Computing All Approximate Enhanced Covers with the 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. In this paper, more general notion based on the enhanced cover is introduced: a k-approximate enhanced cover, where fixed maximum number of errors k in 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. An O(n^2)-time and a O(n)-space algorithm that computes all k-approximate enhanced covers of a string of length n is presented.