Abstract
Using an auxiliary memory smaller than the size of this abstract, the LogLog algorithm makes it possible to estimate in a single pass and within a few percents the number of different words in the whole of Shakespeare’s works. In general the LogLog algorithm makes use of m “small bytes” of auxiliary memory in order to estimate in a single pass the number of distinct elements (the “cardinality”) in a file, and it does so with an accuracy that is of the order of 1/sqrtm. The “small bytes” to be used in order to count cardinalities till N max comprise about loglog N max bits, so that cardinalities well in the range of billions can be determined using one or two kilobytes of memory only. The basic version of the LogLog algorithm is validated by a complete analysis. An optimized version, super–LogLog, is also engineered and tested on real-life data. The algorithm parallelizes optimally.
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References
Alon, N., Matias, Y., Szegedy, M.: The space complexity of approximating the frequency moments. Journal of Computer and System Sciences 58, 137–147 (1999)
Estan, C., Varghese, G.: New directions in traffic measurement and accounting. In: Proceedings of SIGCOMM 2002. ACM Press, New York (2002) (Also: UCSD technical report CS2002-0699, February, 2002; available electronically)
Estan, C., Varghese, G., Fisk, M.: Bitmap algorithms for counting active flows on high speed links. Technical Report CS2003-0738, UCSD (Mar 2003)
Flajolet, P.: Approximate counting: A detailed analysis. BIT 25, 113–134 (1985)
Flajolet, P.: On adaptive sampling. Computing 34, 391–400 (1990)
Flajolet, P., Gourdon, X., Dumas, P.: Mellin transforms and asymptotics: Harmonic sums. Theoretical Computer Science 144(1-2), 3–58 (1995)
Flajolet, P., Martin, G.N.: Probabilistic counting algorithms for data base applications. Journal of Computer and System Sciences 31(2), 182–209 (1985)
Gibbons, P.B., Poosala, V., Acharya, S., Bartal, Y., Matias, Y., Muthukrishnan, S., Ramaswamy, S., Suel, T.: AQUA: System and techniques for approximate query answering. Tech. report, Bell Laboratories, Murray Hill, New Jersey (February 1998)
Jacquet, P., Szpankowski, W.: Analytical depoissonization and its applications. Theoretical Computer Science 201, 1–2 (1998)
Knuth, D.E.: The Art of Computer Programming. Sorting and Searching, vol. 3, 2nd edn. Addison-Wesley, Reading (1998)
Morris, R.: Counting large numbers of events in small registers. Communications of the ACM 21, 840–842 (1978)
Motwani, R., Raghavan, P.: Randomized Algorithms. Cambridge University Press, Cambridge (1995)
Palmer, C.R., Siganos, G., Faloutsos, M., Faloutsos, C., Gibbons, P.: The connectivity and fault-tolerance of the Internet topology. In: Workshop on Network-Related Data Management (NRDM 2001) (2001)
Prodinger, H.: Combinatorics of geometrically distributed random variables: Leftto- right maxima. Discrete Mathematics 153, 253–270 (1996)
Szpankowski, W.: Average-Case Analysis of Algorithms on Sequences. John Wiley, New York (2001)
Whang, K.-Y., Zanden, B.T.V., Taylor, H.M.: A linear-time probabilistic counting algorithm for database applications. TODS 15(2), 208–229 (1990)
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Durand, M., Flajolet, P. (2003). Loglog Counting of Large Cardinalities. In: Di Battista, G., Zwick, U. (eds) Algorithms - ESA 2003. ESA 2003. Lecture Notes in Computer Science, vol 2832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39658-1_55
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DOI: https://doi.org/10.1007/978-3-540-39658-1_55
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