On the computation of multidimensional aggregates

Abstract

At the heart of all OLAP or multidimensional data analysis applications is the ability to simultaneously aggregate across many sets of dimensions. Computing multidimensional aggregates is a performance bottleneck for these applications. This chapter presents fast algorithms for computing a collection of group-bys. We focus on a special case of the aggregation problem — computation of the CUBE operator. The CUBE operator requires computing group-bys on all possible combinations of a list of attributes, and is equivalent to the union of a number of standard group-by operations. We show how the structure of CUBE computation can be viewed in terms of a hierarchy of group-by operations. Our algorithms extend sort-based and hash-based grouping methods with several optimizations, like combining common operations across multiple group-bys, caching, and using pre-computed group-bys for computing other group-bys. Empirical evaluation shows that the resulting algorithms give much better performance compared to straightforward methods. This chapter combines work done concurrently on computing the data cube by two different teams as reported in [SAG96] and [AAD+96b].