The algorithm outputs a dimension schema having the constraints that
state the homogeneity condition. If the set of frozen dimensions are precomputed,
the algorithm runs in time O(fi3), where n is the size of the hierarchy schema, and
f is the number of frozen dimensions.
The transformation described has an important property. The resulting schema is
equivalent to the original schema in that they both model the same set of hierarchy
domains (Hurtado & Gutierrez, 2004). This proves that heterogeneous schemas can
be transformed into canonical schemas without losing information capacity in the
schemas, and without breaking down the hierarchy arrangement of elements.
Handling Structural Heterogeneity in OLAP
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of Idea Group Inc. is prohibited.
Supporting Aggregate Navigation
Integrity constraints can be also used to support aggregate navigation. Hierarchy
schemas enriched with dimension constraints become an adequate abstract model
to infer the correctness of rollup operations if one may want to keep the heterogeneous
structure of the dimension. In some situations it can be useful to keep the
heterogeneous structure, since it allows fewer categories and to more naturally
Figure 11. An unbalanced dimension: (a) hierarchy schema; (b) rollup relation
(a)
(b)
4 Hurtado & Gutierrez
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