Approximate periodicity

Amihood Amir, Estrella Eisenberg, Avivit Levy

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

19 Scopus citations


We consider the question of finding an approximate period in a given string S of length n. Let S′ be a periodic string closest to S under some distance metric. We consider this distance the error of the periodic string, and seek the smallest period that generates a string with this distance to S. In this paper we consider the Hamming and swap distance metrics. In particular, if S is the given string, and S′ is the closest periodic string to S under the Hamming distance, and if that distance is k, we develop an O(nkloglogn) algorithm that constructs the smallest period that defines such a periodic string S′. We call that string the approximate period of S under the Hamming distance. We further develop an O(n 2) algorithm that constructs the approximate period under the swap distance. Finally, we show an O(nlogn) algorithm for finite alphabets, and O(nlog3 n) algorithm for infinite alphabets, that approximates the number of mismatches in the approximate period of the string.

Original languageEnglish
Title of host publicationAlgorithms and Computation - 21st International Symposium, ISAAC 2010, Proceedings
Number of pages12
EditionPART 1
StatePublished - 2010
Event21st Annual International Symposium on Algorithms and Computations, ISAAC 2010 - Jeju Island, Korea, Republic of
Duration: 15 Dec 201017 Dec 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume6506 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference21st Annual International Symposium on Algorithms and Computations, ISAAC 2010
Country/TerritoryKorea, Republic of
CityJeju Island


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