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A Randomized Online Quantile Summary in O(1/epsilon * log(1/epsilon)) Words Felber, David Ostrovsky, Rafail order statistics data stream streaming algorithm A quantile summary is a data structure that approximates to epsilon-relative error the order statistics of a much larger underlying dataset. In this paper we develop a randomized online quantile summary for the cash register data input model and comparison data domain model that uses O((1/epsilon) log(1/epsilon)) words of memory. This improves upon the previous best upper bound of O((1/epsilon) (log(1/epsilon))^(3/2)) by Agarwal et al. (PODS 2012). Further, by a lower bound of Hung and Ting (FAW 2010) no deterministic summary for the comparison model can outperform our randomized summary in terms of space complexity. Lastly, our summary has the nice property that O((1/epsilon) log(1/epsilon)) words suffice to ensure that the success probability is 1 - exp(-poly(1/epsilon)). Schloss Dagstuhl – Leibniz-Zentrum für Informatik David Felber and Rafail Ostrovsky 2015 Is Part Of LIPIcs, Volume 40, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.APPROX-RANDOM.2015.775 urn:nbn:de:0030-drops-53357 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2015.775 eng https://creativecommons.org/licenses/by/3.0/legalcode