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Bourdon, Jérémie; Nebel, Markus; Vallée, Brigitte
On the stack-size of general tries. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, 35 no. 2 (2001), p. 163-185
Texte intégral djvu | pdf | Analyses MR 1862461 | Zbl 1016.68064
Class. Math.: 68P05, 68W40, 94A15
Mots clés: average-case analysis of data-structures, information theory, trie, Mellin analysis

URL stable: http://www.numdam.org/item?id=ITA_2001__35_2_163_0

Résumé

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.

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