Sequential sampling procedures for query size estimation
SIGMOD '92 Proceedings of the 1992 ACM SIGMOD international conference on Management of data
Randomized algorithms
SIGMOD '97 Proceedings of the 1997 ACM SIGMOD international conference on Management of data
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
Approximate computation of multidimensional aggregates of sparse data using wavelets
SIGMOD '99 Proceedings of the 1999 ACM SIGMOD international conference on Management of data
Join synopses for approximate query answering
SIGMOD '99 Proceedings of the 1999 ACM SIGMOD international conference on Management of data
WALRUS: a similarity retrieval algorithm for image databases
SIGMOD '99 Proceedings of the 1999 ACM SIGMOD international conference on Management of data
Approximating multi-dimensional aggregate range queries over real attributes
SIGMOD '00 Proceedings of the 2000 ACM SIGMOD international conference on Management of data
Independence is good: dependency-based histogram synopses for high-dimensional data
SIGMOD '01 Proceedings of the 2001 ACM SIGMOD international conference on Management of data
Wavelet synopses with error guarantees
Proceedings of the 2002 ACM SIGMOD international conference on Management of data
Approximate Query Processing Using Wavelets
VLDB '00 Proceedings of the 26th International Conference on Very Large Data Bases
Dynamic Maintenance of Wavelet-Based Histograms
VLDB '00 Proceedings of the 26th International Conference on Very Large Data Bases
Surfing Wavelets on Streams: One-Pass Summaries for Approximate Aggregate Queries
Proceedings of the 27th International Conference on Very Large Data Bases
Extended wavelets for multiple measures
Proceedings of the 2003 ACM SIGMOD international conference on Management of data
Probabilistic wavelet synopses
ACM Transactions on Database Systems (TODS)
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
Proceedings of the 8th ACM international workshop on Data warehousing and OLAP
Approximation algorithms for wavelet transform coding of data streams
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Wavelet synopses for general error metrics
ACM Transactions on Database Systems (TODS) - Special Issue: SIGMOD/PODS 2004
Compact histograms for hierarchical identifiers
VLDB '06 Proceedings of the 32nd international conference on Very large data bases
Data streams: algorithms and applications
Foundations and Trends® in Theoretical Computer Science
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
Optimal workload-based weighted wavelet synopses
Theoretical Computer Science
A Note on Linear Time Algorithms for Maximum Error Histograms
IEEE Transactions on Knowledge and Data Engineering
Inner-product based wavelet synopses for range-sum queries
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Efficient Process of Top-k Range-Sum Queries over Multiple Streams with Minimized Global Error
IEEE Transactions on Knowledge and Data Engineering
DAWN: an efficient framework of DCT for data with error estimation
The VLDB Journal — The International Journal on Very Large Data Bases
Hierarchical synopses with optimal error guarantees
ACM Transactions on Database Systems (TODS)
Wavelet synopsis for hierarchical range queries with workloads
The VLDB Journal — The International Journal on Very Large Data Bases
The VLDB Journal — The International Journal on Very Large Data Bases
Unrestricted wavelet synopses under maximum error bound
Proceedings of the 12th International Conference on Extending Database Technology: Advances in Database Technology
LCS-Hist: taming massive high-dimensional data cube compression
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
AMID: Approximation of MultI-measured Data using SVD
Information Sciences: an International Journal
GAMPS: compressing multi sensor data by grouping and amplitude scaling
Proceedings of the 2009 ACM SIGMOD International Conference on Management of data
A wavelet transform for efficient consolidation of sensor relations with quality guarantees
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
ISMIS'08 Proceedings of the 17th international conference on Foundations of intelligent systems
Effective processing of continuous group-by aggregate queries in sensor networks
Journal of Systems and Software
Synopses for probabilistic data over large domains
Proceedings of the 14th International Conference on Extending Database Technology
Location-aware type ahead search on spatial databases: semantics and efficiency
Proceedings of the 2011 ACM SIGMOD International Conference on Management of data
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
Constructing optimal wavelet synopses
EDBT'06 Proceedings of the 2006 international conference on Current Trends in Database Technology
An adaptive algorithm for online time series segmentation with error bound guarantee
Proceedings of the 15th International Conference on Extending Database Technology
Synopses for Massive Data: Samples, Histograms, Wavelets, Sketches
Foundations and Trends in Databases
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Several studies have demonstrated the effectiveness of the wavelet, decomposition as a tool for reducing large amounts of data down to compact, wavelet synopses that can be used to obtain fast, accurate approximate answers to user queries. While conventional wavelet synopses are based on greedily minimizing the overall root-mean-squared (i.e., L2-norm) error in the data approximation, recent work has demonstrated that such synopses can suffer from important problems, including severe bias and wide variance in the quality of the data reconstruction, and lack of non-trivial guarantees for individual approximate answers. As a result, probabilistic thresholding schemes have been recently proposed as a means of building wavelet synopses that try to probabilistically control other approximation-error metrics, such as the maximum relative error in data-value reconstruction, which is arguably the most important for approximate query answers and meaningful error guarantees.One of the main open problems posed by this earlier work is whether it is possible to design efficient deterministic wavelet-thresholding algorithms for minimizing non-L2 error metrics that are relevant to approximate query processing systems, such as maximum relative or maximum absolute error. Obviously, such algorithms can guarantee better wavelet synopses and avoid the pitfalls of probabilistic techniques (e.g., "bad" coin-flip sequences) leading to poor solutions. In this paper, we address this problem and propose novel, computationally efficient schemes for deterministic wavelet thresholding with the objective of optimizing maximum-error metrics. We introduce an optimal low polynomial-time algorithm for one-dimensional wavelet thresholding--our algorithm is based on a new Dynamic-Programming (DP) formulation, and can be employed to minimize the maximum relative or absolute error in the data reconstruction. Unfortunately, directly extending our one-dimensional DP algorithm to multi-dimensional wavelets results in a super-exponential increase in time complexity with the data dimensionality. Thus, we also introduce novel, polynomial-time approximation schemes (with tunable approximation guarantees for the target maximum-error metric) for deterministic wavelet thresholding in multiple dimensions.