Analysis of the Size of Antidictionary in DCA

  • Julien Fayolle
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5029)


We analyze the lossless data compression scheme using antidictionary. Its principle is to build the dictionary of a set of words that do not occur in the text (minimal forbidden words). We prove here that the number of words in the antidictionary, i.e., minimum forbidden words, behaves asymptotically linearly in the length of the text under a memoryless model on the generation of texts. The linearity constant is explicited. We use methods from analytic combinatorics.


Asymptotic Behavior Approximate Model Analytic Combinatorics Left Child Intermediate Length 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Barbour, A.D., Holst, L., Janson, S.: Poisson approximation. The Clarendon Press Oxford University Press, New York (1992) (Oxford Science Publications) zbMATHGoogle Scholar
  2. 2.
    Béal, M.-P., Mignosi, F., Restivo, A.: Minimal forbidden words and symbolic dynamics. In: Puech, C., Reischuk, R. (eds.) STACS 1996. LNCS, vol. 1046. Springer, Heidelberg (1996)Google Scholar
  3. 3.
    Crochemore, M., Mignosi, F., Restivo, A., Salemi, S.: Text compression using antidictonaries. In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 261–270. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  4. 4.
    Crochemore, M., Mignosi, F., Restivo, A., Salemi, S.: Data compression using antidictonaries. In: Storer, J. (ed.) Proceedings of the I.E.E.E., Lossless Data Compression, pp. 1756–1768 (2000)Google Scholar
  5. 5.
    Crochemore, M., Navarro, G.: Improved antidictionary based compression. In: SCCC 2002, Chilean Computer Science Society, pp. 7–13. I.E.E.E. CS Press (November 2002)Google Scholar
  6. 6.
    Fayolle, J.: An average-case analysis of basic parameters of the suffix tree. In: Drmota, M., Flajolet, P., Gardy, D., Gittenberger, B. (eds.) Mathematics and Computer Science. Proceedings of a colloquium organized by TU, Wien, Vienna, Austria, pp. 217–227. Birkhäuser, Basel (2004)Google Scholar
  7. 7.
    Fayolle, J.: Compression de données sans perte et combinatoire analytique. PhD thesis, Université Paris VI (2006)Google Scholar
  8. 8.
    Fayolle, J., Ward, M.D.: Analysis of the average depth in a suffix tree under a Markov model. In: Proceedings of the 2005 International Conference on the Analysis of Algorithms (2005), DMTCS. Proceedings of a colloquium organized by Universitat Politècnica de Catalunya, Barcelona, Catalunya, June 2005, pp. 95–104 (2005)Google Scholar
  9. 9.
    Flajolet, P., Gourdon, X., Dumas, P.: Mellin transforms and asymptotics: Harmonic sums. Theoretical Computer Science 144, (1–2), 3–58 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Jacquet, P., Szpankowski, W.: Autocorrelation on words and its applications: analysis of suffix trees by string-ruler approach. Journal of Combinatorial Theory. Series A 66(2), 237–269 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Morita, H., Ota, T.: An upper bound on size of antidictionary. In: Proceedings of SITA 2004 (2004)Google Scholar
  12. 12.
    Ota, T., Morita, H.: One-path ECG lossless compression using antidictionaries. IEICE Trans. Fundamentals (Japanese Edition) J87-A 9, 1187–1195 (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Julien Fayolle
    • 1
  1. 1.LRI; Univ. Paris-Sud, CNRSOrsayFrance

Personalised recommendations