A wavelet framework for adapting data cube views for OLAP

This article presents a method for adaptively representing multidimensional data cubes using wavelet view elements in order to more efficiently support data analysis and querying involving aggregations. The proposed method decomposes the data cubes into an indexed hierarchy of wavelet view elements. The view elements differ from traditional data cube cells in that they correspond to partial and residual aggregations of the data cube. The view elements provide highly granular building blocks for synthesizing the aggregated and range-aggregated views of the data cubes. We propose a strategy for selectively materializing alternative sets of view elements based on the patterns of access of views. We present a fast and optimal algorithm for selecting a non-expansive set of wavelet view elements that minimizes the average processing cost for supporting a population of queries of data cube views. We also present a greedy algorithm for allowing the selective materialization of a redundant set of view element sets which, for measured increases in storage capacity, further reduces processing costs. Experiments and analytic results show that the wavelet view element framework performs better in terms of lower processing and storage cost than previous methods that materialize and store redundant views for online analytical processing (OLAP).

[1]  Ronald R. Coifman,et al.  Entropy-based algorithms for best basis selection , 1992, IEEE Trans. Inf. Theory.

[2]  I. Watson,et al.  VideoZoom Spatio-temporal Video Browser , 1999 .

[3]  Nimrod Megiddo,et al.  Range queries in OLAP data cubes , 1997, SIGMOD '97.

[4]  Shih-Fu Chang,et al.  Transform features for texture classification and discrimination in large image databases , 1994, Proceedings of 1st International Conference on Image Processing.

[5]  Jeffrey D. Ullman,et al.  Index selection for OLAP , 1997, Proceedings 13th International Conference on Data Engineering.

[6]  Shih-Fu Chang,et al.  Joint adaptive space and frequency basis selection , 1997, Proceedings of International Conference on Image Processing.

[7]  Hamid Pirahesh,et al.  Data Cube: A Relational Aggregation Operator Generalizing Group-By, Cross-Tab, and Sub-Totals , 1996, Data Mining and Knowledge Discovery.

[8]  Jeffrey F. Naughton,et al.  An array-based algorithm for simultaneous multidimensional aggregates , 1997, SIGMOD '97.

[9]  Jelena Kovacevic,et al.  Wavelets and Subband Coding , 2013, Prentice Hall Signal Processing Series.

[10]  John R. Smith,et al.  Dynamic assembly of views in data cubes , 1998, PODS '98.

[11]  Edward H. Adelson,et al.  The Laplacian Pyramid as a Compact Image Code , 1983, IEEE Trans. Commun..

[12]  Jeffrey Scott Vitter,et al.  Data cube approximation and histograms via wavelets , 1998, CIKM '98.

[13]  Kenneth A. Ross,et al.  Fast Computation of Sparse Datacubes , 1997, VLDB.

[14]  Curtis E. Dyreson,et al.  Information Retrieval from an Incomplete Data Cube , 1996, VLDB.

[15]  A. Cohen.  Ten Lectures on Wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 61, I. Daubechies, SIAM, 1992, xix + 357 pp. , 1994 .

[16]  Sunita Sarawagi,et al.  Modeling multidimensional databases , 1997, Proceedings 13th International Conference on Data Engineering.

[17]  Jeffrey D. Ullman,et al.  Implementing data cubes efficiently , 1996, SIGMOD '96.

[18]  Jeffrey F. Naughton,et al.  On the Computation of Multidimensional Aggregates , 1996, VLDB.

[19]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[20]  John R. Smith,et al.  An adaptive view element framework for multi-dimensional data management , 1999, CIKM '99.