Continuous Monitoring of Distributed Data Streams over a Time-based Sliding Window

Abstract : The past decade has witnessed many interesting algorithms for maintaining statistics over a data stream. This paper initiates a theoretical study of algorithms for monitoring distributed data streams over a time-based sliding window (which contains a variable number of items and possibly out-of-order items). The concern is how to minimize the communication between individual streams and the root, while allowing the root, at any time, to be able to report the global statistics of all streams within a given error bound. This paper presents communication-efficient algorithms for three classical statistics, namely, basic counting, frequent items and quantiles. The worst-case communication cost over a window is $O(\frac{k} {\epsilon} \log \frac{\epsilon N}{k})$ bits for basic counting and $O(\frac{k}{\epsilon} \log \frac{N}{k})$ words for the remainings, where $k$ is the number of distributed data streams, $N$ is the total number of items in the streams that arrive or expire in the window, and $\epsilon < 1$ is the desired error bound. Matching and nearly matching lower bounds are also obtained.
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Conference papers
Jean-Yves Marion and Thomas Schwentick. 27th International Symposium on Theoretical Aspects of Computer Science - STACS 2010, Mar 2010, Nancy, France. pp.179-190, 2010, Proceedings of the 27th Annual Symposium on the Theoretical Aspects of Computer Science
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Ho-Leung Chan, Tak-Wah Lam, Lap-Kei Lee, Hing-Fung Ting. Continuous Monitoring of Distributed Data Streams over a Time-based Sliding Window. Jean-Yves Marion and Thomas Schwentick. 27th International Symposium on Theoretical Aspects of Computer Science - STACS 2010, Mar 2010, Nancy, France. pp.179-190, 2010, Proceedings of the 27th Annual Symposium on the Theoretical Aspects of Computer Science. <inria-00456120>

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