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On the Right-Seed Array of a String

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Computing and Combinatorics (COCOON 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6842))

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Abstract

We consider the problem of finding the repetitive structure of a given fixed string y. A factor u of y is a cover of y, if every letter of y falls within some occurrence of u in y. A factor v of y is a seed of y, if it is a cover of a superstring of y. There exist linear-time algorithms for solving the minimal cover problem. The minimal seed problem is of much higher algorithmic difficulty, and no linear-time algorithm is known. In this article, we solve one of its variants – computing the minimal and maximal right-seed array of a given string. A right seed of y is the shortest suffix of y that it is a cover of a superstring of y. An integer array RS is the minimal right-seed (resp. maximal right-seed) array of y, if RS[i] is the minimal (resp. maximal) length of right seeds of \(y[0\mathinner{\ldotp\ldotp} i]\). We present an \(\ensuremath{\mathcal{O}}(n\log n)\) time algorithm that computes the minimal right-seed array of a given string, and a linear-time solution to compute the maximal right-seed array by detecting border-free prefixes of the given string.

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Author information

Authors and Affiliations

  1. Dept. of Informatics, King’s College London, London, WC2R 2LS, UK

    Michalis Christou, Maxime Crochemore, Costas S. Iliopoulos & Solon P. Pissis

  2. Université Paris-Est, France

    Maxime Crochemore

  3. Digital Ecosystems & Business Intelligence Institute, Curtin University, GPO Box U1987, Perth, WA, 6845, Australia

    Costas S. Iliopoulos

  4. Dept. of Theoretical Computer Science, Faculty of Information Technology, Czech Technical University in Prague, Czech Republic

    Ondrej Guth

Authors
  1. Michalis Christou
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  2. Maxime Crochemore
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  3. Ondrej Guth
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  4. Costas S. Iliopoulos
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  5. Solon P. Pissis
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Texas-Pan American, 78539, Edinburg, TX, USA

    Bin Fu

  2. Department of Computer Science, University of Texas at Dallas, 75080, Richardson, TX, USA

    Ding-Zhu Du

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© 2011 Springer-Verlag Berlin Heidelberg

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Christou, M., Crochemore, M., Guth, O., Iliopoulos, C.S., Pissis, S.P. (2011). On the Right-Seed Array of a String. In: Fu, B., Du, DZ. (eds) Computing and Combinatorics. COCOON 2011. Lecture Notes in Computer Science, vol 6842. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22685-4_43

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  • DOI: https://doi.org/10.1007/978-3-642-22685-4_43

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22684-7

  • Online ISBN: 978-3-642-22685-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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