English

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

Data Structures and Algorithms 2015-03-20 v1 Discrete Mathematics

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.

Cite

@article{arxiv.1208.3313,
  title  = {A Note on Efficient Computation of All Abelian Periods in a String},
  author = {Maxime Crochemore and Costas Iliopoulos and Tomasz Kociumaka and Marcin Kubica and Jakub Pachocki and Jakub Radoszewski and Wojciech Rytter and Wojciech Tyczyński and Tomasz Waleń},
  journal= {arXiv preprint arXiv:1208.3313},
  year   = {2015}
}
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