Article

Computing the maximal-exponent repeats of an overlap-free string in linear time

Authors:

Golnaz Badkobeh,

Maxime Crochemore,

Chalita ToopsuwanAuthors Info & Claims

SPIRE'12: Proceedings of the 19th international conference on String Processing and Information Retrieval

Pages 61 - 72

https://doi.org/10.1007/978-3-642-34109-0_8

Published: 21 October 2012 Publication History

Abstract

The exponent of a string is the quotient of the string's length over the string's smallest period. The exponent and the period of a string can be computed in time proportional to the string's length. We design an algorithm to compute the maximal exponent of factors of an overlap-free string. Our algorithm runs in linear-time on a fixed-size alphabet, while a naive solution of the question would run in cubic time. The solution for non overlap-free strings derives from algorithms to compute all maximal repetitions, also called runs, occurring in the string. We show there is a linear number of maximal-exponent repeats in an overlap-free string. The algorithm can locate all of them in linear time.

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Cited By

Badkobeh GCrochemore MMercaş R(2017)Counting maximal-exponent factors in wordsTheoretical Computer Science10.1016/j.tcs.2016.02.035658:PA(27-35)Online publication date: 7-Jan-2017
https://dl.acm.org/doi/10.1016/j.tcs.2016.02.035
Kärkkäinen JKempa DPuglisi S(2016)Lazy Lempel-Ziv Factorization AlgorithmsACM Journal of Experimental Algorithmics10.1145/269987621(1-19)Online publication date: 21-Oct-2016
https://dl.acm.org/doi/10.1145/2699876
Belazzougui DKärkkäinen JKempa DPuglisi S(2016)Lempel-Ziv Decoding in External MemoryProceedings of the 15th International Symposium on Experimental Algorithms - Volume 968510.1007/978-3-319-38851-9_5(63-74)Online publication date: 5-Jun-2016
https://dl.acm.org/doi/10.1007/978-3-319-38851-9_5
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Published In

cover image Guide Proceedings

SPIRE'12: Proceedings of the 19th international conference on String Processing and Information Retrieval

October 2012

410 pages

ISBN:9783642341083

Editors:
Liliana Calderón-Benavides
Information Technologies Research Group, Universidad Autónoma de Bucaramanga, Bucaramanga, Colombia
,
Cristina González-Caro
Information Technologies and Research Group, Universidad Autónoma de Bucaramanga, Bucaramanga, Colombia
,
Edgar Chávez
School of Physics and Mathematics, Universidad Michoacana, Edificio B, Ciudad Universitaria,, Morelia, Mexico
,
Nivio Ziviani
Department of Computer Science, Universidade Federal de Minas Gerais, Av. Antonio Carlos 6627, Pampulha, Belo Horizonte, Brazil

Sponsors

Electro Software: Electro Software
Yahoo! Research
Google Inc.
Information Technology Research Group: Information Technology Research Group
Universidad Autónoma de Bucaramanga: Universidad Autónoma de Bucaramanga

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 21 October 2012

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Cited By

Badkobeh GCrochemore MMercaş R(2017)Counting maximal-exponent factors in wordsTheoretical Computer Science10.1016/j.tcs.2016.02.035658:PA(27-35)Online publication date: 7-Jan-2017
https://dl.acm.org/doi/10.1016/j.tcs.2016.02.035
Kärkkäinen JKempa DPuglisi S(2016)Lazy Lempel-Ziv Factorization AlgorithmsACM Journal of Experimental Algorithmics10.1145/269987621(1-19)Online publication date: 21-Oct-2016
https://dl.acm.org/doi/10.1145/2699876
Belazzougui DKärkkäinen JKempa DPuglisi S(2016)Lempel-Ziv Decoding in External MemoryProceedings of the 15th International Symposium on Experimental Algorithms - Volume 968510.1007/978-3-319-38851-9_5(63-74)Online publication date: 5-Jun-2016
https://dl.acm.org/doi/10.1007/978-3-319-38851-9_5
Tanimura YFujishige YI TInenaga SBannai HTakeda M(2015)A Faster Algorithm for Computing Maximal $$\alpha $$-gapped Repeats in a StringProceedings of the 22nd International Symposium on String Processing and Information Retrieval - Volume 930910.1007/978-3-319-23826-5_13(124-136)Online publication date: 1-Sep-2015
https://dl.acm.org/doi/10.1007/978-3-319-23826-5_13

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