Applying OLAP Pre-Aggregation Techniques to ... - Jacobs University

98 5. Pre-Aggregation Support Beyond Basic Aggregate Operations
Figure 5.18. Workload with Poisson Distribution Along x, y, and Uniform Distribution
in t
pre-aggregation when c = 21%. For this instance of the storage space constraint, the
algorithm selected 17 pre-aggreagates. The total cost of computing the workload is
1472. In contrast, computing the workload using the original dataset incurs a cost of
1.63e + 12.
5.5.3 4D Datasets
For 4D datasets, we considered ECHAMT−42 as a typical use case found in
climate modeling. ECHAMT−42 is an energy and mass budget model developed
by the Max-Planck-Institute for Meteorology [16]. We assumed that dimensions x
and y are scaled down by the same scale value. However, the scale values along z and
t may vary according to specific analysis requirements for a given application. If we
look at the sample dimensions of ECHAMT − 42 model shown in Table 5.2, it is
clear that the dimension values along the first three dimensions are much smaller than
those of the fourth dimension (time).
In this experiment, the workload consisted of 1, 137 scaling operations referring to
4D dataset R3. We assumed that the scale vectors followed a Poisson distribution in
each of the four dimensions. The rationale behind this assumption is that scientists
are often interested in a highly selective data set and Poisson distribution fits nicely
for this data access pattern. Values of scale vectors ranged from 2 to 11 in the x, y
dimensions with a mean of 6; from 10 to 19 along the z dimension with a mean of 14,
and from 230 to 239 along t with the mean of 234. Table 5.3 shows the distribution
of the scale factors of all scaling operations in the workload.
We ran the PRE-AGGREGATESSELECTION algorithm for different values of the
storage space constraint. The minimum storage space required to support the root
node of the lattice was 1.25% of the size of the original dataset. Table 5.4 shows the