Abstract
The SQL:2003 standard introduced window functions to enhance the analytical processing capabilities of SQL. The key concept of window functions is to sort the input relation and to compute the aggregate results during a scan of the sorted relation. For multi-dimensional OLAP queries with aggregation groups defined by a general theta condition an appropriate ordering does not exist, though, and hence expensive join-based solutions are required.
In this paper we introduce theta-constrained multi-dimensional aggregation (theta-MDA), which supports multi-dimensional OLAP queries with aggregation groups defined by inequalities. theta-MDA is not based on an ordering of the data relation. Instead, the tuples that shall be considered for computing an aggregate value can be determined by a general theta condition. This facilitates the formulation of complex queries, such as multi-dimensional cumulative aggregates, which are difficult to express in SQL because no appropriate ordering exists. We present algebraic transformation rules that demonstrate how the theta-MDA interacts with other operators of a multi-set algebra. Various techniques for achieving an efficient evaluation of the theta-MDA are investigated, and we integrate them into concrete evaluation algorithms and provide cost formulas. An empirical evaluation with data from the TPC-H benchmark confirms the scalability of the theta-MDA operator and shows performance improvements of up to one order of magnitude over equivalent SQL implementations.