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

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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Contributor : Maxime Crochemore <>
Submitted on : Wednesday, June 26, 2013 - 7:28:03 PM
Last modification on : Friday, April 20, 2018 - 8:38:45 AM

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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, Elsevier, 2013, 113 (3), pp.74-77. ⟨10.1016/j.ipl.2012.11.001⟩. ⟨hal-00837005⟩

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