An analytic approach to the asymptotic variance of trie statistics and related structures

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• 作者：Michael Fuchs^a ; ^{mfuchs@math.nctu.edu.tw" class="auth_mail} ; Hsien-Kuei Hwang^b ; ^{hkwhang@stat.sinica.edu.tw" class="auth_mail} ; Vytas Zacharovas^c ; ^{vytas.zacharovas@mif.vu.lt" class="auth_mail}
• 关键词：Digital trees ; Binomial splitting process ; Mellin transform ; Variance ; Periodic fluctuations ; Contention resolution algorithms
• 刊名：Theoretical Computer Science
• 出版年：27 March, 2014
• 年：2014
• 卷：527
• 期：Complete
• 页码：1-36
• 全文大小：1061 K

文摘

We develop analytic tools for the asymptotics of general trie statistics, which are particularly advantageous for clarifying the asymptotic variance. Many concrete examples are discussed for which new Fourier expansions are given. The tools are also useful for other splitting processes with an underlying binomial distribution. We specially highlight Philippe Flajolet's contribution in the analysis of these random structures.