Finding the Cyclic Covers of a String.

We introduce the concept of cyclic covers, which generalizes the classical notion of covers in strings. Given any nonempty string X of length n , a factor W of X is called a cyclic cover if every position of X belongs to an occurrence of a cyclic shift of W . Two cyclic covers are distinct if one is not a cyclic shift of the other. The cyclic cover problem requires finding all distinct cyclic covers of X . We present an algorithm that solves the cyclic cover problem in time. This is based on finding a well-structured set of standard occurrences of a constant number of factors of a cyclic cover candidate W , computing the regions of X covered by cyclic shifts of W , extending those factors, and taking the union of the results.