| In OLAP warehouses, data consists of facts modeled as points in multidimensional spaces. Dimensions themselves have structure, represented by a directed graph of categories, called hierarchy schema, a set of members for each category, and a child/parent relation between members. Some facts may be the result of cube views, which are queries that aggregate raw facts to more coarse-grained spaces defined by categories taken from sets of dimensions. A powerful technique in OLAP data processing, known as aggregate navigation, is to find queries that derive the cube views from other precomputed cube views. Such queries are inferred from the hierarchy schemas involved. This inference process, however, works under a strong assumption on the regularity of the data. In particular, it does not account for structural heterogeneity, a phenomenon that arises when several dimensions representing the same conceptual entity, but with different categories, are mixed into a single dimension. In this thesis we propose a natural extension of OLAP data modeling and aggregate navigation to deal with structural heterogeneity. In our approach, cube views are extended to cope with heterogeneous dimensions. A novel class of integrity constraints, dimension constraints, that enriches the semantics of hierarchy schemas, is proposed to capture heterogeneity and to support the inference task in aggregate navigation. The modeling of heterogeneity provides significant flexibility for representing dimensions, a property not encountered in traditional models for homogeneous dimensions. We investigate this feature in our model and study the problem of restructuring dimension schemas. We present a series of results that give conceptual insight into the problem, which include a notion of dimension schema equivalence, algorithms for testing it, and a sound and complete set of transformations for the structural manipulation of dimension schemas. |
