## The Annals of Applied Probability

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

### A Study of Trie-Like Structures Under the Density Model

#### Abstract

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

**Source**

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

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoap/1177005709

**Digital Object Identifier**

doi:10.1214/aoap/1177005709

**Mathematical Reviews number (MathSciNet)**

MR1161060

**Zentralblatt MATH identifier**

0758.68051

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]

Secondary: 68U05: Computer graphics; computational geometry [See also 65D18]

**Keywords**

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

#### Citation

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. https://projecteuclid.org/euclid.aoap/1177005709