{"title":"The facility location problem with maximum distance constraint","authors":"Xiaowei Li, Xiwen Lu","doi":"10.1016/j.ipl.2023.106447","DOIUrl":null,"url":null,"abstract":"<div><p>Motivated by practical problems, we investigate the facility location problem with maximum distance constraint, which requires that the distance from each customer to open facilities must not exceed a given threshold value of <em>L</em>. The goal is to minimise the sum of the opening costs of the facilities. We show that this problem is NP-hard and analyse its lower bound. As no <span><math><mo>(</mo><mi>α</mi><mo>,</mo><mn>1</mn><mo>)</mo></math></span>-approximation algorithm with <span><math><mi>α</mi><mo><</mo><mn>3</mn></math></span> exists, we provide a (3,1)-approximation algorithm that violates the maximum distance constraint. Based on this algorithm, we propose a 3-approximation algorithm for the <em>k</em>-supplier problem. The difference between this algorithm and the previous one in <span>[12]</span> is that the proposed algorithm avoids the construction of many bottleneck graphs, making the proposed algorithm less demanding in terms of memory and more suitable for large-scale problems.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"184 ","pages":"Article 106447"},"PeriodicalIF":0.7000,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Information Processing Letters","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S002001902300090X","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
Motivated by practical problems, we investigate the facility location problem with maximum distance constraint, which requires that the distance from each customer to open facilities must not exceed a given threshold value of L. The goal is to minimise the sum of the opening costs of the facilities. We show that this problem is NP-hard and analyse its lower bound. As no -approximation algorithm with exists, we provide a (3,1)-approximation algorithm that violates the maximum distance constraint. Based on this algorithm, we propose a 3-approximation algorithm for the k-supplier problem. The difference between this algorithm and the previous one in [12] is that the proposed algorithm avoids the construction of many bottleneck graphs, making the proposed algorithm less demanding in terms of memory and more suitable for large-scale problems.
期刊介绍：
Information Processing Letters invites submission of original research articles that focus on fundamental aspects of information processing and computing. This naturally includes work in the broadly understood field of theoretical computer science; although papers in all areas of scientific inquiry will be given consideration, provided that they describe research contributions credibly motivated by applications to computing and involve rigorous methodology. High quality experimental papers that address topics of sufficiently broad interest may also be considered.
Since its inception in 1971, Information Processing Letters has served as a forum for timely dissemination of short, concise and focused research contributions. Continuing with this tradition, and to expedite the reviewing process, manuscripts are generally limited in length to nine pages when they appear in print.
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