Towards a Solution to the “Runs” Conjecture

  • Maxime Crochemore
  • Lucian Ilie
  • Liviu Tinta
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5029)


The “runs” conjecture, proposed by [Kolpakov and Kucherov, 1999], states that the number of occurrences of maximal repetitions (runs) in a string of length n is at most n. The best bound to date, due to [Crochemore and Ilie, 2007], is 1.6n. Here we improve very much this bound using a combination of theory and computer verification. Our best bound is 1.048n but actually solving the conjecture seems to be now only a matter of time.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Maxime Crochemore
    • 1
    • 2
  • Lucian Ilie
    • 3
  • Liviu Tinta
    • 3
  1. 1.Department of Computer ScienceKing’s College LondonLondonUK
  2. 2.Institut Gaspard-MongeUniversité Paris-EstMarne-la-ValléeFrance
  3. 3.Department of Computer ScienceUniversity of Western OntarioLondonCanada

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