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 |
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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 |
Pages | 2:1–2:14 |
ISBN (Print) | 9783959770811 |
DOIs | |
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 |
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Volume | 112 |
ISSN (Print) | 1868-8969 |
Conference
Conference | 26th European Symposium on Algorithms, ESA 2018 |
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Country/Territory | Finland |
City | Helsinki |
Period | 20/08/18 → 22/08/18 |
Bibliographical note
Funding Information: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
Publisher Copyright:
© Amihood Amir, Gad M. Landau, Shoshana Marcus, and Dina Sokol.
Keywords
- Pattern matching algorithms
- Periodicity
- Repetitions
- Two-dimensional
ASJC Scopus subject areas
- Software