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

3.3 Summary 61
Slicing
The slicing operation extracts lower-dimensional sections from a raster. Array Algebra
accomplishes the slicing operation by indicating the slicing position in the desired
dimension. Thus, the operation reduces the dimensionality of the raster by one. For
example, consider the following query:
Query 3.2.24. Slice raster A along the second dimension at position 50.
The query is solved by specifying the slicing position as follows:
3.3 Summary
MARRAY sdom(A),(x,y,z) (A[x, 50, z])
By examining the fundamental structure of Geo-raster operations and breaking
down their computational steps into a few basic Array Algebra operators, we determine
that Geo-raster operations can be broken down into the following classes:
• COND and MARRAY combined operations. Operations whose computation
requires both MARRAY and COND operators:
add, count, average, maximum, minimum, majority, minority, histogram, diversity,
variance, standard deviation, scaling, edge detection, and local drain
directions.
• MARRAY exclusive operations. Operations whose computation requires only
the MARRAY operator:
arithmetic, trigonometric, boolean, logical, overlay, reclassification, proximity,
translation, slicing, and slope/aspect.
• SORT operations. Operations whose computation requires the SORT operator:
top-k, median.
• AFFINE transformations. Special cases of affine transformations partially or
not yet supported by Array Algebra: rotation and scaling.
This classification allows us to identify a set of operations that require data summarization
and thus are potential candidates to be treated with pre-aggregation techniques:
add, count, average, maximum, minimum, majority, minority, histogram, diversity,
variance, standard deviation, scaling, edge detection, and local drain directions.
Table 3.3 summarizes the usage of Array Algebra operators for each operation
discussed in Section 3.2.