What can we learn about suffix trees from independent tries?

Abstract

A suffix tree of a word is a digital tree that is built from suffixes of the underlying word. We consider words that are random sequences built from independent symbols over a finite alphabet. Our main finding shows that the depths in a suffix tree are asymptotically equivalent to the depths in a digital tree that stores independent keys (i.e., independent digital trees known also as tries). More precisely, we prove that the depths in a suffix tree build from the first n suffixes of a random word are normally distributed with the mean asymptotically equivalent to 1/h1 log n and the variance α·log n, where h1 is the entropy of the alphabet, and α is a parameter of the probabilistic model. Our results provide new insights into asymptotic properties of compression schemes, and therefore find direct applications in computer sciences and telecommunications, most notably in coding theory, theory of languages, and design and analysis of algorithms.