Maintaining Stream Statistics over Sliding Windows
SIAM Journal on Computing
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ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
A simple algorithm for finding frequent elements in streams and bags
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SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A simpler and more efficient deterministic scheme for finding frequent items over sliding windows
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Sketching asynchronous streams over a sliding window
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Time-decaying aggregates in out-of-order streams
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A deterministic algorithm for summarizing asynchronous streams over a sliding window
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
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In an asynchronous data stream, the data items may be out of order with respect to their original timestamps. This paper gives a space-efficient data structure to maintain such a data stream so that it can approximate the frequent item set over a sliding time window with sufficient accuracy. Prior to our work, Cormode et al. [3] have the best solution, with space complexity $O(\frac{1}{\varepsilon} \log W \log (\frac{\varepsilon B}{\log W}) \min\{\log W, \frac{1}{\varepsilon}\}\log U)$, where ε is the given error bound, W and B are parameters of the sliding window, and U is the number of all possible item names. Our solution reduces the space to $O(\frac{1}{\varepsilon} \log W \log (\frac{\varepsilon B}{\log W}))$. We also unify the study of synchronous and asynchronous data stream by quantifying the delay of the data items. When the delay is zero, our solution matches the space complexity of the best solution to the synchronous data streams [8].