Optimality of some algorithms to detect quasiperiodicities

Richard Groult (1) , Gwenaël Richomme (1, 2, 3)

1 MIS - Modélisation, Information et Systèmes - UR UPJV 4290
2 ARITH - Arithmétique informatique
3 UPVM - Université Paul-Valéry - Montpellier 3

Improving a 1993 algorithm of Apostolico and Ehrenfeucht, independently Iliopoulos and Mouchard in 1999 and Brodal and Pedersen in 2000 provided O(nlog(n)) algorithms to determine all maximal quasiperiodicities of a word of length n. We show here the optimality of this bound providing an infinite family of words w containing O(|w|log|w|) maximal quasiperiodicities. We also show that this bound is not reached for the celebrated family of Fibonacci words.

Mots clés: Fibonacci words; quasiperiodicity; repetitions in words

Domaines: Mathématique discrète [cs.DM]

Richard Groult, Gwenaël Richomme. Optimality of some algorithms to detect quasiperiodicities. Theoretical Computer Science, 2010, 411 (34-36), pp.3110-3122. ⟨10.1016/j.tcs.2010.04.039⟩. ⟨hal-00599751⟩