Probabilistic analysis of generalized suffix trees

Abstract

Suffix trees find several applications in computer science and telecommunications, most notably in algorithms on strings, data compressions and codes. We consider in a probabilistic framework a family of generalized suffix trees — called b-suffix trees — built from the first n suffixes of a random word. In this family of trees, a noncompact suffix trees (i.e., such that every edge is labeled by a single symbol) is represented by b= 1, and a compact suffix tree (i.e., without unary nodes) is asymptotically equivalent to b → ∞. Several parameters of b-suffix trees are of interest, namely the typical depth, the depth of insertion, the height, the external path length, and so forth. We establish some results concerning typical, that is, almost sure (a.s.), behavior of these parameters. These findings are used to obtain several insights into certain algorithms on words and universal data compression schemes.