Wednesday, June 10, 2015

Taylor Polynomial Estimator for Estimating Frequency Moments

We present a randomized algorithm for estimating the pth moment Fp of the frequency vector of a data stream in the general update (turnstile) model to within a multiplicative factor of 1±ϵ, for p>2, with high constant confidence. For 0<ϵ1, the algorithm uses space O(n12/pϵ2+n12/pϵ4/plog(n)) words. This improves over the current bound of O(n12/pϵ24/plog(n)) words by Andoni et. al. in \cite{ako:arxiv10}. Our space upper bound matches the lower bound of Li and Woodruff \cite{liwood:random13} for ϵ=(log(n))Ω(1) and the lower bound of Andoni et. al. \cite{anpw:icalp13} for ϵ=Ω(1).
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