Database Modeling & Design Fourth Edition- P38: Database technology has evolved rapidly in the three decades since the rise and eventual dominance of relational database systems. While many specialized database systems (object-oriented, spatial, multimedia, etc.) have found substantial user communities in the science and engineering fields, relational systems remain the dominant database technology for business enterprises. | 172 CHAPTER 8 Business Intelligence a 3 lefts Pa 3 C3 1 bin a 2 lefts P2 .3 C2 3 bins a 1 left Pi 3 C1 3 bins a 0 lefts P0 3 C0 1 bin Figure Example of a binomial multifractal distribution tree The values of P and k can be estimated based on sample data. The algorithm used in Faloutsos Matias and Silberschatz 1996 has three inputs the number of rows in the sample the frequency of the most commonly occurring value and the number of distinct aggregate rows in the sample. The value of P is calculated based on the frequency of the most commonly occurring value. They begin with k P Log2 Distinct rows in sample and then adjust k upwards recalculating P until a good fit to the number of distinct rows in the sample is found. Other distribution models can be utilized to predict the size of a view based on sample data. For example the use of the Pareto distribution model has been explored Nadeau and Teorey 2003 . Another possibility is to find the best fit to the sample data for multiple distribution models calculate which model is most likely to produce the given sample data and then use that model to predict the number of rows for the full data set. This would require calculation for each distribution model considered but should generally result in more accurate estimates. Online Analytical Processing OLAP 173 Selection of Materialized Views Most of the published works on the problem of materialized view selection are based on the hypercube lattice structure Harinarayan Rajara-man and Ullman 1996 . The hypercube lattice structure is a special case of the product graph structure where the number of hierarchical levels for each dimension is two. Each dimension can either be included or excluded from a given view. Thus the nodes in a hypercube lattice structure represent the power set of the dimensions. Figure illustrates the hypercube lattice structure with an example Harinarayan
