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Computing String Covers in Sublinear Time

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String Processing and Information Retrieval (SPIRE 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14899))

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Abstract

In the word RAM model, a string T of length n over an integer alphabet of size \(\sigma \) can be represented in \(\mathcal {O}(n /\log _\sigma n)\) space. We show that a representation of all covers of T can be computed in the optimal \(\mathcal {O}(n/\log _\sigma n)\) time; in particular, the shortest cover can be computed within this time. We also design an \(\mathcal {O}(n(\log \sigma + \log \log n)/\log n)\)-sized data structure that computes in \(\mathcal {O}(1)\) time any element of the so-called (shortest) cover array of T, that is, the length of the shortest cover of any given prefix of T. As a by-product, we describe the structure of the cover array of Fibonacci strings. On the negative side, we show that the shortest cover of a length-n string cannot be computed using \(o(n/\log n)\) operations in the PILLAR model of Charalampopoulos, Kociumaka, and Wellnitz (FOCS 2020).

J. Radoszewski—Supported by the Polish National Science Center, grant no. 2022/46/E/ST6/00463

W. Zuba—Supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101034253.

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Authors and Affiliations

  1. University of Warsaw, Warsaw, Poland

    Jakub Radoszewski

  2. CWI, Amsterdam, The Netherlands

    Wiktor Zuba

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  1. Jakub Radoszewski
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Correspondence to Wiktor Zuba .

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  1. University of Verona, Verona, Italy

    Zsuzsanna Lipták

  2. Federal University of Amazonas, Manaus, Brazil

    Edleno Moura

  3. Michoacan University of Saint Nicholas of Hidalgo, Morelia, Mexico

    Karina Figueroa

  4. Northeastern University, Boston, MA, USA

    Ricardo Baeza-Yates

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Radoszewski, J., Zuba, W. (2025). Computing String Covers in Sublinear Time. In: Lipták, Z., Moura, E., Figueroa, K., Baeza-Yates, R. (eds) String Processing and Information Retrieval. SPIRE 2024. Lecture Notes in Computer Science, vol 14899. Springer, Cham. https://doi.org/10.1007/978-3-031-72200-4_21

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