{"title":"Total (restrained) domination in unit disk graphs","authors":"Yu Yang , Cai-Xia Wang , Shou-Jun Xu","doi":"10.1016/j.ic.2024.105210","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"300 ","pages":"Article 105210"},"PeriodicalIF":0.8000,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Information and Computation","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0890540124000750","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
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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