# A Note on Easy and Efficient Computation of Full Abelian Periods of a Word

2 TIBS - LITIS - Equipe Traitement de l'information en Biologie Santé
LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes
Abstract : Constantinescu and Ilie (Bulletin of the EATCS 89, 167-170, 2006) introduced the idea of an Abelian period with head and tail of a finite word. An Abelian period is called full if both the head and the tail are empty. We present a simple and easy-to-implement $O(n\log\log n)$-time algorithm for computing all the full Abelian periods of a word of length $n$ over a constant-size alphabet. Experiments show that our algorithm significantly outperforms the $O(n)$ algorithm proposed by Kociumaka et al. (Proc. of STACS, 245-256, 2013) for the same problem.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-01956126
Contributor : Thierry Lecroq Connect in order to contact the contributor
Submitted on : Friday, December 14, 2018 - 9:09:20 PM
Last modification on : Thursday, September 1, 2022 - 11:13:28 AM

### Identifiers

• HAL Id : hal-01956126, version 1
• ARXIV : 1510.00634

### Citation

Gabriele Fici, Thierry Lecroq, Arnaud Lefebvre, Elise Prieur-Gaston, William F. Smyth. A Note on Easy and Efficient Computation of Full Abelian Periods of a Word. 2018. ⟨hal-01956126⟩

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