On the Maximal Sum of Exponents of Runsin a String

  • Maxime Crochemore
  • Marcin Kubica
  • Jakub Radoszewski
  • Wojciech Rytter
  • Tomasz Waleń
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6460)


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 exponent of a run is defined as |v|/p and is ≥ 2. We show new bounds on the maximal sum of exponents of runs in a string of length n. Our upper bound of 4.1 n is better than the best previously known proven bound of 5.6 n by Crochemore & Ilie (2008). The lower bound of 2.035 n, obtained using a family of binary words, contradicts the conjecture of Kolpakov & Kucherov (1999) that the maximal sum of exponents of runs in a string of length n is smaller than 2n.


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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Maxime Crochemore
    • 1
    • 3
  • Marcin Kubica
    • 2
  • Jakub Radoszewski
    • 2
  • Wojciech Rytter
    • 2
    • 4
  • 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.Dept. of Math. and InformaticsCopernicus UniversityToruńPoland

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