Each category represents a level of abstraction upon which facts are
aggregated. For example, in a dimension that models the products of a retailer,
shown in Figure 1, we have a category Product which rolls up to a Brand category,
which in turn rolls up to the top category All. The elements of the dimensions are
grouped into the categories and connected by a child/parent relationship, which
yields a hierarchy of elements which parallels the hierarchy of categories. Following
terminology from Jagadish et al. (1999) and from Hurtado et al. (2005), we refer
to the hierarchies of categories and elements respectively as hierarchy schema and
hierarchy domain.
Each element of a dimension can be viewed as having a structure on its own. This
structure of an element is the subgraph of the hierarchy schema induced by the
ancestors of that element and their child/parent relationship. In our example of
Figure 1, the Product element p1 has the entire hierarchy schema as structure, and
Handling Structural Heterogeneity in OLAP 2
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the Brand element b2 only has the substructure composed by the categories Brand
and All. Nevertheless, all the elements in the same category have the same structure
in this dimension.
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