That is, the cube view at G??™ can be correctly computed by a rollup operation
from G to G??™. In the terminology of Harinarayan et al. (1996), G??™ depends on
G. Thus dependency between granularities corresponds to reachability in the cube
dependence graph. Of course, in order for this to happen the aggregate function
involved should be distributive. A distributive aggregate function can be computed
on a set of measures by partitioning the set into disjoint subsets, aggregating each
separately, and then computing the aggregation of these partial results with another
aggregate function (which in many cases is the same function). Among the SQL
aggregate functions, COUNT, SUM, MIN, and MAX are distributive. As we will
see later, in this setting, the correctness of the rollup operations requires the dimensions
to be homogeneous.
Summarizability
The notion of summarizability was proposed to study aggregate navigation for statistical
objects and OLAP dimensions (Hurtado & Mendelzon, 2001, 2002; Hurtado et
al., 2005; Lehner et al., 1998; Lenz & Shoshani, 1997). Summarizability refers to the
conditions upon which a rollup operation defined over a single dimension is correct;
that is, summarizability corresponds to dependence for single categories taken from
a fixed dimension. For the one-dimensional case, the cube dependence graph is just
Figure 6.
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