A randomized online quantile summary in O(1/ɛ log 1/ɛ) words

A quantile summary is a data structure that approximates to ε-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( ε log 1 ε ) words of memory. This improves upon the previous best upper bound of O( ε log 3/2 1 ε ) by Agarwal et al. [1]. Further, by a lower bound of Hung and Ting [4] 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( ε log 1 ε ) words suffice to ensure that the success probability is 1−e −poly(1/ε). 1998 ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems, G.3 Probability and Statistics