Period recovery of strings over the Hamming and edit distances

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

doi:10.1016/j.tcs.2017.10.026

Period recovery of strings over the Hamming and edit distances

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

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

A string T of length m is periodic in P of length p if P is a substring of T and T[i]=T[i+p] for all 0≤i≤m−p−1 and m≥2p. The shortest such prefix, P, is called the period of T (i.e., P=T[0..p−1]). 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 a string T 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(nlog⁡n)-time algorithm, where τ is given as ⌊[Formula presented]⌋ for ϵ>0. For the edit distance case, τ=⌊[Formula presented]⌋ and ϵ>0, we provide an O(n^4/3)-time algorithm.

Original language	English
Pages (from-to)	2-18
Number of pages	17
Journal	Theoretical Computer Science
Volume	710
DOIs	https://doi.org/10.1016/j.tcs.2017.10.026
State	Published - 1 Feb 2018

Bibliographical note

Publisher Copyright:
© 2017 Elsevier B.V.

Funding

We thank the anonymous referees for their comments and suggestions. Amihood Amir was partially supported by the Israel Science Foundation grant 571/14 , and grant No. 2014028 from the United States-Israel Binational Science Foundation (BSF). Mika Amit and Gad M. Landau were partially supported by the Israel Science Foundation grant 571/14 , grant No. 2014028 from the United States-Israel Binational Science Foundation (BSF) and DFG . Dina Sokol was partially supported by the United States-Israel Binational Science Foundation (BSF) grant No. 2014028 .

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

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10.1016/j.tcs.2017.10.026

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title = "Period recovery of strings over the Hamming and edit distances",

abstract = "A string T of length m is periodic in P of length p if P is a substring of T and T[i]=T[i+p] for all 0≤i≤m−p−1 and m≥2p. The shortest such prefix, P, is called the period of T (i.e., P=T[0..p−1]). 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 a string T 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(nlog⁡n)-time algorithm, where τ is given as ⌊[Formula presented]⌋ for ϵ>0. For the edit distance case, τ=⌊[Formula presented]⌋ and ϵ>0, we provide an O(n4/3)-time algorithm.",

keywords = "Approximate periodicity, Edit distance, Hamming distance, Period recovery",

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AU - Amir, Amihood

AU - Amit, Mika

AU - Landau, Gad M.

AU - Sokol, Dina

PY - 2018/2/1

Y1 - 2018/2/1

N2 - A string T of length m is periodic in P of length p if P is a substring of T and T[i]=T[i+p] for all 0≤i≤m−p−1 and m≥2p. The shortest such prefix, P, is called the period of T (i.e., P=T[0..p−1]). 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 a string T 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(nlog⁡n)-time algorithm, where τ is given as ⌊[Formula presented]⌋ for ϵ>0. For the edit distance case, τ=⌊[Formula presented]⌋ and ϵ>0, we provide an O(n4/3)-time algorithm.

AB - A string T of length m is periodic in P of length p if P is a substring of T and T[i]=T[i+p] for all 0≤i≤m−p−1 and m≥2p. The shortest such prefix, P, is called the period of T (i.e., P=T[0..p−1]). 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 a string T 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(nlog⁡n)-time algorithm, where τ is given as ⌊[Formula presented]⌋ for ϵ>0. For the edit distance case, τ=⌊[Formula presented]⌋ and ϵ>0, we provide an O(n4/3)-time algorithm.

KW - Approximate periodicity

KW - Edit distance

KW - Hamming distance

KW - Period recovery

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Period recovery of strings over the Hamming and edit distances

Abstract

Bibliographical note

Funding

Keywords

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