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

By Tomasz Kociumaka, Jakub Radoszewski and Wojciech Rytter


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

Topics: Abelian period, greatest common divisor, Data processing Computer science
Publisher: LIPIcs - Leibniz International Proceedings in Informatics. 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)
Year: 2013
DOI identifier: 10.4230/LIPIcs.STACS.2013.245
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