Optimality of some algorithms to detect quasiperiodicities
Improving a 1993 algorithm of Apostolic and Ehrenfeucht, independently Iliopoulos and Mouchard in 1999 and Brodal and Pedersen in 2000 provided O(n log(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(vertical bar w vertical bar log vertical bar w vertical bar) maximal quasiperiodicities. We also show that this bound is not reached for the celebrated family of Fibonacci words. (C) 2010 Elsevier B.V. All rights reserved.
quasiperiodicity fibonacci words repetitions in words