The space complexity of approximating the frequency moments
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Wavelet-based histograms for selectivity estimation
SIGMOD '98 Proceedings of the 1998 ACM SIGMOD international conference on Management of data
Wavelets for computer graphics: theory and applications
Wavelets for computer graphics: theory and applications
Wavelet synopses with error guarantees
Proceedings of the 2002 ACM SIGMOD international conference on Management of data
Data streams: algorithms and applications
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Surfing Wavelets on Streams: One-Pass Summaries for Approximate Aggregate Queries
Proceedings of the 27th International Conference on Very Large Data Bases
Deterministic wavelet thresholding for maximum-error metrics
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
SHIFT-SPLIT: I/O efficient maintenance of wavelet-transformed multidimensional data
Proceedings of the 2005 ACM SIGMOD international conference on Management of data
Wavelet synopsis for data streams: minimizing non-euclidean error
Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining
Space efficiency in synopsis construction algorithms
VLDB '05 Proceedings of the 31st international conference on Very large data bases
One-pass wavelet synopses for maximum-error metrics
VLDB '05 Proceedings of the 31st international conference on Very large data bases
Approximation algorithms for wavelet transform coding of data streams
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Fast approximate wavelet tracking on streams
EDBT'06 Proceedings of the 10th international conference on Advances in Database Technology
Optimal workload-based weighted wavelet synopses
ICDT'05 Proceedings of the 10th international conference on Database Theory
Subquadratic algorithms for workload-aware haar wavelet synopses
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
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The wavelet decomposition is a proven tool for constructing concise synopses of massive data sets and rapid changing data streams, which can be used to obtain fast approximate, with accuracy guarantees, answers. In this work we present a generic formulation for the problem of constructing optimal wavelet synopses under space constraints for various error metrics, both for static and streaming data sets. We explicitly associate existing work and categorize it according to the previous problem formulation and, further, we present our current work and identify its contributions in this context. Various interesting open problems are described and our future work directions are clearly stated.