Approximating Large Frequency Moments with O(n1-2/k) Bits

In this paper we consider the problem of approximating frequency moments in the streaming model. Given a stream D = {p1, p2, . . . , pm} of numbers from {1, . . . , n}, a frequency of i is defined as fi = |{j : pj = i}|. The k-th frequency moment of D is defined as Fk = ∑n i=1 f k i . In this paper we give an upper bound on the space required to find a k-th frequency moment of O(n1−2/k) bits that matches, up to a constant factor, the lower bound of [46] for constant and constant k. Our algorithm makes a single pass over the stream and works for any constant k > 3.