Approximate medians and other quantiles in one pass and with limited memory
SIGMOD '98 Proceedings of the 1998 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
Data cube approximation and histograms via wavelets
Proceedings of the seventh international conference on Information and knowledge management
Approximate computation of multidimensional aggregates of sparse data using wavelets
SIGMOD '99 Proceedings of the 1999 ACM SIGMOD international conference on Management of data
Synopsis data structures for massive data sets
External memory algorithms
Optimal and approximate computation of summary statistics for range aggregates
PODS '01 Proceedings of the twentieth 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
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Approximate Query Processing Using Wavelets
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
Approximation and learning techniques in database systems
Approximation and learning techniques in database systems
"-Synopses: A System for Run-Time Management of Remote Synopses
ICDE '04 Proceedings of the 20th International Conference on Data Engineering
Deterministic wavelet thresholding for maximum-error metrics
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Optimal workload-based weighted wavelet synopses
ICDT'05 Proceedings of the 10th international conference on Database Theory
Optimal workload-based weighted wavelet synopses
Theoretical Computer Science
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
Hierarchically compressed wavelet synopses
The VLDB Journal — The International Journal on Very Large Data Bases
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
| Hi-index | 0.00 |
In recent years wavelet based synopses were shown to be effective for approximate queries in database systems. The simplest wavelet synopses are constructed by computing the Haar transform over a vector consisting of either the raw-data or the prefix-sums of the data, and using a greedy-euristic to select the wavelet coefficients that are kept in the synopsis. The greedy-heuristic is known to be optimal for point queries w.r.t. the mean-squared-error, but no similar efficient optimality result was known for range-sum queries, for which the effectiveness of such synopses was only shown experimentally. We construct an operator that defines a norm that is equivalent to the mean-squared error over all possible range-sum queries, where the norm is measured on the prefix-sums vector. We show that the Haar basis (and in fact any wavelet basis) is orthogonal w.r.t. the inner product defined by this novel operator. This allows us to use Parseval-based thresholding, and thus obtain the first linear time construction of a provably optimal wavelet synopsis for range-sum queries. We show that the new thresholding is very similar to the greedy-heuristic that is based on point queries. For the case of range-sum queries over the raw data, we define a similar operator, and show that Haar basis is not orthogonal w.r.t. the inner product defined by this operator.