Daniel Baxbaxa and Maxk Sullivan. Quasi-Cubes: A Space-Efficient Way to Support Approximate Multidimensional Databases. Technical Report ISSE-TR-98-03, School of Information Technology and Engineering, George Mason University, Fairfax, Virginia, October 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....is often extremely large. Due to the high dimensionality and large data volume, it becomes impractical to evaluate the exact range query results on line. Many other algorithms have been proposed for query estimation with different precision, e.g. histogram [8] random sampling [9] Quasi Cubes [10] wavelet transform [11] etc. Vitter et al. 11] are the first to propose using wavelet transforms on data cubes to answer range sum queries. In [11, 12, 13] wavelet transforms are used to provide quick estimations of range sum queries. By storing only a few wavelet transform coefficients to ....

Daniel Baxbaxa and Maxk Sullivan. Quasi-Cubes: A Space-Efficient Way to Support Approximate Multidimensional Databases. Technical Report ISSE-TR-98-03, School of Information Technology and Engineering, George Mason University, Fairfax, Virginia, October 1998.

....dimensional space. Still, a major concern with SGRID and indeed with any clustering technique is the computational overhead and the related scalability issue. We show that this overhead is bounded and easily adjustable. We also compare SGRID and MHIST with a technique similar to the Quasi Cubes in [1]. This compares another algorithm based on regression and a fixed grid partitioning of the datacube (REGR) with the adpative SGRID and MHIST strategies and therefore is a very interesting experiment. Discriminate handling of outliers is important to avoid large errors in the approximation. A few ....

....and progressive refinement of regions satisfying a given query. The main drawback of this technique is the need to identify and quantify a distribution and this is often not possible. SGRID adapts the grid to patterns in raw data and doesn t need user intervention. Quasi Cubes were presented in [1] as an effective way to support approximate datacubes using regression. This technique is used in our experiments for comparison. We have mentioned in section 1 some of the advantages of histograms. Simple histograms are frequently used in commercial systems for selectivity estimation in query ....

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D. Barbara and M. Sullivan, "Quasi-Cubes: A space-efficient way to support approximate multidimensional databases," Technical Report, ISE Dept., September 1997.

....cells as cell(data) where the cell position is also determined by computation on the indices. Variable grid strategies use alternative algorithms to partition the space into buckets dynamically. There are recent proposals for both fixed grid and variable grid algorithms. Regression is used in [1] and wavelets in [11] These are fixed grid techniques that use the approximation function and occasionally outliers to obtain a higher adaptability. Mhist [5] is a variable grid technique. In this paper we consider mainly fixed grid techniques because, by storing only the reduced values (molap ....

....avg) Fixed Grid (fgrid) This FG technique divides the space into equal sized regions and computes the average for each one. It is stored as a multidimensional array as cell[avg] Regression (regr) We used the implementation of linear regression described in QuasiCubes [1]. This FG technique approximates the values in a column or row bucket by a line described by the parameters m and b in y = m x b and stores (m,b) in the bucket cell in a multidimensional array: cell[ m,b) Wavelets (wav) The wavelets technique (FG) was proposed for selectivity estimation ....

D. Barbara and M. Sullivan, Quasi-Cubes: A space-efficient way to support approximate multidimensional databases," Technical Report, ISE Dept., September 1997.

....and a coarse to fine traversal is proposed that improves speed by condensing cells of less that the minimum support. Histogram based approaches also exist [13] as well as approximations such as histogram compression using the DCT transform [17] or wavelets [24] Perhaps closest to our approach is [1], which uses linear regression to model DataCubes. Bitmaps are relatively recent method for efficiently computing counts from highly compressed bitmapped information about the properties of records in the database. They are exact techniques. Unlike the DataCube and Bayesian networks, bitmaps do ....

Daniel Barbara. Quasi-cubes: A space-efficient way to support approximate multidimensional databases. Technical report, ISE Dept., George Mason University, 1998.

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