Problem 13: Effects of Subsampling

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Suggested by Yossi Matias
Source Kanpur 2006
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When processing very fast streams, it is not feasible to run a streaming algorithm on the entire stream, even one that can process each element in $O(1)$ time. Rather it is necessary to sample from the stream and to process the sub-stream using a streaming algorithm. For standard problems such as estimating $F_0$, how does the sub-sampling affect that the accuracy of the streaming algorithms? How should the sampling rate and the per-element time-complexity of a streaming algorithm be traded-off to achieve optimal results?

Another way to formalize this question, suggested by Muthukrishnan, is in terms of what part of the stream to skip and which to stream. A formal definition of the model and algorithms for estimating $F_2$ and others can be found in [BhattacharyyaMMY-07].