The Space Complexity of Approximating the Frequency Moments

The frequency moments of a sequence containing mi elements of type i, for 1 i n, are the numbers Fk = n i=1 mk 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(1) space. Applications to data bases are mentioned as well.

• Type: Conference
• Year: 1996
• Where: STOC
• Authors: Noga Alon, Yossi Matias, Mario Szegedy
• Keywords: Algorithms, Frequency Moments, Sequence Containing Mi, Space Complexity, STOC 1996