Approximate periodicity in strings

Abstract

In many application areas (for instance, DNA sequence analysis), it becomes important to compute various kinds of "approximate period" of a given string y. Here we discuss three such approximate periods and the algorithms which compute them: an Abelian generator, a cover, and a seed. Let u be a substring of y. Then u is an Abelian generator of y iff y is a concatenation of substrings which are permutations of u; u is a cover of y iff every letter of y is contained in an occurrence of u in y; and u is a seed of y iff y is a substring of a string y′ with cover u. Observe that, according to these definitions, y is an Abelian generator, a cover, and a seed of itself.