BIT Numerical Mathematics

, Volume 25, Issue 1, pp 113–134 | Cite as

Approximate counting: A detailed analysis

  • Philippe Flajolet
Part I Computer Science Ordinary Papers


Approximate counting is an algorithm proposed by R. Morris which makes it possible to keep approximate counts of large numbers in small counters. The algorithm is useful for gathering statistics of a large number of events as well as for applications related to data compression (Todd et al.). We provide here a complete analysis of approximate counting which establishes good convergence properties of the algorithm and allows to quantify precisely complexity-accuracy tradeoffs.


Detailed Analysis Computational Mathematic Convergence Property Complete Analysis Data Compression 
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.
    L. Comtel,L'Analyse Combinatoire, 2 vol., P.U.F., Paris (1970).Google Scholar
  2. 2.
    G. Doetsch,Handbuch der Laplace Transformation, Birkhauser Verlag, Basel (1955).Google Scholar
  3. 3.
    P. Flajolet and N. Martin,Probabilistic counting, in Proc. 24th Annual Symp. on Foundations of Comp. Sc., Tucson, Arizona (1984), pp. 76–82.Google Scholar
  4. 4.
    R. G. Gallager,Variations on a theme by Huffmann, IEEE Trans. IT, 24 (1978) pp. 669–674.Google Scholar
  5. 5.
    L. Kleinrock,Queuing Systems, Wiley Interscience, New York (1976).Google Scholar
  6. 6.
    D. E. Knuth,The Art of Computer Programming: Sorting and Searching, Addison-Wesley, Reading (1973).Google Scholar
  7. 7.
    G. Langdon and J. Rissanen,Compression of black white images with binary arithmetic coding, IEEE Trans. on Communications (1981).Google Scholar
  8. 8.
    R. Morris,Counting large numbers of events in small registers, Comm. ACM, 21 (1978), pp. 840–842.CrossRefGoogle Scholar
  9. 9.
    S. Todd, N. Martin, G. Langdon and D. Helman,Dynamic statistics collection for compression coding, Unpublished manuscript, 12 p. (1981).Google Scholar
  10. 10.
    E. T. Whittaker and G. N. Watson,A Course in Modern Analysis, (1907); 4th edition, Cambridge Univ. Press, 1927.Google Scholar

Copyright information

© BIT Foundations 1985

Authors and Affiliations

  • Philippe Flajolet
    • 1
  1. 1.INRIA, Domaine de Voluceau-RocquencourtLe Chesnay CEDEXFrance

Personalised recommendations