Two-dimensional maximal repetitions

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

doi:10.4230/LIPIcs.ESA.2018.2

Two-dimensional maximal repetitions

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

Department of Computer Science

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

2 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 a matrix. The main contribution of this paper is the presentation of the first algorithm for locating all maximal 2D repetitions in a matrix. The algorithm is efficient and straightforward, with runtime O(n² log n log log n + ρ log n), where n² is the size of the input, and ρ is the number of 2D repetitions in the output.

Original language	English
Title of host publication	26th European Symposium on Algorithms, ESA 2018
Editors	Hannah Bast, Grzegorz Herman, Yossi Azar
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Print)	9783959770811
DOIs	https://doi.org/10.4230/LIPIcs.ESA.2018.2
State	Published - 1 Aug 2018
Event	26th European Symposium on Algorithms, ESA 2018 - Helsinki, Finland Duration: 20 Aug 2018 → 22 Aug 2018

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	112
ISSN (Print)	1868-8969

Conference

Conference	26th European Symposium on Algorithms, ESA 2018
Country/Territory	Finland
City	Helsinki
Period	20/08/18 → 22/08/18

Bibliographical note

Publisher Copyright:
© Amihood Amir, Gad M. Landau, Shoshana Marcus, and Dina Sokol.

Funding

Partially supported by the Israel Science Foundation grant 571/14 and Grant No. 2014028 from the United States-Israel Binational Science Foundation (BSF). 2 Partially supported by the Israel Science Foundation grant 571/14 and Grant No. 2014028 from the United States-Israel Binational Science Foundation (BSF). 3 Partially supported by Grant No. 2014028 from the United States-Israel Binational Science Foundation

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

Keywords

Pattern matching algorithms
Periodicity
Repetitions
Two-dimensional

Access to Document

10.4230/LIPIcs.ESA.2018.2

Cite this

Amir, A., Landau, G. M., Marcus, S., & Sokol, D. (2018). Two-dimensional maximal repetitions. In H. Bast, G. Herman, & Y. Azar (Eds.), 26th European Symposium on Algorithms, ESA 2018 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 112). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ESA.2018.2

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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 a matrix. The main contribution of this paper is the presentation of the first algorithm for locating all maximal 2D repetitions in a matrix. The algorithm is efficient and straightforward, with runtime O(n2 log n log log n + ρ log n), where n2 is the size of the input, and ρ is the number of 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",

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Amir, A, Landau, GM, Marcus, S & Sokol, D 2018, Two-dimensional maximal repetitions. in H Bast, G Herman & Y Azar (eds), 26th European Symposium on Algorithms, ESA 2018. Leibniz International Proceedings in Informatics, LIPIcs, vol. 112, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 26th European Symposium on Algorithms, ESA 2018, Helsinki, Finland, 20/08/18. https://doi.org/10.4230/LIPIcs.ESA.2018.2

Two-dimensional maximal repetitions. / Amir, Amihood; Landau, Gad M.; Marcus, Shoshana et al.
26th European Symposium on Algorithms, ESA 2018. ed. / Hannah Bast; Grzegorz Herman; Yossi Azar. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2018. (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 112).

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

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Two-dimensional maximal repetitions

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Keywords

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