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On the Stack-Size of General Tries

Published online by Cambridge University Press:  15 April 2002

Jérémie Bourdon ,
Markus Nebel  and
Brigitte Vallée
Jérémie Bourdon
Affiliation:
GREYC, Université de Caen, 14032 Caen, France; (Jeremie.Bourdon@info.unicaen.fr)
Markus Nebel
Affiliation:
FB Informatik, Johann Wolfgang Goethe-Universität, 60054 Frankfurt a. M., Germany; (nebel@sads.informatik.uni-frankfurt.de)
Brigitte Vallée
Affiliation:
GREYC, Université de Caen, 14032 C aen, France; (Brigitte.Vallee@info.unicaen.fr)
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Abstract

Digital trees or tries are a general purpose flexible data structure that implements dictionaries built on words. The present paper is focussed on the average-case analysis of an important parameter of this tree-structure, i.e., the stack-size. The stack-size of a tree is the memory needed by a storage-optimal preorder traversal. The analysis is carried out under a general model in which words are produced by a source (in the information-theoretic sense) that emits symbols. Under some natural assumptions that encompass all commonly used data models (and more), we obtain a precise average-case and probabilistic analysis of stack-size. Furthermore, we study the dependency between the stack-size and the ordering on symbols in the alphabet: we establish that, when the source emits independent symbols, the optimal ordering arises when the most probable symbol is the last one in this order.

Keywords

Average-case analysis of data-structuresinformation theorytrieMellin analysis.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 35 , Issue 2 , March 2001 , pp. 163 - 185
Copyright
© EDP Sciences, 2001

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