On-line analytical processing provides multidimensional data analysis, through extensive computation based on aggregation, along many dimensions and hierarchies. To accelerate query-response time, pre-computed results are often stored for later retrieval. This adds a prohibitive storage overhead when applied to the whole set of aggregates. In this paper we describe a novel approach which provides the means for the efficient selection, computation and storage of multidimensional aggregates. The approach identifies redundant aggregates, by inspection, thus allowing only distinct aggregates to be computed and stored. We propose extensions to relational theory and also present new algorithms for implementing the approach, providing a solution which is both scalable and low in complexity. The experiments were conducted using real and synthetic datasets and demonstrate that significant savings in computation time and storage space can be achieved when redundant aggregates are eliminated. Savings have also been shown to increase as dimensionality increases. Finally, the implications of this work affect the indexing and maintenance of views and the user interface.