Asymptotic normality for the size of graph tries built from M-ary tree labelings

Graph tries are a new and interesting data structure proposed by Jacquet in 2014. They generalize the classical trie data structure which has found many applications in computer science and is one of the most popular data structure on words. For his generalization, Jacquet considered the size (or sp...

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Published inTheoretical computer science Vol. 968; p. 114011
Main Authors Fuchs, Michael, Yu, Tsan-Cheng
Format Journal Article
LanguageEnglish
Published Elsevier B.V 11.08.2023
Subjects
Central limit theorem
Graph tries
Method of moments
Space requirement
Tries
Graph tries
Space requirement
Central limit theorem
Tries
Method of moments
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Abstract Graph tries are a new and interesting data structure proposed by Jacquet in 2014. They generalize the classical trie data structure which has found many applications in computer science and is one of the most popular data structure on words. For his generalization, Jacquet considered the size (or space requirement) and derived an asymptotic expansion for the mean and the variance when graph tries are built from n independently chosen random labelings of a rooted M-ary tree. Moreover, he conjectured a central limit theorem for the (suitably normalized) size as the number of labelings tends to infinity. In this paper, we verify this conjecture with the method of moments.
AbstractList Graph tries are a new and interesting data structure proposed by Jacquet in 2014. They generalize the classical trie data structure which has found many applications in computer science and is one of the most popular data structure on words. For his generalization, Jacquet considered the size (or space requirement) and derived an asymptotic expansion for the mean and the variance when graph tries are built from n independently chosen random labelings of a rooted M-ary tree. Moreover, he conjectured a central limit theorem for the (suitably normalized) size as the number of labelings tends to infinity. In this paper, we verify this conjecture with the method of moments.
ArticleNumber 114011
Author Yu, Tsan-Cheng
Fuchs, Michael
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10.1016/S0196-6774(02)00210-9
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10.1016/j.tcs.2014.01.024
10.1016/0304-3975(94)00306-4
10.1016/S0304-3975(97)00167-9
10.1214/aoap/1075828056
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Keywords Graph tries
Space requirement
Central limit theorem
Tries
Method of moments
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Snippet Graph tries are a new and interesting data structure proposed by Jacquet in 2014. They generalize the classical trie data structure which has found many...
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SubjectTerms Central limit theorem
Graph tries
Method of moments
Space requirement
Tries
Title Asymptotic normality for the size of graph tries built from M-ary tree labelings
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