This dimension is a more complex heterogeneous version
that models electronic products and CDs of a retailer.
Implications for Summarizability
In a heterogeneous dimension the rollup operations are not necessarily correct.
Stated in OLAP terminology, in heterogeneous dimensions summarizability does
not necessarily correspond to reachability in the hierarchy schema. That is, we cannot
infer the correctness of rollup operations just by viewing the hierarchy schema.
As an example, the rollup operation
ROLLUP Brand TO Category
is not correct in the dimension of Figure 4, since some products would not be
counted in the derivation. In general, under heterogeneity, hierarchy schemas may
have inconsistent paths, that is, paths c1 ??° c2 ??° c3 ??° ... cn in the hierarchy schema
for which some category i+1 is not summarizable from its preceding category i in
the path. As an example, the following hierarchy path is inconsistent in the dimension
of Figure 7:
Handling Structural Heterogeneity in OLAP 4
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Product ??° ElectricalCategory ??° Category ??° Department ??° All.
In contrast, the path Product ??° Brand ??° Company ??° All is consistent for the same
dimension.
Figure 7. A heterogeneous dimension: (a) hierarchy schema; (b) hierarchy domain
(a)
(b)
42 Hurtado & Gutierrez
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