Wavelet-based histograms for selectivity estimation
SIGMOD '98 Proceedings of the 1998 ACM SIGMOD international conference on Management of data
Self-tuning histograms: building histograms without looking at data
SIGMOD '99 Proceedings of the 1999 ACM SIGMOD international conference on Management of data
Fast, small-space algorithms for approximate histogram maintenance
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
How to evaluate multiple range-sum queries progressively
Proceedings of the twenty-first ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Wavelet synopses with error guarantees
Proceedings of the 2002 ACM SIGMOD international conference on Management of data
Tree-Structured Haar Transforms
Journal of Mathematical Imaging and Vision
Approximation of functions over redundant dictionaries using coherence
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal Histograms with Quality Guarantees
VLDB '98 Proceedings of the 24rd International Conference on Very Large Data Bases
ICICLES: Self-Tuning Samples for Approximate Query Answering
VLDB '00 Proceedings of the 26th International Conference on Very Large Data Bases
Extended wavelets for multiple measures
Proceedings of the 2003 ACM SIGMOD international conference on Management of data
LEO: An autonomic query optimizer for DB2
IBM Systems Journal
Deterministic wavelet thresholding for maximum-error metrics
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
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
Approximation algorithms for wavelet transform coding of data streams
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A fast approximation scheme for probabilistic wavelet synopses
SSDBM'2005 Proceedings of the 17th international conference on Scientific and statistical database management
A study on workload-aware wavelet synopses for point and range-sum queries
DOLAP '06 Proceedings of the 9th ACM international workshop on Data warehousing and OLAP
Efficient and effective explanation of change in hierarchical summaries
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
Exploiting duality in summarization with deterministic guarantees
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
Hierarchical synopses with optimal error guarantees
ACM Transactions on Database Systems (TODS)
Unrestricted wavelet synopses under maximum error bound
Proceedings of the 12th International Conference on Extending Database Technology: Advances in Database Technology
Multiplicative synopses for relative-error metrics
Proceedings of the 12th International Conference on Extending Database Technology: Advances in Database Technology
On Multidimensional Wavelet Synopses for Maximum Error Bounds
DASFAA '09 Proceedings of the 14th International Conference on Database Systems for Advanced Applications
Hierarchically compressed wavelet synopses
The VLDB Journal — The International Journal on Very Large Data Bases
Optimality and scalability in lattice histogram construction
Proceedings of the VLDB Endowment
Building data synopses within a known maximum error bound
APWeb/WAIM'07 Proceedings of the joint 9th Asia-Pacific web and 8th international conference on web-age information management conference on Advances in data and web management
Constructing optimal wavelet synopses
EDBT'06 Proceedings of the 2006 international conference on Current Trends in Database Technology
Synopses for Massive Data: Samples, Histograms, Wavelets, Sketches
Foundations and Trends in Databases
Wavelet synopsis: setting unselected coefficients to zero is not optimal
DEXA'07 Proceedings of the 18th international conference on Database and Expert Systems Applications
Finding the minimum number of elements with sum above a threshold
Information Sciences: an International Journal
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Given a signal A of N dimensions, the problem is to obtain a representation R for it that is a linear combination of vectors in the dictionary H of Haar wavelets. The quality of the representation R is determined by B, the number of vectors from H used, and δ, the error between R and A. Traditionally, δ has been the sum squared error ε R=∑i (R[i]–A[i])2, in which case, Parseval's theorem from 1799 helps solve the problem of finding the R with smallest εR in O(N) time. Recently, motivated by database applications, researchers have sought other notions of error such as workload-aware error, or $\epsilon_{{\mathbf R}}^{\pi}=\sum_i \pi[i] ({\mathbf R}[i]-{\mathbf A}[i])^2$, where π[i] is the workload or the weight for i, and maximum pointwise absolute error, eg., $\epsilon_{{\mathbf R}}^{\infty}=\max_i |{\mathbf R}[i]-{\mathbf A}[i]|$. Recent results give Ω(N2) time algorithms for finding R that minimize these errors. We present subquadratic algorithms for versions of these problems. We present a near-linear time algorithm to minimize ε Rπ when π is compressible. To minimize ε R∞, we give an O(N2−− ε) time algorithm. These algorithms follow a natural dynamic programming approach developed recently, but the improvements come from exploiting local structural properties of the Haar wavelet representations of signals we identify. Sparse approximation theory is a mature area of Mathematics that has traditionally studied signal representations with Haar wavelets. It is interesting that the past few years have seen new problems in this area motivated by Computer Science concerns: we pose a few new additional problems and some partial results.