License: Creative Commons Attribution-NoDerivs 3.0 Unported license (CC BY-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2013.245
URN: urn:nbn:de:0030-drops-39387
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2013/3938/
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Kociumaka, Tomasz ; Radoszewski, Jakub ; Rytter, Wojciech

Fast Algorithms for Abelian Periods in Words and Greatest Common Divisor Queries

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Abstract

We present efficient algorithms computing all Abelian periods of two types in a word. Regular Abelian periods are computed in O(n log log{n}) randomized time which improves over the best previously known algorithm by almost a factor of n. The other algorithm, for full Abelian periods, works in O(n) time. As a tool we develop an O(n) time construction of a data structure that allows O(1) time gcd(i,j) queries for all 1 <= i,j <= n, this is a result of independent interest.

BibTeX - Entry

@InProceedings{kociumaka_et_al:LIPIcs:2013:3938,
  author =	{Tomasz Kociumaka and Jakub Radoszewski and Wojciech Rytter},
  title =	{{Fast Algorithms for Abelian Periods in Words and Greatest Common Divisor Queries}},
  booktitle =	{30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
  pages =	{245--256},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-50-7},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{20},
  editor =	{Natacha Portier and Thomas Wilke},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2013/3938},
  URN =		{urn:nbn:de:0030-drops-39387},
  doi =		{10.4230/LIPIcs.STACS.2013.245},
  annote =	{Keywords: Abelian period, greatest common divisor}
}

Keywords: Abelian period, greatest common divisor
Collection: 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)
Issue Date: 2013
Date of publication: 26.02.2013

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