License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2018.2
URN: urn:nbn:de:0030-drops-94652
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9465/
Amir, Amihood ;
Landau, Gad M. ;
Marcus, Shoshana ;
Sokol, Dina
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 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(n^2 log n log log n+ rho log n), where n^2 is the size of the input, and rho is the number of 2D repetitions in the output.
BibTeX - Entry
@InProceedings{amir_et_al:LIPIcs:2018:9465,
author = {Amihood Amir and Gad M. Landau and Shoshana Marcus and Dina Sokol},
title = {{Two-Dimensional Maximal Repetitions}},
booktitle = {26th Annual European Symposium on Algorithms (ESA 2018)},
pages = {2:1--2:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-081-1},
ISSN = {1868-8969},
year = {2018},
volume = {112},
editor = {Yossi Azar and Hannah Bast and Grzegorz Herman},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/9465},
URN = {urn:nbn:de:0030-drops-94652},
doi = {10.4230/LIPIcs.ESA.2018.2},
annote = {Keywords: pattern matching algorithms, repetitions, periodicity, two-dimensional}
}
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Keywords: |
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pattern matching algorithms, repetitions, periodicity, two-dimensional |
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Collection: |
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26th Annual European Symposium on Algorithms (ESA 2018) |
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Issue Date: |
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2018 |
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Date of publication: |
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14.08.2018 |
