{"title":"On minimal rectilinear Steiner trees in all dimensions","authors":"T. Snyder","doi":"10.1145/98524.98596","DOIUrl":null,"url":null,"abstract":"It is proved that the length of the longest possible minimum rectilinear Steiner tree of <italic>n</italic> points in the unit <italic>d</italic>-cube is asymptotic to Β<subscrpt><italic>d</subscrpt>n</italic> d-1/d, where Β<subscrpt><italic>d</italic></subscrpt>. In addition to replicating Chung and Graham's exact determination of Β<subscrpt>2</subscrpt> = 1, this generalization yields tight new bounds such as 1 ≤ Β<subscrpt>3</subscrpt> < 1.191 and 1 < Β<subscrpt>4</subscrpt> < √<italic>2</italic>.","PeriodicalId":113850,"journal":{"name":"SCG '90","volume":"7 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1990-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SCG '90","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/98524.98596","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 11
Abstract
It is proved that the length of the longest possible minimum rectilinear Steiner tree of n points in the unit d-cube is asymptotic to Βdn d-1/d, where Βd. In addition to replicating Chung and Graham's exact determination of Β2 = 1, this generalization yields tight new bounds such as 1 ≤ Β3 < 1.191 and 1 < Β4 < √2.
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