problem and the minimum total restrained domination problem are NP-complete for grid graphs (a subclass of unit disk graphs), thereby strengthening the result on the total domination decision problem in unit disk graphs established by Jena et al. (2021). Then, we present a linear-time 6.387-approximation algorithm for the minimum total domination problem in unit disk graphs, improving upon the previous algorithm with a ratio of 8 by Jena et al. (2021). Finally, we propose a linear-time 10.387-approximation algorithm and a PTAS for the minimum total restrained domination problem in unit disk graphs.

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来源期刊

Information and Computation 工程技术-计算机：理论方法

CiteScore

2.30

自引率

0.00%

发文量

119

审稿时长

140 days

期刊介绍： Information and Computation welcomes original papers in all areas of theoretical computer science and computational applications of information theory. Survey articles of exceptional quality will also be considered. Particularly welcome are papers contributing new results in active theoretical areas such as -Biological computation and computational biology- Computational complexity- Computer theorem-proving- Concurrency and distributed process theory- Cryptographic theory- Data base theory- Decision problems in logic- Design and analysis of algorithms- Discrete optimization and mathematical programming- Inductive inference and learning theory- Logic & constraint programming- Program verification & model checking- Probabilistic & Quantum computation- Semantics of programming languages- Symbolic computation, lambda calculus, and rewriting systems- Types and typechecking