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arXiv · 1208.3313

A Note on Efficient Computation of All Abelian Periods in a String

Maxime Crochemore·Costas Iliopoulos·Tomasz Kociumaka·Marcin Kubica·Jakub Pachocki·Jakub Radoszewski·Wojciech Rytter·Wojciech Tyczyński·Tomasz Waleń
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Abstract

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.

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Maxime Crochemore, Costas Iliopoulos, Tomasz Kociumaka, Marcin Kubica, Jakub Pachocki, Jakub Radoszewski, Wojciech Rytter, Wojciech Tyczyński, Tomasz Waleń. 2012-08-16. A Note on Efficient Computation of All Abelian Periods in a String. https://arxiv.org/abs/1208.3313

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