Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
The space complexity of approximating the frequency moments
Journal of Computer and System Sciences
Sampling from a moving window over streaming data
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
Maintaining Stream Statistics over Sliding Windows
SIAM Journal on Computing
Estimating Rarity and Similarity over Data Stream Windows
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Maintaining variance and k-medians over data stream windows
Proceedings of the twenty-second ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Correlating synchronous and asynchronous data streams
Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
An improved data stream algorithm for frequency moments
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
An information statistics approach to data stream and communication complexity
Journal of Computer and System Sciences - Special issue on FOCS 2002
Moment: Maintaining Closed Frequent Itemsets over a Stream Sliding Window
ICDM '04 Proceedings of the Fourth IEEE International Conference on Data Mining
Approximate counts and quantiles over sliding windows
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Optimal approximations of the frequency moments of data streams
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Simpler algorithm for estimating frequency moments of data streams
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Maintaining significant stream statistics over sliding windows
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
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Sketching asynchronous streams over a sliding window
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Stable distributions, pseudorandom generators, embeddings, and data stream computation
Journal of the ACM (JACM)
Data streams: algorithms and applications
Foundations and Trends® in Theoretical Computer Science
Data Streams: Models and Algorithms (Advances in Database Systems)
Data Streams: Models and Algorithms (Advances in Database Systems)
Longest increasing subsequences in windows based on canonical antichain partition
Theoretical Computer Science
Time-decaying sketches for sensor data aggregation
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Estimating the sortedness of a data stream
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal sampling from sliding windows
Proceedings of the twenty-eighth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
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In the streaming model, elements arrive sequentially and can be observed only once. Maintaining statistics and aggregates is an important and nontrivial task in this model. These tasks become even more challenging in the sliding windows model, where statistics must be maintained only over the most recent $n$ elements. In their pioneering paper, Datar et al. [SIAM J. Comput., 31 (2002), pp. 1794-1813] presented the exponential histogram, an effective method for estimating statistics on sliding windows. In this paper we present a novel smooth histogram method that is more general and achieves stronger bounds than the exponential histogram. In particular, the smooth histogram method improves the approximation error rate obtained via exponential histograms. Furthermore, the smooth histogram method not only captures and improves multiple previous results on sliding windows but also extends the class of functions that can be approximated on sliding windows. In particular, we provide the first approximation algorithms for the following functions: $L_p$ norms, frequency moments, the length of the increasing subsequence, and the geometric mean.