Understanding Maximal Repetitions in Strings

Abstract

The cornerstone of any algorithm computing all repetitions in a string of length $n$ in {mathcal O(n) time is the fact that the number of runs (or maximal repetitions) is {mathcal O(n). We give a simple proof of this result. As a consequence of our approach, the stronger result concerning the linearity of the sum of exponents of all runs follows easily