On the Number of Prefix and Border Tables

  • Julien Clément
  • Laura Giambruno
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8392)


For some text algorithms, the real measure for the complexity analysis is not the string itself but its structure stored in its prefix table (or border table, as border and prefix tables can be proved to be equivalent). We give a new upper bound on the number of prefix tables for strings of length n (on any alphabet) which is of order (1 + φ) n (with \(\varphi={{1+\sqrt{5}}\over{2}}\) the golden mean) and present also a lower bound.


Regular Expression Stirling Number Combinatorial Class Combinatorial Description Empty Element 
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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Julien Clément
    • 1
  • Laura Giambruno
    • 1
  1. 1.GREYC, CNRS-UMR 6072Université de Caen, EnsicaenCaenFrance

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