{"title":"A replacement for Voronoi diagrams of near linear size","authors":"Sariel Har-Peled","doi":"10.1109/SFCS.2001.959884","DOIUrl":null,"url":null,"abstract":"For a set P of n points in R/sup d/, we define a new type of space decomposition. The new diagram provides an /spl epsi/-approximation to the distance function associated with the Voronoi diagram of P, while being of near linear size, for d/spl ges/2. This contrasts with the standard Voronoi diagram that has /spl Omega/ (n/sup [d/2]/) complexity in the worst case.","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"70 9-10","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2001-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"178","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings 2001 IEEE International Conference on Cluster Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFCS.2001.959884","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 178
Abstract
For a set P of n points in R/sup d/, we define a new type of space decomposition. The new diagram provides an /spl epsi/-approximation to the distance function associated with the Voronoi diagram of P, while being of near linear size, for d/spl ges/2. This contrasts with the standard Voronoi diagram that has /spl Omega/ (n/sup [d/2]/) complexity in the worst case.
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