There
may be several nodes with no ancestors (bottom categories). A hierarchy path is a
path of categories from a bottom category to the top category. As an example, the
graphs in the left-hand sides of Figures 1, 2, and 4 are hierarchy schemas.
The notion of hierarchy schema presented has two differences with the traditional
notion for homogeneous dimensions. First, we allow more than one bottom category.
This is important in order for the model to allow unbalanced dimensions, a
structural adaptation of dimension models, which will be explained in what follows.
Second, the model allows shortcuts in the hierarchy schema. A shortcut is a path of
length greater than one between a pair of adjacent categories. As an example, the
path Brand ??° Category ??° Department ??° All in Figure 4a is a shortcut. Shortcuts
are important in heterogeneous data because they allow the modeling of the situation
where an element skips a parent category when going to a higher category. As
an example, the city of Washington may skip the category State and go directly to
the category Country in a dimension representing locations.
Hierarchy Domain
The hierarchy domain is the graph that models the hierarchical arrangement of
the elements of the dimension. It is also formalized with a DAG, where the nodes
represent the elements of the dimension. Formally, the hierarchy domain is a pair
(M, <), where M is the set of elements of the dimension and < represents the child/
parent relationship between elements.
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