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Extracting Powers and Periods in a String from Its Runs Structure

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String Processing and Information Retrieval (SPIRE 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6393))

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Abstract

A breakthrough in the field of text algorithms was the discovery of the fact that the maximal number of runs in a string of length n is O(n) and that they can all be computed in O(n) time. We study some applications of this result. New simpler O(n) time algorithms are presented for a few classical string problems: computing all distinct kth string powers for a given k, in particular squares for k = 2, and finding all local periods in a given string of length n. Additionally, we present an efficient algorithm for testing primitivity of factors of a string and computing their primitive roots. Applications of runs, despite their importance, are underrepresented in existing literature (approximately one page in the paper of Kolpakov & Kucherov, 1999). In this paper we attempt to fill in this gap. We use Lyndon words and introduce the Lyndon structure of runs as a useful tool when computing powers. In problems related to periods we use some versions of the Manhattan skyline problem.

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Author information

Authors and Affiliations

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

    Maxime Crochemore & Costas Iliopoulos

  2. Dept. of Mathematics, Computer Science and Mechanics, University of Warsaw, Warsaw, Poland

    Marcin Kubica, Jakub Radoszewski, Wojciech Rytter & Tomasz Waleń

  3. Université Paris-Est, France

    Maxime Crochemore

  4. Digital Ecosystems & Business Intelligence Institute, Curtin University of Technology, Perth, WA, 6845, Australia

    Costas Iliopoulos

  5. Dept. of Math. and Informatics, Copernicus University, Toruń, Poland

    Wojciech Rytter

Authors
  1. Maxime Crochemore
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  2. Costas Iliopoulos
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  3. Marcin Kubica
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  4. Jakub Radoszewski
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  5. Wojciech Rytter
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  6. Tomasz Waleń
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Editor information

Editors and Affiliations

  1. School of Physics and Mathematics, Edificio "B", Universidad Michoacana, Ciudad Universitaria, 5800, Morelia, Mich., Mexico

    Edgar Chavez

  2. Dept. of Computer Science and Enginerring, University of California, 92521, Riverside, CA, USA

    Stefano Lonardi

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Crochemore, M., Iliopoulos, C., Kubica, M., Radoszewski, J., Rytter, W., Waleń, T. (2010). Extracting Powers and Periods in a String from Its Runs Structure. In: Chavez, E., Lonardi, S. (eds) String Processing and Information Retrieval. SPIRE 2010. Lecture Notes in Computer Science, vol 6393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16321-0_27

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  • DOI: https://doi.org/10.1007/978-3-642-16321-0_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16320-3

  • Online ISBN: 978-3-642-16321-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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