Estimating small frequency moments of data stream: a characteristic function approach

We consider the problem of estimating the first moment of a data stream defined as F1 = ∑ i∈{1,2,...,n}∣fi∣ to within 1± -relative error with high probability. Several algorithms are wellknown for this problem including the median estimator over p-stable sketches by Indyk [11], the geometric means estimator over p-stable sketches by Li [13] and the Hss sketch based algorithm in [8]. The current best algorithm is given by Kane, Nelson and Woodruff in [12] that uses space O( −2 log(mM)) and is proved to be space-optimal. In this paper, we present a novel, space-optimal algorithm for estimating Fp with an elementary analysis that is based on the characteristic function of stable distributions.