We give a space-optimal algorithm with update time O(log^2(1/eps)loglog(1/eps)) for (1+eps)-approximating the pth frequency moment, 0 < p < 2, of a length-n vector updated in a data stream. This provides a nearly exponential improvement in the update time complexity over the previous space-optimal algorithm of [Kane-Nelson-Woodruff, SODA 2010], which had update time Omega(1/eps^2).
@article{arxiv.1007.4191,
title = {Fast Moment Estimation in Data Streams in Optimal Space},
author = {Daniel M. Kane and Jelani Nelson and Ely Porat and David P. Woodruff},
journal= {arXiv preprint arXiv:1007.4191},
year = {2010}
}