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Lower Bounds for the Number of Repetitions in 2D Strings

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String Processing and Information Retrieval (SPIRE 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12944))

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Abstract

A 2D string is simply a 2D array. We continue the study of the combinatorial properties of repetitions in such strings over the binary alphabet, namely the number of distinct tandems, distinct quartics, and runs. First, we construct an infinite family of \(n\times n\) 2D strings with \(\varOmega (n^{3})\) distinct tandems. Second, we construct an infinite family of \(n\times n\) 2D strings with \(\varOmega (n^{2}\log n)\) distinct quartics. Third, we construct an infinite family of \(n\times n\) 2D strings with \(\varOmega (n^{2}\log n)\) runs. This resolves an open question of Charalampopoulos, Radoszewski, Rytter, Waleń, and Zuba [ESA 2020], who asked if the number of distinct quartics and runs in an \(n\times n\) 2D string is \(\mathcal {O}(n^{2})\).

P. Gawrychowski—Partially supported by the Bekker programme of the Polish National Agency for Academic Exchange (PPN/BEK/2020/1/00444).

S. Ghazawi and G. M. Landau—Partially supported by the Israel Science Foundation grant 1475/18, and Grant No. 2018141 from the United States-Israel Binational Science Foundation (BSF).

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Author information

Authors and Affiliations

  1. Institute of Computer Science, University of Wrocław, Wrocław, Poland

    Paweł Gawrychowski

  2. Department of Computer Science, University of Haifa, Haifa, Israel

    Samah Ghazawi & Gad M. Landau

  3. NYU Tandon School of Engineering, New York University, Brooklyn, NY, USA

    Gad M. Landau

Authors
  1. Paweł Gawrychowski
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  2. Samah Ghazawi
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  3. Gad M. Landau
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Editor information

Editors and Affiliations

  1. Université de Rouen Normandie, Mont-St-Aignan, France

    Thierry Lecroq

  2. CNRS, CRIStAL, Villeneuve d'Ascq, France

    Hélène Touzet

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Gawrychowski, P., Ghazawi, S., Landau, G.M. (2021). Lower Bounds for the Number of Repetitions in 2D Strings. In: Lecroq, T., Touzet, H. (eds) String Processing and Information Retrieval. SPIRE 2021. Lecture Notes in Computer Science(), vol 12944. Springer, Cham. https://doi.org/10.1007/978-3-030-86692-1_15

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  • DOI: https://doi.org/10.1007/978-3-030-86692-1_15

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