Issue |
RAIRO-Theor. Inf. Appl.
Volume 35, Number 2, March-April 2001
|
|
---|---|---|
Page(s) | 163 - 185 | |
DOI | https://doi.org/10.1051/ita:2001114 | |
Published online | 15 April 2002 |
On the Stack-Size of General Tries
1
GREYC, Université de Caen, 14032 Caen, France; (Jeremie.Bourdon@info.unicaen.fr)
2
FB Informatik, Johann Wolfgang Goethe-Universität, 60054 Frankfurt a. M., Germany;
(nebel@sads.informatik.uni-frankfurt.de)
3
GREYC, Université de Caen, 14032 C
aen, France; (Brigitte.Vallee@info.unicaen.fr)
Received:
27
September
2000
Accepted:
March
2001
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.
Mathematics Subject Classification: 68P05 / 68W40 / 94A15
Key words: Average-case analysis of data-structures / information theory / trie / Mellin analysis.
© EDP Sciences, 2001
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