{"title":"A linear-time algorithm for the center problem in weighted cycle graphs","authors":"Taekang Eom , Hee-Kap Ahn","doi":"10.1016/j.ipl.2024.106495","DOIUrl":null,"url":null,"abstract":"<div><p>We study the problem of computing the center of cycle graphs whose vertices are weighted. The distance from a vertex to a point of the graph is defined as the weight of the vertex times the length of the shortest path between the vertex and the point. The weighted center of the graph is a point of the graph such that the maximum distance of the vertices of the graph to the point is minimum among all points of the graph. We present an <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span>-time algorithm for the discrete and continuous weighted center problem on cycle graphs with <em>n</em> vertices. Our algorithm improves upon the best known algorithm that takes <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo></math></span> time. Moreover, it is optimal for the weighted center problem of cycle graphs.</p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"186 ","pages":"Article 106495"},"PeriodicalIF":0.7000,"publicationDate":"2024-04-04","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/S0020019024000255","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
We study the problem of computing the center of cycle graphs whose vertices are weighted. The distance from a vertex to a point of the graph is defined as the weight of the vertex times the length of the shortest path between the vertex and the point. The weighted center of the graph is a point of the graph such that the maximum distance of the vertices of the graph to the point is minimum among all points of the graph. We present an -time algorithm for the discrete and continuous weighted center problem on cycle graphs with n vertices. Our algorithm improves upon the best known algorithm that takes time. Moreover, it is optimal for the weighted center problem of cycle graphs.
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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