Analysing Efficiency Methods of Polynomial Complexity Degree in Multidimensional OLAP Cube Data Decomposition

Abstract

The article investigates the problems of reduction (decomposition) of multidimensional data models in terms of hypercube OLAP-structures. Describes the case when a data structure is defined by the array that slices and dices the hypercube into the odd number of subcubes, and this set of subcube structures becomes decomposed. Defines an exact upper bound for increasing a computational performance of methods to analyze OLAP-data on subcubes, which determines the decomposition approach efficiency in comparison with the OLAP-data analysis on a complete unreduced hypercube. A compared efficiency of the hypercube decomposition into two subcubes on the sets consisting of the even and odd number of subcube structures has shown that with considerable data partitioning for methods of a polynomial complexity degree the decomposition efficiency essentially is independent on this factor and rises with increasing complexity degree of methods applied.When using the mathematical methods to study decomposition (reduction) of large hyper-cubes of multidimensional data of analytical OLAP systems into subcube components, there is a need to find conditions for minimising the computational complexity of methods to solve the problems of the OLAP hyper-cube analysis during data decomposition in comparison with using these methods for analyzing large amounts of information that is accumulated directly in the hyper-cubes of multidimensional OLAP-data to establish the criteria for decreasing or increasing computational performance when applying methods on the subcube components (reduction methods) as compared to applying these methods on a hypercube (non-reduction or traditional methods), depending on one or another degree of complexity of complex methods.The article provides an accurate quantitative estimate of decreasing computational complexity of reduction methods for analyzing OLAP-cubes as compared to the non-reduction methods in the case when said methods have the polynomial complexity and the original hypercube array of data comprises the odd number of subcubes.