Fast optimal algorithms for computing all the repeats in a string

Abstract

Given a string x = x[1..n] on an alphabet of size a, and a threshold pmin = 1, we first describe a new algorithm PSY1 that, based on suffix array construction, computes all the complete nonextendible repeats in x of length p = pmin. PSY1 executes in Θ(n) time independent of alphabet size and is an order of magnitude faster than the two other algorithms previously proposed for this problem. Second, we describe a new fast algorithm PSY2 for computing all complete supernonextendible repeats in x that also executes in Θ(n) time independent of alphabet size, thus asymptotically faster than methods previously proposed. Both algorithms require 9n bytes of storage, including preprocessing (with a minor caveat for PSY1). We conclude with a brief discussion of applications to bioinformatics and data compression.