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

9 Scopus citations

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

Publisher Copyright:
© 2019 Elsevier B.V.

Funding

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). 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).

Funders	Funder number
Bonfils-Stanton Foundation
Bloom's Syndrome Foundation
United States-Israel Binational Science Foundation	2014028
Israel Science Foundation	571/14

Keywords

Pattern matching algorithms
Periodicity
Repetitions
Two-dimensional

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10.1016/j.tcs.2019.07.006

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AU - Sokol, Dina

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KW - Repetitions

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Two-dimensional maximal repetitions

Abstract

Bibliographical note

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Keywords

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