On the stack-size of general tries
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 35 (2001) no. 2, pp. 163-185.

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.

Classification: 68P05,  68W40,  94A15
Keywords: average-case analysis of data-structures, information theory, trie, Mellin analysis
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     title = {On the stack-size of general tries},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {163--185},
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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, Volume 35 (2001) no. 2, pp. 163-185. http://www.numdam.org/item/ITA_2001__35_2_163_0/

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