A hybrid technique for estimating frequency moments over data streams

The problem of estimating the k frequency moment Fk, for any non-negative integral value of k, over a data stream by looking at the items exactly once as they arrive, was considered in a seminal paper by Alon, Matias and Szegedy [1, 2]. They present a sampling based algorithm to estimate Fk where, k ≥ 2, using space Õ(n1−1/k)). Coppersmith and Kumar [7] and [10], using different methods, present algorithms for estimating Fk with space complexity Õ(n1−1/(k−1)). In this paper, we present an algorithm for estimating Fk with space complexity Õ(n1−2/(k+1)), for k > 2, thereby, improving the space complexity compared to the algorithms in [1, 2, 7, 10] for k ≥ 4.