On approximate enhanced covers under Hamming distance

Abstract

A border p of a string x is an enhanced cover of x if the number of positions of x that lie within some occurrence of p is the maximum among all borders of x. (String p is a border of x if p is both a proper prefix and a suffix of x.) In this paper, two more general notions based on enhanced covers are introduced: a k-approximate enhanced cover and a relaxed k-approximate enhanced cover, where a fixed maximum number of errors k under the Hamming distance is considered. The k-approximate enhanced cover of x is its border, and its k-approximate occurrences are also considered in the covered number of positions of x. The relaxed k-approximate enhanced cover of x is a factor of x and a k-approximate border of x. Algorithms that compute all the variations of k-approximate enhanced covers mentioned above are presented in this paper.