{"title":"The Variance of the Number of 2-Protected Nodes in a Trie","authors":"Jeffrey Gaither, Mark Daniel Ward","doi":"10.1137/1.9781611973037.6","DOIUrl":null,"url":null,"abstract":"We derive an asymptotic expression for the variance of the number of 2-protected nodes (neither leaves nor parents of leaves) in a binary trie. In an unbiased trie on n leaves we find, for example, that the variance is approximately: 934n plus small fluctuations (also of order n); but our result covers the general (biased) case as well. Our proof relies on the asymptotic similarities between a trie and its Poissonized counterpart, whose behavior we glean via the Mellin transform and singularity analysis.","PeriodicalId":340112,"journal":{"name":"Workshop on Analytic Algorithmics and Combinatorics","volume":"97 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2013-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Workshop on Analytic Algorithmics and Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/1.9781611973037.6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 7
Abstract
We derive an asymptotic expression for the variance of the number of 2-protected nodes (neither leaves nor parents of leaves) in a binary trie. In an unbiased trie on n leaves we find, for example, that the variance is approximately: 934n plus small fluctuations (also of order n); but our result covers the general (biased) case as well. Our proof relies on the asymptotic similarities between a trie and its Poissonized counterpart, whose behavior we glean via the Mellin transform and singularity analysis.
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