A note on efficient computation of all Abelian periods in a string

Maxime Crochemore (1, 2) , Costas S. Iliopoulos (2) , Tomasz Kociumaka (3) , Marcin Kubica (3) , Jakub Pachocki (3) , Jakub Radoszewski (3) , Wojciech Rytter (3) , Wojciech Tyczynski (3) , Tomasz Walen (3)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 Informatics
3 Institute of Informatics [Warsaw]

We derive a simple efficient algorithm for Abelian periods knowing all Abelian squares in a string. An efficient algorithm for the latter problem was given by Cummings and Smyth in 1997. By the way we show an alternative algorithm for Abelian squares. We also obtain a linear time algorithm finding all "long" Abelian periods. The aim of the paper is a (new) reduction of the problem of all Abelian periods to that of (already solved) all Abelian squares which provides new insight into both connected problems.

Mots clés: Algorithms; Abelian period; Abelian square

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

Maxime Crochemore, Costas S. Iliopoulos, Tomasz Kociumaka, Marcin Kubica, Jakub Pachocki, et al.. A note on efficient computation of all Abelian periods in a string. Information Processing Letters, 2013, 113 (3), pp.74-77. ⟨10.1016/j.ipl.2012.11.001⟩. ⟨hal-00837005⟩