Ten lectures on wavelets
Rank $M$ Wavelets with $N$ Vanishing Moments
SIAM Journal on Matrix Analysis and Applications
Range queries in OLAP data cubes
SIGMOD '97 Proceedings of the 1997 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
Using wavelet decomposition to support progressive and approximate range-sum queries over data cubes
Proceedings of the ninth international conference on Information and knowledge management
ProPolyne: A Fast Wavelet-Based Algorithm for Progressive Evaluation of Polynomial Range-Sum Queries
EDBT '02 Proceedings of the 8th International Conference on Extending Database Technology: Advances in Database Technology
Data Cube: A Relational Aggregation Operator Generalizing Group-By, Cross-Tab, and Sub-Total
ICDE '96 Proceedings of the Twelfth International Conference on Data Engineering
Hierarchical Prefix Cubes for Range-Sum Queries
VLDB '99 Proceedings of the 25th International Conference on Very Large Data Bases
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
Relative Prefix Sums: An Efficient Approach for Querying Dynamic OLAP Data Cubes
ICDE '99 Proceedings of the 15th International Conference on Data Engineering
Attribute value reordering for efficient hybrid OLAP
DOLAP '03 Proceedings of the 6th ACM international workshop on Data warehousing and OLAP
Fast range query estimation by N-level tree histograms
Data & Knowledge Engineering
SHIFT-SPLIT: I/O efficient maintenance of wavelet-transformed multidimensional data
Proceedings of the 2005 ACM SIGMOD international conference on Management of data
An Optimal Linear Time Algorithm for Quasi-Monotonic Segmentation
ICDM '05 Proceedings of the Fifth IEEE International Conference on Data Mining
Supporting mobile decision making with association rules and multi-layered caching
Decision Support Systems
Hierarchical bin buffering: Online local moments for dynamic external memory arrays
ACM Transactions on Algorithms (TALG)
Business intelligence for small and middle-sized entreprises
ACM SIGMOD Record
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Data mining and related applications often rely on extensive range sum queries and thus, it is important for these queries to scale well. Range sum queries in data cubes can be achieved in time O(1) using prefix sum aggregates but prefix sum update costs are proportional to the size of the data cube O(nd). Using the Relative Prefix Sum (RPS) method, the update costs can be reduced to the root of the size of the data cube O(nd/2). We present a new family of base b wavelet algorithms further reducing the update costs to O (nd/β) for β as large as we want while preserving constant-time queries. We also show that this approach leads to O(logd n) query and update methods twice as fast as Haarbased methods. Moreover, since these new methods are pyramidal, they provide incrementally improving estimates.