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May, 1992 A Study of Trie-Like Structures Under the Density Model
Luc Devroye
Ann. Appl. Probab. 2(2): 402-434 (May, 1992). DOI: 10.1214/aoap/1177005709


We consider random tries constructed from sequences of i.i.d. random variables with a common density $f$ on $\lbrack 0, 1 \rbrack$ (i.e., paths down the tree are carved out by the bits in the binary expansions of the random variables). The depth of insertion of a node and the height of a node are studied with respect to their limit laws and their weak and strong convergence properties. In addition, laws of the iterated logarithm are obtained for the height of a random trie when $\int f^2 < \infty$. Finally, we study two popular improvements of the trie, the $\mathrm{PATRICIA}$ tree and the digital search tree, and show to what extent they improve over the trie.


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Luc Devroye. "A Study of Trie-Like Structures Under the Density Model." Ann. Appl. Probab. 2 (2) 402 - 434, May, 1992.


Published: May, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0758.68051
MathSciNet: MR1161060
Digital Object Identifier: 10.1214/aoap/1177005709

Primary: 60D05
Secondary: 68U05

Keywords: digital search tree , height of a tree , probabilistic analysis , strong convergence , Trie

Rights: Copyright © 1992 Institute of Mathematical Statistics


Vol.2 • No. 2 • May, 1992
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