Abstract
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.
Similar content being viewed by others
Bibliography
L. Comtel,L'Analyse Combinatoire, 2 vol., P.U.F., Paris (1970).
G. Doetsch,Handbuch der Laplace Transformation, Birkhauser Verlag, Basel (1955).
P. Flajolet and N. Martin,Probabilistic counting, in Proc. 24th Annual Symp. on Foundations of Comp. Sc., Tucson, Arizona (1984), pp. 76–82.
R. G. Gallager,Variations on a theme by Huffmann, IEEE Trans. IT, 24 (1978) pp. 669–674.
L. Kleinrock,Queuing Systems, Wiley Interscience, New York (1976).
D. E. Knuth,The Art of Computer Programming: Sorting and Searching, Addison-Wesley, Reading (1973).
G. Langdon and J. Rissanen,Compression of black white images with binary arithmetic coding, IEEE Trans. on Communications (1981).
R. Morris,Counting large numbers of events in small registers, Comm. ACM, 21 (1978), pp. 840–842.
S. Todd, N. Martin, G. Langdon and D. Helman,Dynamic statistics collection for compression coding, Unpublished manuscript, 12 p. (1981).
E. T. Whittaker and G. N. Watson,A Course in Modern Analysis, (1907); 4th edition, Cambridge Univ. Press, 1927.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Flajolet, P. Approximate counting: A detailed analysis. BIT 25, 113–134 (1985). https://doi.org/10.1007/BF01934993
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01934993