The Generalized Pre-Grouping Transformation: Aggregate-Query Optimization in the Presence of Dependencies

One of the recently proposed techniques for the efficient evaluation of OLAP aggregate queries is the usage of clustering access methods. These methods store the fact table of a data warehouse clustered according to the dimension hierarchies using special attributes called hierarchical surrogate keys. In the presence of these access methods new processing and optimization techniques have been recently proposed. One important such optimization technique, called Hierarchical Pre-Grouping, uses the hierarchical surrogate keys in order to aggregate the fact table tuples as early as possible and to avoid redundant joins. In this paper, we study the Pre-Grouping transformation, attempting to generalize its applicability and identify its relationship to other similar transformations. Our results include a general algebraic definition of the Pre-Grouping transformation along with the formal definition of sufficient conditions for applying the transformation. Using a provided theorem we show that Pre-Grouping can be applied in the presence of functional and inclusion dependencies without the explicit usage of hierarchical surrogate keys. An additional result of our study is the definition of the Surrogate-Join transformation that can modify a join condition using a number of dependencies. To our knowledge, Surrogate-Join does not belong to any of the Semantic Query Transformation types discussed in the past.