Kane, Daniel M.Nelson, JelaniPorat, ElyWoodruff, David P.2015-01-222011Kane, Daniel M., Jelani Nelson, Ely Porat, and David P. Woodruff. 2011. "Fast Moment Estimation in Data Streams in Optimal Space." In Proceedings of the Forty-Third Annual ACM Symposium on Theory of Computing: STOC '11, June 6-8, 2011, San Jose, CA: 745-754. New York, NY: ACM.978-1-4503-0691-1http://nrs.harvard.edu/urn-3:HUL.InstRepos:13792657We give a space-optimal streaming algorithm with update time \(O(log^2(1/\epsilon)loglog(1/\epsilon))\) for approximating the pth frequency moment, 0 < p < 2, of a length-n vector updated in a data stream up to a factor of \(1 \pm \epsilon\). This provides a nearly exponential improvement over the previous space optimal algorithm of [Kane-Nelson-Woodruff, SODA 2010], which had update time \(\Omega(1/\epsilon^2)\). When combined with the work of [Harvey-Nelson-Onak, FOCS 2008], we also obtain the first algorithm for entropy estimation in turnstile streams which simultaneously achieves near-optimal space and fast update time.en-USalgorightmtheorydata stream algorightmfrequency momentsConference Paper2015-01-13Daniel M. Kane, Jelani Nelson, Ely Porat, David P. Woodruff2015-01-2210.1145/1993636.1993735