Period recovery over the hamming and edit distances

Amihood Amir; Mika Amit; Gad M. Landau; Dina Sokol

doi:10.1007/978-3-662-49529-2_5

Period recovery over the hamming and edit distances

Amihood Amir, Mika Amit, Gad M. Landau, Dina Sokol

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Scopus citations

Abstract

A string S of length n has period P of length p if S[i] = S[i+p] for all 1 ≤ i ≤ n−p and n ≥ 2p. The shortest such substring, P, is called the period of S, and the string S is called periodic in P. In this paper we investigate the period recovery problem. Given a string S of length n, find the primitive period(s) P such that the distance between S and the string that is periodic in P is below a threshold τ. We consider the period recovery problem over both the Hamming distance and the edit distance. For the Hamming distance case, we present an O(n log n) time algorithm, where τ is given as (Formula Presented), for 0 < ε < 1. For the edit distance case, (Formula Presented), and we provide an O(n^4/3) time algorithm.

Original language	English
Title of host publication	LATIN 2016
Subtitle of host publication	Theoretical Informatics - 12th Latin American Symposium, Proceedings
Editors	Gonzalo Navarro, Evangelos Kranakis, Edgar Chávez
Publisher	Springer Verlag
Pages	55-67
Number of pages	13
ISBN (Print)	9783662495285
DOIs	https://doi.org/10.1007/978-3-662-49529-2_5
State	Published - 2016
Event	12th Latin American Symposium on Theoretical Informatics, LATIN 2016 - Ensenada, Mexico Duration: 11 Apr 2016 → 15 Apr 2016

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9644
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	12th Latin American Symposium on Theoretical Informatics, LATIN 2016
Country/Territory	Mexico
City	Ensenada
Period	11/04/16 → 15/04/16

Bibliographical note

Publisher Copyright:
© Springer International Publishing Switzerland 2016.

Funding

D. Sokol—Partially supported by the United States-Israel Binational Science Foundation (BSF) grant No. 2014028. M. Amit—Partially supported by the Israel Science Foundation grant 571/14, grant No. 2014028 from the United States-Israel Binational Science Foundation (BSF) and DFG. A. Amir—Partially supported by the Israel Science Foundation grant 571/14, and grant No. 2014028 from the United States-Israel Binational Science Foundation (BSF).

Funders	Funder number
Deutsche Forschungsgemeinschaft
United States-Israel Binational Science Foundation
Israel Science Foundation	571/14, 2014028

Keywords

Approximate periodicity
Edit distance
Hamming distance
Period recovery

Access to Document

10.1007/978-3-662-49529-2_5

Cite this

Amir, A., Amit, M., Landau, G. M., & Sokol, D. (2016). Period recovery over the hamming and edit distances. In G. Navarro, E. Kranakis, & E. Chávez (Eds.), LATIN 2016: Theoretical Informatics - 12th Latin American Symposium, Proceedings (pp. 55-67). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9644). Springer Verlag. https://doi.org/10.1007/978-3-662-49529-2_5

Amir, Amihood ; Amit, Mika ; Landau, Gad M. et al. / Period recovery over the hamming and edit distances. LATIN 2016: Theoretical Informatics - 12th Latin American Symposium, Proceedings. editor / Gonzalo Navarro ; Evangelos Kranakis ; Edgar Chávez. Springer Verlag, 2016. pp. 55-67 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "A string S of length n has period P of length p if S[i] = S[i+p] for all 1 ≤ i ≤ n−p and n ≥ 2p. The shortest such substring, P, is called the period of S, and the string S is called periodic in P. In this paper we investigate the period recovery problem. Given a string S of length n, find the primitive period(s) P such that the distance between S and the string that is periodic in P is below a threshold τ. We consider the period recovery problem over both the Hamming distance and the edit distance. For the Hamming distance case, we present an O(n log n) time algorithm, where τ is given as (Formula Presented), for 0 < ε < 1. For the edit distance case, (Formula Presented), and we provide an O(n4/3) time algorithm.",

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author = "Amihood Amir and Mika Amit and Landau, {Gad M.} and Dina Sokol",

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Amir, A, Amit, M, Landau, GM & Sokol, D 2016, Period recovery over the hamming and edit distances. in G Navarro, E Kranakis & E Chávez (eds), LATIN 2016: Theoretical Informatics - 12th Latin American Symposium, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9644, Springer Verlag, pp. 55-67, 12th Latin American Symposium on Theoretical Informatics, LATIN 2016, Ensenada, Mexico, 11/04/16. https://doi.org/10.1007/978-3-662-49529-2_5

Period recovery over the hamming and edit distances. / Amir, Amihood; Amit, Mika; Landau, Gad M. et al.
LATIN 2016: Theoretical Informatics - 12th Latin American Symposium, Proceedings. ed. / Gonzalo Navarro; Evangelos Kranakis; Edgar Chávez. Springer Verlag, 2016. p. 55-67 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9644).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N1 - Publisher Copyright: © Springer International Publishing Switzerland 2016.

PY - 2016

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N2 - A string S of length n has period P of length p if S[i] = S[i+p] for all 1 ≤ i ≤ n−p and n ≥ 2p. The shortest such substring, P, is called the period of S, and the string S is called periodic in P. In this paper we investigate the period recovery problem. Given a string S of length n, find the primitive period(s) P such that the distance between S and the string that is periodic in P is below a threshold τ. We consider the period recovery problem over both the Hamming distance and the edit distance. For the Hamming distance case, we present an O(n log n) time algorithm, where τ is given as (Formula Presented), for 0 < ε < 1. For the edit distance case, (Formula Presented), and we provide an O(n4/3) time algorithm.

AB - A string S of length n has period P of length p if S[i] = S[i+p] for all 1 ≤ i ≤ n−p and n ≥ 2p. The shortest such substring, P, is called the period of S, and the string S is called periodic in P. In this paper we investigate the period recovery problem. Given a string S of length n, find the primitive period(s) P such that the distance between S and the string that is periodic in P is below a threshold τ. We consider the period recovery problem over both the Hamming distance and the edit distance. For the Hamming distance case, we present an O(n log n) time algorithm, where τ is given as (Formula Presented), for 0 < ε < 1. For the edit distance case, (Formula Presented), and we provide an O(n4/3) time algorithm.

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Amir A, Amit M, Landau GM, Sokol D. Period recovery over the hamming and edit distances. In Navarro G, Kranakis E, Chávez E, editors, LATIN 2016: Theoretical Informatics - 12th Latin American Symposium, Proceedings. Springer Verlag. 2016. p. 55-67. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-662-49529-2_5

Period recovery over the hamming and edit distances

Abstract

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Keywords

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