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STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
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SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
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SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
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ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
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ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
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ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
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FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
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CIKM '03 Proceedings of the twelfth international conference on Information and knowledge management
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ICDE '05 Proceedings of the 21st International Conference on Data Engineering
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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
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LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
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Journal of Computer and System Sciences
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WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
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In this paper, we introduce the Significant One Counting problem. Let ε and θ be respectively some user-specified error bound and threshold. The input of the problem is a stream of bits. We need to maintain some data structure that allows us to estimate the number of 1-bits in a sliding window of size n such that whenever there are at least θn 1-bits in the window, the relative error of the estimate is guaranteed to be at most ε. When θ 1/n, our problem becomes the Basic Counting problem proposed by Datar et al. [ACM-SIAM Symposium on Discrete Algorithms (2002), pp. 635--644]. We prove that any data structure for the Significant One Counting problem must use at least Ω(1/ε log2 1/θ + log ε θn) bits of memory. We also design a data structure for the problem that matches this memory bound and supports constant query and update time. Note that for fixed θ and ε, our data structure uses O(log n) bits of memory, while any data structure for the Basic Counting problem needs Ω(log2 n) bits in the worst case.