Computing the Minimum k-Cover of a String

We study the minimum k-cover problem. For a given string x of length n and an integer k, the minimum k-cover is the minimum set of k-substrings that covers x. We show that the on-line algorithm that has been proposed by Iliopoulos and Smyth [IS92] is not correct. We prove that the problem is in fact NP-hard. Furthermore, we propose two greedy algorithms that are implemented and tested on different kind of data.