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group elements into categories. A smaller number of categories might exponentially
decrease the number of cube views we may need to handle and store in star and
snowflake realizations.
We next show that the problem of testing the correctness of a rollup operation (that
is, summarizability) reduces to an inference problem over dimension constraints.
Rollup operations can be generalized rollup operations to allow the combination
of several granularities (Hurtado & Mendelzon, 2001, 2002; Hurtado et al., 2005).
This is needed since one may obtain a cube view by combining other cube views
in heterogeneous dimensions. As an example in the dimension of Figure 4 the cube
view CV[All] can be computed by the following rollup operator, that combines the
cube views CV[MusicCategory] and CV[ElectricalCategory]:
ROLLUP MusicCategory,ElectricalCategory TO All.
In order to check the correctness of this operation, two constraints about (a) disjointness
and (b) completeness of the categories combined should be inferred from
a dimension schema D that models the dimension. Therefore the problem reduces
to testing the following constraints:
(a) ?¬ ??©Product,MusicCat,All??? ??? ?¬ ??©Product,ElectricalCat,All???
(b) ??©Product,MusicCat,All??? ??? ??©Product,ElectricalCat,All???.
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