Computing maximal-exponent factors in an overlap-free word

Golnaz Badkobeh (1) , Maxime Crochemore (2)

1 Informatics
2 inconnu temporaire UPEMLV

The exponent of a word is the quotient of its length over its smallest period. The exponent and the period of a word can be computed in time proportional to the word length. We design an algorithm to compute the maximal exponent of all factors of an overlap-free word. Our algorithm runs in linear-time on a fixed-size alphabet, while a naive solution of the question would run in cubic time. The solution for non overlap-free words derives from algorithms to compute all maximal repetitions, also called runs, occurring in the word. We also show there is a linear number of occurrences of maximal-exponent factors in an overlap-free word. Their maximal number lies between 0.66n and 2.25n in a word of length n. The algorithm can additionally locate all of them in linear time.

Mots clés: Word; string; repetition; power; repeat; periodicity; word; exponent; return word; algorithm; automaton

Domaines: Algorithme et structure de données [cs.DS]

Golnaz Badkobeh, Maxime Crochemore. Computing maximal-exponent factors in an overlap-free word . Journal of Computer and System Sciences, 2016. ⟨hal-01806284⟩