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# The Space Complexity of Approximating the Frequency Moments

@inproceedings{Alon1996TheSC, title={The Space Complexity of Approximating the Frequency Moments}, author={Noga Alon and Yossi Matias and Mario Szegedy}, booktitle={STOC}, year={1996} }

- Published 1996 in STOC
DOI:10.1145/237814.237823

The frequency moments of a sequence containing mi elements of type i, for 1 ≤ i ≤ n, are the numbers Fk = ∑n i=1m k i . We consider the space complexity of randomized algorithms that approximate the numbers Fk, when the elements of the sequence are given one by one and cannot be stored. Surprisingly, it turns out that the numbers F0, F1 and F2 can be approximated in logarithmic space, whereas the approximation of Fk for k ≥ 6 requires n space. Applications to data bases are mentioned as well.

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