Modelling and Optimisation Issues for Multidimensional Databases

Abstract On-Line Analytical Processing (OLAP) is a trend in database technology based on the multidimensional view of data. Although multidimensional data cubes form the basic logical data model for OLAP applications, there seems to be no agreement on a common model for cubes. In this paper we propose, a logical model for cubes based on the key observation that a cube is not a self-existing entity, but rather a view over an underlying data set. The model is powerful enough to capture all the commonly encountered OLAP operations such as selection, roll-up and drill-down, through a sound and complete algebra. We accompany our model with results on processing cube operations and provide syntactic characterisations for the problem of cube usability (i.e., the problem of using the tuples of a cube to compute another cube). As part of the solution to this problem, we have developed algorithms to check whether (a) the marginal conditions of two cubes are appropriate for a rewriting, in the presence of aggregation hierarchies and (b) an implication exists between two selection conditions that involve functionally dependent attributes (levels of aggregation in our context). For the latter, we have extended the well-known set of axioms for conjunctive query containment [Ullm89] with axioms describing the role of the functional dependencies. Finally, we present a rewriting algorithm for the cube usability problem.