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

2.1 Array Databases 17
Figure 2.2 shows a graphical classification of grid functions according to map algebra.
Figure 2.2. Map Algebra Functions
Map algebra is primarily oriented toward 2D static data. Each layer is associated
with a particular moment or period of time, and analytical operations are intended to
deal with spatial relationships. In its original form, map algebra was never intended
to handle spatial data with a temporal component.
2.1.3 Multidimensional Data Models
AQL
Libkin et al. [63] presented an array data model called AQL that embeds array support
into specific nested relational calculus and treats arrays as functions rather than
collection types. The AQL data model combines complex objects such as sets, bags,
and lists with multidimensional arrays. To express complex object values, the core
calculus on which AQL is based has been extended with concepts such as comprehensions,
pattern matching, and block structures that strengthen the expressive power of
the language. Still, AQL does not provide a declarative mechanism to define the order
in which queries manipulate data.
Array Manipulation Language (AML)
AML is a query language for multidimensional array data [80]. The model is aimed
towards applications in image databases, particularly for remote sensing, but it is customizable
to support a wide variety of application domains. An interesting characteristic
of this language is the use of bit patterns, an array indexing mechanism that
allows for a more powerful access structure to arrays. AML’s algebra consists of three
operators that enable the manipulation of arrays: subsample, merge, and apply. Each
operator takes one or more arrays as arguments, and produces an array as result. Subsample
is a unary operator that eliminates cells from an array by cutting out slices.
Merge is a binary operator that combines two arrays defined over the same domain.
The Apply operator applies a user-defined function to an array, thereby producing a
new array. All AML operators take bit patterns as parameters.