Optimization for queries with holistic functions

The early grouping technique is a method for optimizing aggregate queries. It provides more opportunities for the query optimizers to find optimal plans because all possible placements of the GROUP-BY operators in the query trees are considered during the optimization process. However, to employ this technique, the aggregate function in the query must be distributive. Using this property, the evaluation of the GROUP-BY operator can be started without all the relations being joined (i.e. without the entire input being constructed). For queries with non-distributive (or holistic) aggregate functions, the evaluation of the GROUP-BY operators has to wait until the entire input is formed, since these aggregate functions cannot be decomposed into sub-aggregate functions and their computations depend on the entire set of the input. As a result, to evaluate queries with non-distributive aggregate functions, all the relations must be joined before the GROUP-BY operator can be evaluated. Although the decomposition of the holistic aggregate functions is not obvious, we compute auxiliary information (the count) on the subsets of the input data, which is later used by the consolidating function as an aid to compute the original holistic aggregate functions. Since the computation of the count [using the function COUNT ()] is distributive, this auxiliary information can be computed before all the relations are joined. By extending the ability of the early grouping technique to handle aggregate queries with holistic aggregate functions, we provide the optimizers with more opportunities to find optimal plans.