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Approximate periodicity in strings

Smyth, W.F. (1997) Approximate periodicity in strings. Utilitas Mathematica, 51 . pp. 125-135.

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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.

Publication Type: Journal Article
Publisher: Utilitas Mathematica Publishing Inc
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