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

2.2 On-Line Analytical Processing (OLAP) 25
2.1.7 Summary
Array database theory is gradually entering its consolidation phase. The notion
of arrays as functions mapping points of some hypercube-shaped domain to values
of some range set is commonly accepted. Two main modeling paradigms are used:
calculus and algebra. Multidimensional data models embed arrays into the relational
world, either by providing conceptual stubs like Array Algebra, or by adding relational
capabilities explicitly such as AQL and RAM. Notably, aggregate query processing
plays a critical role given the large volumes of the arrays. Our study shows
that pre-aggregation techniques focus only on 2D datasets, and that support is limited
to one particular operation: scaling. We distinguish the pyramid approach as the
most popular method for speeding up scaling operations on 2D datasets; despite its
known limitations such as hard-wired interpolation and lack of support for datasets of
higher dimensions. Advances on hardware graphics are enabling quicker and more
accurate visualization and navigation capabilities for raster imagery. However, little
work has been reported on how array database technology is progressively exploiting
these hardware advances. A critical gap with respect to pre-aggregation is the lack of
support for aggregate operations other than 2D scaling.
2.2 On-Line Analytical Processing (OLAP)
Data warehousing/OLAP is an application domain where complex multidimensional
aggregates on large databases have been studied intensively. Typically, a data
warehouse collects business data from one or multiple sources so that the desired financial,
marketing, and business analyses can be performed. These kinds of analyses
can detect trends and anomalies, make projections, and make business decisions
[41]. When such analysis predominantly involves aggregate queries, it is called
on-line analytical processing, or OLAP [38, 39]. To understand the mechanism of
pre-computation, the following subsections review different approaches to structuring
multidimensional data, storage mechanisms and operations in OLAP.
2.2.1 OLAP Data model
The multidimensional OLAP model begins with the observation that the factors
that influence decision-making processes are related to enterprise-specific facts, such
as sales, shipments, hospital admissions, surgeries, and so on. [68]. Instances of a
fact subsequently correspond to events that occur. For example, every sale or shipment
carried out is an event. Each fact is described by the values of a set of relevant
measures providing quantitative descriptions of events, e.g., sales receipts, amounts
shipped, hospital admission costs, and surgery times are all measures.
In OLAP, information is viewed conceptually as cubes that consist of descriptive
categories (dimensions) and quantitative values (measures) [26, 81, 69, 83]. In the scientific
literature, measures are at times called variables, metrics, properties, attributes,
or indicators. Figure 2.7 illustrates a 3D OLAP data cube where business events