Two-dimensional maximal repetitions

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

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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 languageEnglish
Title of host publication26th European Symposium on Algorithms, ESA 2018
EditorsHannah Bast, Grzegorz Herman, Yossi Azar
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages2:1–2:14
ISBN (Print)9783959770811
DOIs
StatePublished - 1 Aug 2018
Event26th European Symposium on Algorithms, ESA 2018 - Helsinki, Finland
Duration: 20 Aug 201822 Aug 2018

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume112
ISSN (Print)1868-8969

Conference

Conference26th European Symposium on Algorithms, ESA 2018
Country/TerritoryFinland
CityHelsinki
Period20/08/1822/08/18

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

Cite this