Richard C. Tillquist, Rafael M. Frongillo, Manuel E. Lladser
{"title":"Getting the Lay of the Land in Discrete Space: A Survey of Metric Dimension and Its Applications","authors":"Richard C. Tillquist, Rafael M. Frongillo, Manuel E. Lladser","doi":"10.1137/21m1409512","DOIUrl":null,"url":null,"abstract":"SIAM Review, Volume 65, Issue 4, Page 919-962, November 2023. <br/> The metric dimension of a graph is the smallest number of nodes required to identify all other nodes uniquely based on shortest path distances. Applications of metric dimension include discovering the source of a spread in a network, canonically labeling graphs, and embedding symbolic data in low-dimensional Euclidean spaces. This survey gives a self-contained introduction to metric dimension and an overview of the quintessential results and applications. We discuss methods for approximating the metric dimension of general graphs, and specific bounds and asymptotic behavior for deterministic and random families of graphs. We conclude with related concepts and directions for future work.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":null,"pages":null},"PeriodicalIF":10.8000,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"28","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Review","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/21m1409512","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 28
Abstract
SIAM Review, Volume 65, Issue 4, Page 919-962, November 2023. The metric dimension of a graph is the smallest number of nodes required to identify all other nodes uniquely based on shortest path distances. Applications of metric dimension include discovering the source of a spread in a network, canonically labeling graphs, and embedding symbolic data in low-dimensional Euclidean spaces. This survey gives a self-contained introduction to metric dimension and an overview of the quintessential results and applications. We discuss methods for approximating the metric dimension of general graphs, and specific bounds and asymptotic behavior for deterministic and random families of graphs. We conclude with related concepts and directions for future work.
期刊介绍：
Survey and Review feature papers that provide an integrative and current viewpoint on important topics in applied or computational mathematics and scientific computing. These papers aim to offer a comprehensive perspective on the subject matter.
Research Spotlights publish concise research papers in applied and computational mathematics that are of interest to a wide range of readers in SIAM Review. The papers in this section present innovative ideas that are clearly explained and motivated. They stand out from regular publications in specific SIAM journals due to their accessibility and potential for widespread and long-lasting influence.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
