A cube dependence graph
40 Hurtado & Gutierrez
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the hierarchy schema, and consequently in traditional OLAP models (homogeneous
dimensions) summarizability is equivalent to reachability in the hierarchy schema.
Anomalies Caused by Heterogeneity
The main role of the schema of a dimension is to guide users in the application
of OLAP operations and to prevent users from formulating erroneous operations.
Heterogeneity may turn hierarchy schemas into entangled structures for visualizing
OLAP data and formulating correct aggregate operations.
Complexity of Heterogeneous Dimensions
In the presence of heterogeneity the hierarchy schema may become awkward. A
heterogeneous dimension comprising a dozen product types may carry more than
100 categories, and some of them would be empty for almost every element of the
dimension (Kimball, 1996). The problem is not only that some categories are not
valid for some elements, but that different combinations of categories and paths
may not be valid, and the hierarchy schema does not provide enough semantics
to understand this. Consequently, it may be difficult for users to understand the
hierarchy domain by visualizing the hierarchy schema, as can be observed in the
dimension of Figure 7.
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