Space-efficient online computation of quantile summaries
SIGMOD '01 Proceedings of the 2001 ACM SIGMOD international conference on Management of data
Estimating simple functions on the union of data streams
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
Maintaining stream statistics over sliding windows: (extended abstract)
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Distributed streams algorithms for sliding windows
Proceedings of the fourteenth annual ACM symposium on Parallel algorithms and architectures
A note on efficient aggregate queries in sensor networks
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Approximate counts and quantiles over sliding windows
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
A simpler and more efficient deterministic scheme for finding frequent items over sliding windows
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Communication-efficient distributed monitoring of thresholded counts
Proceedings of the 2006 ACM SIGMOD international conference on Management of data
A geometric approach to monitoring threshold functions over distributed data streams
Proceedings of the 2006 ACM SIGMOD international conference on Management of data
Sketching asynchronous streams over a sliding window
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Algorithms for distributed functional monitoring
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Distributed computation of the mode
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
Sketching and Streaming Entropy via Approximation Theory
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Optimal tracking of distributed heavy hitters and quantiles
Proceedings of the twenty-eighth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Functional Monitoring without Monotonicity
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Optimal sampling from distributed streams
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Continuous distributed monitoring: a short survey
Proceedings of the First International Workshop on Algorithms and Models for Distributed Event Processing
Efficient computation of frequent and top-k elements in data streams
ICDT'05 Proceedings of the 10th international conference on Database Theory
Geometric optimization problems over sliding windows
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
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The area of distributed monitoring requires tracking the value of a function of distributed data as new observations are made. An important case is when attention is restricted to only a recent time period, such as the last hour of readings--the sliding window case. In this paper, we introduce a novel paradigm for handling such monitoring problems, which we dub the "forward/backward" approach. This view allows us to provide optimal or near-optimal solutions for several fundamental problems, such as counting, tracking frequent items, and maintaining order statistics. The resulting protocols improve on previous work or give the first solutions for some problems, and operate efficiently in terms of space and time needed. Specifically, we obtain optimal $O(\frac{k}{\epsilon } \log (\epsilon n/k))$ communication per window of n updates for tracking counts and heavy hitters with accuracy ε across k sites; and near-optimal communication of $O(\frac{k}{\epsilon } \log^2(1/\epsilon) \log (n/k))$ for quantiles. We also present solutions for problems such as tracking distinct items, entropy, and convex hull and diameter of point sets.