{"title":"树中2保护节点数的方差","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":"{\"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}","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}
The Variance of the Number of 2-Protected Nodes in a Trie
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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