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Computing Covers Under Substring Consistent Equivalence Relations

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String Processing and Information Retrieval (SPIRE 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12303))

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Abstract

Covers are a kind of quasiperiodicity in strings. A string C is a cover of another string T if any position of T is inside some occurrence of C in T. The shortest and longest cover arrays of T have the lengths of the shortest and longest covers of each prefix of T, respectively. The literature has proposed linear-time algorithms computing longest and shortest cover arrays taking border arrays as input. An equivalence relation \(\approx \) over strings is called a substring consistent equivalence relation (SCER) iff \(X \approx Y\) implies (1) \(|X| = |Y|\) and (2) \(X[i:j] \approx Y[i:j]\) for all \(1 \le i \le j \le |X|\). In this paper, we generalize the notion of covers for SCERs and prove that existing algorithms to compute the shortest cover array and the longest cover array of a string T under the identity relation will work for any SCERs taking the accordingly generalized border arrays.

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Notes

  1. 1.

    In some references it is called superprimitive, reserving the term “primitive” for strings that cannot be represented as \(S^k\) for some string S and integer \(k \ge 2\).

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Authors and Affiliations

  1. Graduate School of Information Sciences, Tohoku University, Sendai, Japan

    Natsumi Kikuchi, Diptarama Hendrian, Ryo Yoshinaka & Ayumi Shinohara

Authors
  1. Natsumi Kikuchi
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  2. Diptarama Hendrian
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  3. Ryo Yoshinaka
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  4. Ayumi Shinohara
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Corresponding author

Correspondence to Natsumi Kikuchi .

Editor information

Editors and Affiliations

  1. CISE Department, University of Florida, Gainesville, FL, USA

    Christina Boucher

  2. Department of Computer Science, University of Central Florida, Orlando, FL, USA

    Sharma V. Thankachan

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Kikuchi, N., Hendrian, D., Yoshinaka, R., Shinohara, A. (2020). Computing Covers Under Substring Consistent Equivalence Relations. In: Boucher, C., Thankachan, S.V. (eds) String Processing and Information Retrieval. SPIRE 2020. Lecture Notes in Computer Science(), vol 12303. Springer, Cham. https://doi.org/10.1007/978-3-030-59212-7_10

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  • DOI: https://doi.org/10.1007/978-3-030-59212-7_10

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  • Online ISBN: 978-3-030-59212-7

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