## The Annals of Applied Probability

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

Luc Devroye

#### 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

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