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On the Maximal Number of Cubic Runs in a String

  • Maxime Crochemore
  • Costas Iliopoulos
  • Marcin Kubica
  • Jakub Radoszewski
  • Wojciech Rytter
  • Tomasz Waleń
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Maxime Crochemore
    • 1
    • 3
  • Costas Iliopoulos
    • 1
    • 4
  • Marcin Kubica
    • 2
  • Jakub Radoszewski
    • 2
  • Wojciech Rytter
    • 2
    • 5
  • Tomasz Waleń
    • 2
  1. 1.King’s College LondonLondonUK
  2. 2.Dept. of Mathematics, Computer Science and MechanicsUniversity of WarsawWarsawPoland
  3. 3.Université Paris-EstFrance
  4. 4.Digital Ecosystems & Business Intelligence InstituteCurtin University of TechnologyPerthAustralia
  5. 5.Dept. of Math. and InformaticsCopernicus UniversityToruńPoland

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