A Generalized Suffix Tree and its (Un)expected Asymptotic Behaviors

Suux trees nd several applications in computer science and telecommunications, most notably in algorithms on strings, data compressions and codes. Despite this, very little is known about their typical behaviors. In a probabilistic framework, we consider a family of suux trees { further called b-suux trees { built from the rst n suuxes of a random word. In this family a noncompact suux tree (i.e., such that every edge is labeled by a single symbol) is represented by b = 1, and a compact suux tree (i.e., without unary nodes) is asymptotically equivalent to b ! 1 as n ! 1. We study several parameters of b-suux trees, namely: the depth of a given suux, the depth of insertion, the height and the shortest feasible path. Some new results concerning typical (i.e., almost sure) behaviors of these parameters are established. These ndings are used to obtain several insights into certain algorithms on words, molecular biology and universal data compression schemes.