LIPIcs.STACS.2013.245.pdf
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Fast Algorithms for Abelian Periods in Words and Greatest Common Divisor Queries
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30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Theoretical Aspects of Computer Science (STACS) - License:
Creative Commons Attribution-NoDerivs 3.0 Unported license
- Publication Date: 2013-02-26
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Tomasz Kociumaka, Jakub Radoszewski, and Wojciech Rytter. Fast Algorithms for Abelian Periods in Words and Greatest Common Divisor Queries. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 245-256, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
https://doi.org/10.4230/LIPIcs.STACS.2013.245
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.
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Keywords
- Abelian period
- greatest common divisor
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