Lower Bounds for Quantile Estimation in Random-Order and Multi-pass Streaming

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, 1, 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 adversarialorder models: using Ω(polylog n) space, exact selection requires Ω(log n) passes in the adversarial-order model while O(log log n) passes are sufficient in the random-order model.

• Type: Conference
• Year: 2007
• Where: ICALP
• Authors: Sudipto Guha, Andrew McGregor
• Keywords: Data Stream Model, ICALP 2007, Lower Bounds, Stream, Theoretical Computer Science