License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.ESA.2018.2
URN: urn:nbn:de:0030-drops-94652
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Amir, Amihood ; Landau, Gad M. ; Marcus, Shoshana ; Sokol, Dina

Two-Dimensional Maximal Repetitions

LIPIcs-ESA-2018-2.pdf (0.5 MB)


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

  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 =		{},
  URN =		{urn:nbn:de:0030-drops-94652},
  doi =		{10.4230/LIPIcs.ESA.2018.2},
  annote =	{Keywords: pattern matching algorithms, repetitions, periodicity, two-dimensional}

Keywords: pattern matching algorithms, repetitions, periodicity, two-dimensional
Collection: 26th Annual European Symposium on Algorithms (ESA 2018)
Issue Date: 2018
Date of publication: 14.08.2018

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