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

86 5. Pre-Aggregation Support Beyond Basic Aggregate Operations
• Dataset R2. Consists of a 3D raster object with spatial domain [0 : 11299, 0 :
10459, 0 : 3650]. The dataset contains 3214 tiles, each with a spatial domain of
[0 : 512, 0 : 512, 0 : 512]. The total number of cells composing the raster object
is 43 trillions.
• Dataset R3. Consists of a 4D raster object with spatial domain [0 : 10150, 0 :
7259, 0 : 2430, 0 : 75640]. The dataset contains 197,070 tiles, each with a
spatial domain of [0 : 512, 0 : 512, 0 : 512, 0 : 512]. The total number of cells
composing the raster object is 1.35e+16.
In the rest of this section, we present the results of our experiments according to
the dimensionality of the data.
5.5.1 2D Datasets
In this experiment the workload consisted of 12800 scaling operations defined for
dataset R1.
Uniform Distribution
The scaling vectors of the queries in the workload were uniformly distributed. Scale
vectors were integers ranging from 2 to 256. Per observations in practice, we assumed
that both dimensions were coupled. We considered a storage space constraint of 35%,
which is slightly higher than the additional storage space taken by image pyramids.
The PRE-AGGREGATESSELECTION algorithm yields 12 pre-aggregates for this test
where we executed scaling operations with scale vectors 2, 4, 6, 11, 15, 22, 32, 46, 67, 95,
137 and 182. The cost of computing the workload using these pre-aggregates is
18, 565. In contrast, image pyramids selects scaling operations with scale vectors:
2, 4, 8, 16, 32, 64, 128, and 256, and requires 33% additional storage space. Image
pyramids computes the workload at a cost of 29, 166. The results of this experiment
show that the pre-aggregates selected by our algorithm provide an improved performance
for scaling operations over image pyramids. The cost of computing the workload
using our algorithm is 36% less than that incurred by image pyramids, at a price
of 2% additional storage space.
Fig. 5.2(a) shows the distribution of the scale vectors of all queries in the workload.
The pre-aggregates selected by image pyramids and our pre-aggregation selection algorithm
are shown in Fig. 5.2(b) and 5.2(c), respectively.
Poisson Distribution
The workload for this experiment consisted of scaling operations where the scale vectors
had a Poisson distribution, and the mean value of the scale vector equaled 50. The
PRE-AGGREGATES-SELECTION algorithm yields 33 pre-aggregates for this test that
executed scaling operations using scale vectors from 34 to 66. The cost of computing
the workload using these pre-aggregates is 42, 455. In contrast, image pyramids