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arXiv · 1510.00634

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

Gabriele Fici·Thierry Lecroq·Arnaud Lefebvre·Élise Prieur-Gaston·William F. Smyth
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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.

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Gabriele Fici, Thierry Lecroq, Arnaud Lefebvre, Élise Prieur-Gaston, William F. Smyth. 2015-10-02. A Note on Easy and Efficient Computation of Full Abelian Periods of a Word. https://doi.org/10.1016/j.dam.2015.09.024

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