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

5.5 Experimental Results 89
(a) Selected queries for pre-aggregation by image pyramids
(b) Selected queries for pre-aggregation by our pre-aggregation selection algorithm
Figure 5.4. Selected Queries for Pre-Aggregation
required by both approaches: image pyramids requires 33% additional storage space,
while our algorithm only requires 5% additional space.
Fig. 5.5(a) shows the distribution of the scale vectors for all queries in the workload.
The pre-aggregates selected by image pyramids are shown in Fig. 5.6(a). Image
pyramids allocates space for pre-aggregates with scale factors 2, 4, 8, 16, 32, 128, and
256 in each dimension. In contrast, our pre-aggregation selection algorithm selected
one query, shown in Fig. 5.6(b). Although our algorithm makes more efficient use
of storage space and computes the workload faster than image pyramids, this kind of
scenario is not likely to occur in practice. The storage overhead is simply not justified.
However, users may benefit from having a system that automatically pre-aggregates
such operations with minimum overhead, a capability that can be provided by using
our algorithm.
Step Distribution
We now consider a scenario where scale vectors are distributed in various ranges of
frequencies, i.e. in a step distribution. The PRE-AGGREGATESSELECTION algorithm
yields 6 pre-aggregates for this test, where scaling operations are executed with scale