{"title":"A study of random Weyl trees","authors":"L. Devroye, Amar Goudjil","doi":"10.1002/(SICI)1098-2418(199805)12:3%3C271::AID-RSA4%3E3.0.CO;2-S","DOIUrl":null,"url":null,"abstract":"We study binary search trees constructed from Weyl sequences fnng; n 1, where is an irrational and f:g denotes \\mod 1\". We explore various properties of the structure of these trees, and relate them to the continued fraction expansion of. If H n is the height of the tree with n nodes when is chosen at random and uniformly on 0; 1], then we show that in probability, H n (12== 2) log n log log n.","PeriodicalId":303496,"journal":{"name":"Random Struct. Algorithms","volume":"31 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1998-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Random Struct. Algorithms","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/(SICI)1098-2418(199805)12:3%3C271::AID-RSA4%3E3.0.CO;2-S","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 5
Abstract
We study binary search trees constructed from Weyl sequences fnng; n 1, where is an irrational and f:g denotes \mod 1". We explore various properties of the structure of these trees, and relate them to the continued fraction expansion of. If H n is the height of the tree with n nodes when is chosen at random and uniformly on 0; 1], then we show that in probability, H n (12== 2) log n log log n.
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