On Maximal Unbordered Factors

  • Alexander Loptev
  • Gregory Kucherov
  • Tatiana StarikovskayaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9133)


Given a string \(S\) of length \(n\), its maximal unbordered factor is the longest factor which does not have a border. In this work we investigate the relationship between \(n\) and the length of the maximal unbordered factor of \(S\). We prove that for the alphabet of size \(\sigma \ge 5\) the expected length of the maximal unbordered factor of a string of length \(n\) is at least \(0.99 n\) (for sufficiently large values of \(n\)). As an application of this result, we propose a new algorithm for computing the maximal unbordered factor of a string.


Linear Time Minimal Period Empty String Alphabet Size Expected Running Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors would like to thank the anonymous reviewers whose suggestions greatly improved the quality of this work.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Alexander Loptev
    • 1
  • Gregory Kucherov
    • 2
  • Tatiana Starikovskaya
    • 3
    Email author
  1. 1.Higher School of EconomicsMoscowRussia
  2. 2.Laboratoire d’Informatique Gaspard MongeUniversité Paris-Est and CNRSMarne-la-vallée, ParisFrance
  3. 3.University of BristolBristolUK

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