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

TL;DR

This paper introduces a simple, efficient $O(n\log\log n)$ algorithm for computing all full Abelian periods of a word, outperforming previous $O(n)$ solutions in practice.

Contribution

It presents a novel, easy-to-implement algorithm for full Abelian periods with improved theoretical and practical performance.

Findings

The new algorithm runs faster than previous methods in experiments.

It achieves $O(n\log\log n)$ time complexity for the problem.

Experimental results demonstrate significant performance improvements.

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.