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ICALP
2009
Springer

Revisiting the Direct Sum Theorem and Space Lower Bounds in Random Order Streams

10 years 9 months ago
Revisiting the Direct Sum Theorem and Space Lower Bounds in Random Order Streams
Estimating frequency moments and Lp distances are well studied problems in the adversarial data stream model and tight space bounds are known for these two problems. There has been growing interest in revisiting these problems in the framework of random-order streams. The best space lower bound known for computing the kth frequency moment in random-order streams is (n1-2.5/k ) by Andoni et al., and it is conjectured that the real lower bound shall be (n1-2/k ). In this paper, we resolve this conjecture. In our approach, we revisit the direct sum theorem developed by Bar-Yossef et al. in a random-partition private messages model and provide a tight (n1-2/k / ) space lower bound for any -pass algorithm that approximates the frequency moment in random-order stream model to a constant factor. Finally, we also introduce the notion of space-entropy tradeoffs in random order streams, as a means of studying intermediate models between adversarial and fully random order streams. We show an almo...
Sudipto Guha, Zhiyi Huang
Added 03 Dec 2009
Updated 03 Dec 2009
Type Conference
Year 2009
Where ICALP
Authors Sudipto Guha, Zhiyi Huang
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