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

Chapter 5
Pre-Aggregation Support Beyond
Basic Aggregate Operations
In this chapter we investigate the problem of offering pre-aggregation support to nonstandard
aggregate operations such as scaling and edge detection. We discuss issues
found while attempting to provide a pre-aggregation framework for all non-standard
aggregate operations. We then justify our reasons for focusing on scaling operations.
We adapt the framework and cost model presented in Chapter 4 to support scaling operations.
Finally, we discuss the efficiency of our algorithms based on a performance
analysis covering 2D, 3D and 4D datasets. We indicate how our approach generalizes
and outperforms well-known 2D image pyramids widely used in Web mapping.
5.1 Non-Standard Aggregate Operations
As shown in Chapter 2, aggregate operations are not limited to queries using basic
aggregate functions. In the GIS domain, operations such as scaling, edge detection,
and those related to terrain analysis also require data summarization and may therefore
benefit from pre-aggregation. See Table 3.3 for a complete list of operations requiring
summarization. Finding a general pre-aggregation approach for computing those
kinds of operations, however, it introduces additional complications when compared
to finding pre-aggregates using basic aggregate functions.
Basic aggregate functions each consolidate the values of a group of cells and return
a scalar value. The value may represent the total sum, the number of cells, the maximum
or minimum cell value, or the average value of the affected cells. Affected cells
are determined by the spatial domain defined in the predicate of the query. In contrast,
the computation of a scaling operation may require consolidating the cell values of a
group of cells to calculate each cell value in the output raster. The affected cells are
determined by both the resampling method and scale vector as described in Chapter 3.
A similar situation occurs with edge detection. The affected cells are determined by
the size and values of the applied Sobel filter. For simplicity, we refer to those kinds
of operations as non-standard aggregate operations.
There is an important concern that must now be taken into account. From Chap-
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