Modeling multidimensional databases, cubes and cube operations

Online analytical processing (OLAP) is a trend in database technology, which has attracted the interest of a lot of research work. OLAP is based on the multidimensional view of data, supported either by multidimensional databases (MOLAP) or relational engines (ROLAP). We propose a model for multidimensional databases. Dimensions, dimension hierarchies and cubes are formally introduced. We also introduce cube operations (changing of levels in the dimension hierarchy, function application, navigation etc.). The approach is based on the notion of the base cube, which is used for the calculation of the results of cube operations. We focus our approach on the support of a series of operations on cubes (i.e., the preservation of the results of previous operations and the applicability of aggregate functions in a series of operations). Furthermore, we provide a mapping of the multidimensional model to the relational model and to multidimensional arrays.