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International Conference on Language and Automata Theory and Applications

LATA 2010: Language and Automata Theory and Applications pp 227–238Cite as

On the Maximal Number of Cubic Runs in a String

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6031))

Abstract

A run is an inclusion maximal occurrence in a string (as a subinterval) of a repetition v with a period p such that 2p ≤ |v|. The maximal number of runs in a string of length n has been thoroughly studied, and is known to be between 0.944 n and 1.029 n. In this paper we investigate cubic runs, in which the shortest period p satisfies 3p ≤ |v|. We show the upper bound of 0.5 n on the maximal number of such runs in a string of length n, and construct an infinite sequence of words over binary alphabet for which the lower bound is 0.406 n.

Research supported in part by the Royal Society, UK.

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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. Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Avinguda Catalunya, 35, 43002, Tarragona, Spain

    Adrian-Horia Dediu  & Carlos Martín-Vide  & 

  2. Fachbereich IV - Informatik, Universität Trier, Campus II, Behringstraße, 54286, Trier, Germany

    Henning Fernau

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Crochemore, M., Iliopoulos, C., Kubica, M., Radoszewski, J., Rytter, W., Waleń, T. (2010). On the Maximal Number of Cubic Runs in a String. In: Dediu, AH., Fernau, H., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2010. Lecture Notes in Computer Science, vol 6031. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13089-2_19

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  • DOI: https://doi.org/10.1007/978-3-642-13089-2_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13088-5

  • Online ISBN: 978-3-642-13089-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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