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.
|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|
|State||Published - 1 Aug 2018|
|Event||26th European Symposium on Algorithms, ESA 2018 - Helsinki, Finland|
Duration: 20 Aug 2018 → 22 Aug 2018
|Name||Leibniz International Proceedings in Informatics, LIPIcs|
|Conference||26th European Symposium on Algorithms, ESA 2018|
|Period||20/08/18 → 22/08/18|
Bibliographical noteFunding 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
© Amihood Amir, Gad M. Landau, Shoshana Marcus, and Dina Sokol.
- Pattern matching algorithms
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