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. Introduction. As shown by an easy information-theoretic argument, maintaining a counter whose values may range in the interval 1 to M essentially necessitates log,M bits. This lower bound is of course achieved by a 1 standard binary counter. R. Morris [8] has proposed a probabilistic algorithm that maintains an

Citations

644	A Course of Modern Analysis - Whittaker, Watson - 1996
167	The art of computer programming. In: Sorting and Searching - Knuth - 1997
60	Probabilistic counting - Flajolet - 1983
45	Counting large numbers of events in small registers - Morris - 1978
15	Analyse Combinatoire - Comtet - 1970
9	Handbuch der Laplace Transformation I, Birkhäuser Verlag - Doetsch - 1971
1	Variations on u theme by Huffmann - Gallager - 1978
1	Queuing Systems, Wiley Interscience - Kleinrock - 1976
1	Compression of black white images with binary arithmetic coding - Langdon, Rissanen - 1981
1	Dynamic statistics collection for compression coding, Unpublished manuscript - Todd, Martin, et al. - 1981