Two-dimensional maximal repetitions

Amihood Amir; Gad M. Landau; Shoshana Marcus; Dina Sokol

doi:10.1016/j.tcs.2019.07.006

Two-dimensional maximal repetitions

Amihood Amir, Gad M. Landau, Shoshana Marcus, Dina Sokol

Department of Computer Science

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

Abstract

Maximal repetitions or runs in strings have a wide array of applications and thus have been extensively studied. In this paper, we extend this notion to 2-dimensions, precisely defining a maximal 2D repetition. We provide initial bounds on the number of maximal 2D repetitions that can occur in an n×n array. The main contribution of this paper is the presentation of the first algorithm for locating all maximal 2D repetitions. The algorithm is efficient and straightforward, with runtime O(n²log⁡n+ρ), where n² is the size of the input array and ρ is the number of maximal 2D repetitions in the output.

Original language	English
Pages (from-to)	49-61
Number of pages	13
Journal	Theoretical Computer Science
Volume	812
DOIs	https://doi.org/10.1016/j.tcs.2019.07.006
State	Published - 6 Apr 2020

Bibliographical note

Funding Information:
The authors would like to thank the anonymous referee for his suggestions that have improved this manuscript. The first and second authors are partially supported by the Israel Science Foundation grant 571/14. The first, second, and fourth authors are partially supported by Grant No. 2014028 from the United States-Israel Binational Science Foundation (BSF).

Funding Information:
The first and second authors are partially supported by the Israel Science Foundation grant 571/14 . The first, second, and fourth authors are partially supported by Grant No. 2014028 from the United States-Israel Binational Science Foundation (BSF).

Publisher Copyright:
© 2019 Elsevier B.V.

Keywords

Pattern matching algorithms
Periodicity
Repetitions
Two-dimensional

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science (all)

Access to Document

10.1016/j.tcs.2019.07.006

Cite this

@article{ec46ea67541e4c2ab590dd6bd8cd5e77,

title = "Two-dimensional maximal repetitions",

abstract = "Maximal repetitions or runs in strings have a wide array of applications and thus have been extensively studied. In this paper, we extend this notion to 2-dimensions, precisely defining a maximal 2D repetition. We provide initial bounds on the number of maximal 2D repetitions that can occur in an n×n array. The main contribution of this paper is the presentation of the first algorithm for locating all maximal 2D repetitions. The algorithm is efficient and straightforward, with runtime O(n2log⁡n+ρ), where n2 is the size of the input array and ρ is the number of maximal 2D repetitions in the output.",

keywords = "Pattern matching algorithms, Periodicity, Repetitions, Two-dimensional",

author = "Amihood Amir and Landau, {Gad M.} and Shoshana Marcus and Dina Sokol",

note = "Funding Information: The authors would like to thank the anonymous referee for his suggestions that have improved this manuscript. The first and second authors are partially supported by the Israel Science Foundation grant 571/14. The first, second, and fourth authors are partially supported by Grant No. 2014028 from the United States-Israel Binational Science Foundation (BSF). Funding Information: The first and second authors are partially supported by the Israel Science Foundation grant 571/14 . The first, second, and fourth authors are partially supported by Grant No. 2014028 from the United States-Israel Binational Science Foundation (BSF). Publisher Copyright: {\textcopyright} 2019 Elsevier B.V.",

year = "2020",

month = apr,

day = "6",

doi = "10.1016/j.tcs.2019.07.006",

language = "English",

volume = "812",

pages = "49--61",

journal = "Theoretical Computer Science",

issn = "0304-3975",

publisher = "Elsevier",

}

TY - JOUR

T1 - Two-dimensional maximal repetitions

AU - Amir, Amihood

AU - Landau, Gad M.

AU - Marcus, Shoshana

AU - Sokol, Dina

N1 - Funding Information: The authors would like to thank the anonymous referee for his suggestions that have improved this manuscript. The first and second authors are partially supported by the Israel Science Foundation grant 571/14. The first, second, and fourth authors are partially supported by Grant No. 2014028 from the United States-Israel Binational Science Foundation (BSF). Funding Information: The first and second authors are partially supported by the Israel Science Foundation grant 571/14 . The first, second, and fourth authors are partially supported by Grant No. 2014028 from the United States-Israel Binational Science Foundation (BSF). Publisher Copyright: © 2019 Elsevier B.V.

PY - 2020/4/6

Y1 - 2020/4/6

N2 - Maximal repetitions or runs in strings have a wide array of applications and thus have been extensively studied. In this paper, we extend this notion to 2-dimensions, precisely defining a maximal 2D repetition. We provide initial bounds on the number of maximal 2D repetitions that can occur in an n×n array. The main contribution of this paper is the presentation of the first algorithm for locating all maximal 2D repetitions. The algorithm is efficient and straightforward, with runtime O(n2log⁡n+ρ), where n2 is the size of the input array and ρ is the number of maximal 2D repetitions in the output.

AB - Maximal repetitions or runs in strings have a wide array of applications and thus have been extensively studied. In this paper, we extend this notion to 2-dimensions, precisely defining a maximal 2D repetition. We provide initial bounds on the number of maximal 2D repetitions that can occur in an n×n array. The main contribution of this paper is the presentation of the first algorithm for locating all maximal 2D repetitions. The algorithm is efficient and straightforward, with runtime O(n2log⁡n+ρ), where n2 is the size of the input array and ρ is the number of maximal 2D repetitions in the output.

KW - Pattern matching algorithms

KW - Periodicity

KW - Repetitions

KW - Two-dimensional

UR - http://www.scopus.com/inward/record.url?scp=85068867728&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2019.07.006

DO - 10.1016/j.tcs.2019.07.006

M3 - Article

AN - SCOPUS:85068867728

SN - 0304-3975

VL - 812

SP - 49

EP - 61

JO - Theoretical Computer Science

JF - Theoretical Computer Science

ER -

Two-dimensional maximal repetitions

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this