Online Detection of Repetitions with Backtracking

In this paper we present two algorithms for the following problem: given a string and a rational e > 1, detect in the online fashion the earliest occurrence of a repetition of exponent ≥ e in the string. 1. The first algorithm works in O(n log σ) time and linear space, where n is the length of the input string and σ is the number of distinct letters. This algorithm is relatively simple and requires much less memory than the previously known solution with the same working time and space. 2. The second algorithm supports the backtrack operation removing the last letter of the input string. This algorithm runs in O(n logm) time and O(m) space, where m is the maximal length of a string generated during the execution of a given sequence of n read and backtrack operations.