Understanding maximal repetitions in strings

Maxime Crochemore (1, 2) , Lucian Ilie (3)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 DCS - Department of Computer Science
3 Department of Computer Science

The cornerstone of any algorithm computing all repetitions in a string of length n in O(n) time is the fact that the number of runs (or maximal repetitions) is O(n). We give a simple proof of this result. As a consequence of our approach, the stronger result concerning the linearity of the sum of exponents of all runs follows easily.

Mots clés: combinatorics on words; repetitions in strings; runs; maximal repetitions; maximal periodicities; sum of exponents

Domaines: Algorithme et structure de données [cs.DS]; Combinatoire [math.CO]

Maxime Crochemore, Lucian Ilie. Understanding maximal repetitions in strings. STACS 2008, Feb 2008, Bordeaux, France. pp.11-16. ⟨hal-00208087⟩