Communication complexity
The space complexity of approximating the frequency moments
Journal of Computer and System Sciences
Space lower bounds for distance approximation in the data stream model
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
An information statistics approach to data stream and communication complexity
Journal of Computer and System Sciences - Special issue on FOCS 2002
Optimal approximations of the frequency moments of data streams
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Simpler algorithm for estimating frequency moments of data streams
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Tight lower bounds for selection in randomly ordered streams
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Robust lower bounds for communication and stream computation
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Tight Lower Bounds for Multi-pass Stream Computation Via Pass Elimination
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Stream Order and Order Statistics: Quantile Estimation in Random-Order Streams
SIAM Journal on Computing
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Lower bounds for number-in-hand multiparty communication complexity, made easy
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Space-efficient estimation of statistics over sub-sampled streams
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Tight bounds for distributed functional monitoring
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Communication steps for parallel query processing
Proceedings of the 32nd symposium on Principles of database systems
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Estimating frequency moments and L p 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 k th frequency moment in random-order streams is *** (n 1 *** 2.5/k ) by Andoni et al., and it is conjectured that the real lower bound shall be *** (n 1 *** 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 *** (n 1 *** 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 almost tight space-entropy tradeoff for L *** distance and a non-trivial tradeoff for L p distances.