Departmental Papers (CIS)

Date of this Version

August 2007

Document Type

Book Chapter

Comments

Postprint version. Published in Lecture Notes in Computer Science, Volume 4596, Automata, Languages and Programming, August 2007, pages 704-715.
Publisher URL: http://dx.doi.org/10.1007/978-3-540-73420-8_61

Abstract

We present lower bounds on the space required to estimate the quantiles of a stream of numerical values. Quantile estimation is perhaps the most studied problem in the data stream model and it is relatively well understood in the basic single-pass data stream model in which the values are ordered adversarially. Natural extensions of this basic model include the random-order model in which the values are ordered randomly (e.g. [21,5,13,11,12]) and the multi-pass model in which an algorithm is permitted a limited number of passes over the stream (e.g. [6,7,1,19,2,6,7,19,2]). We present lower bounds that complement existing upper bounds [21,11] in both models. One consequence is an exponential separation between the random-order and adversarial-order models: using Ω(polylog n) space, exact selection requires Ω(log n) passes in the adversarial-order model while O(loglog n) passes are sufficient in the random-order model.

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Date Posted: 19 March 2008

This document has been peer reviewed.