The Annals of Applied Probability

A Study of Trie-Like Structures Under the Density Model

Luc Devroye

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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.

Article information

Ann. Appl. Probab., Volume 2, Number 2 (1992), 402-434.

First available in Project Euclid: 19 April 2007

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Zentralblatt MATH identifier


Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 68U05: Computer graphics; computational geometry [See also 65D18]

Trie digital search tree probabilistic analysis strong convergence height of a tree


Devroye, Luc. A Study of Trie-Like Structures Under the Density Model. Ann. Appl. Probab. 2 (1992), no. 2, 402--434. doi:10.1214/aoap/1177005709.

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