Two-dimensional maximal repetitions

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

Research output: Contribution to journalArticlepeer-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 an n×n array. The main contribution of this paper is the presentation of the first algorithm for locating all maximal 2D repetitions. The algorithm is efficient and straightforward, with runtime O(n2log⁡n+ρ), where n2 is the size of the input array and ρ is the number of maximal 2D repetitions in the output.

Original languageEnglish
Pages (from-to)49-61
Number of pages13
JournalTheoretical Computer Science
Volume812
DOIs
StatePublished - 6 Apr 2020

Bibliographical note

Funding Information:
The authors would like to thank the anonymous referee for his suggestions that have improved this manuscript. The first and second authors are partially supported by the Israel Science Foundation grant 571/14. The first, second, and fourth authors are partially supported by Grant No. 2014028 from the United States-Israel Binational Science Foundation (BSF).

Funding Information:
The first and second authors are partially supported by the Israel Science Foundation grant 571/14 . The first, second, and fourth authors are partially supported by Grant No. 2014028 from the United States-Israel Binational Science Foundation (BSF).

Publisher Copyright:
© 2019 Elsevier B.V.

Keywords

  • Pattern matching algorithms
  • Periodicity
  • Repetitions
  • Two-dimensional

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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