The space complexity of approximating the frequency moments

Abstract

The frequency moments of a sequence containing mi elements of type i, 1≤i≤n, are the numbers Fk=Σni=1mki. 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 nΩ(1) space. Applications to data bases are mentioned as well. © 1999 Academic Press.