A general central limit theorem for shape parameters of m-ary tries and PATRICIA tries

Michael Fuchs, Chung Kuei Lee

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

Tries and PATRICIA tries are fundamental data structures in computer science with numerous applications. In a recent paper, a general framework for obtaining the mean and variance of additive shape parameters of tries and PATRICIA tries under the Bernoulli model was proposed. In this note, we show that a slight modification of this framework yields a central limit theorem for shape parameters, too. This central limit theorem contains many of the previous central limit theorems from the literature and it can be used to prove recent conjectures and derive new results. As an example, we will consider a refinement of the size of tries and PATRICIA tries, namely, the number of nodes of fixed outdegree and obtain (univariate and bivariate) central limit theorems. Moreover, trivariate central limit theorems for size, internal path length and internal Wiener index of tries and PATRICIA tries are derived as well.

Original languageEnglish
Article numberP1.68
JournalElectronic Journal of Combinatorics
Volume21
Issue number1
DOIs
StatePublished - 24 Mar 2014

Keywords

  • Digital trees
  • Moments
  • Multivariate limit laws
  • Nodes of fixed out-degree
  • Total path length
  • Wiener index

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