Advertisement

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)

Abstract

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.

Keywords

Regular Expression Stirling Number Combinatorial Class Combinatorial Description Empty Element 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bland, W., Kucherov, G., Smyth, W.F.: Prefix Table Construction and Conversion. In: Lecroq, T., Mouchard, L. (eds.) IWOCA 2013. LNCS, vol. 8288, pp. 41–53. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  2. 2.
    Clement, J., Crochemore, M., Rindone, G.: Reverse engineering prefix tables. In: Albers, S., Marion, J.-Y. (eds.) 26th International Symposium on Theoretical Aspects of Computer Science (STACS 2009). Leibniz International Proceedings in Informatics (LIPIcs), vol. 3, pp. 289–300. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik (2009)Google Scholar
  3. 3.
    Crochemore, M., Hancart, C., Lecroq, T.: Algorithms on strings. Cambridge University Press, Cambridge (2007)CrossRefzbMATHGoogle Scholar
  4. 4.
    Duval, J.-P., Lecroq, T., Lefebvre, A.: Border array on bounded alphabet. Journal of Automata, Languages and Combinatorics 10(1), 51–60 (2005)zbMATHMathSciNetGoogle Scholar
  5. 5.
    Duval, J.-P., Lecroq, T., Lefebvre, A.: Efficient validation and construction of border arrays and validation of string matching automata. RAIRO-Theoretical Informatics and Applications 43(2), 281–297 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Flajolet, P., Sedgewick, R.: Analytic Combinatorics. Cambridge University Press, Cambridge (2009)CrossRefzbMATHGoogle Scholar
  7. 7.
    Franek, F., Gao, S., Lu, W., Ryan, P.J., Smyth, W.F., Sun, Y., Yang, L.: Verifying a border array in linear time. Journal on Combinatorial Mathematics and Combinatorial Computing 42, 223–236 (2002)zbMATHMathSciNetGoogle Scholar
  8. 8.
    Gusfield, D.: Algorithms on strings, trees and sequences: computer science and computational biology. Cambridge University Press, Cambridge (1997)CrossRefzbMATHGoogle Scholar
  9. 9.
    Knuth, D.: The average time for carry propagation. Indagationes Mathematicae 40, 238–242 (1978)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Moore, D., Smyth, W.F., Miller, D.: Counting distinct strings. Algorithmica 23(1), 1–13 (1999)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

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

Personalised recommendations