Computing the Maximal-Exponent Repeats of an Overlap-Free String in Linear Time

Abstract

The exponent of a string is the quotient of the string's length over the string's smallest period. The exponent and the period of a string can be computed in time proportional to the string's length. We design an algorithm to compute the maximal exponent of factors of an overlap-free string. Our algorithm runs in linear-time on a fixed-size alphabet, while a naive solution of the question would run in cubic time. The solution for non overlap-free strings derives from algorithms to compute all maximal repetitions, also called runs, occurring in the string. We show there is a linear number of maximal-exponent repeats in an overlap-free string. The algorithm can locate all of them in linear time.