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2 1. INTRODUCTION
Second, multidimensional models lie at the core of On-Line Analytical Processing (OLAP)
systems.Such systems provide fast answers to queries that aggregate large amounts of so-called detail
data to find overall trends, and they present the results in a multidimensional fashion. Consequently,
a multidimensional data organization has proven to be particularly well suited for OLAP. The
company behind the so-called “BI Verdict” provides an acid test for OLAP by defining OLAP as
“Fast Analysis of Shared Multidimensional Information” (FASMI) [70]. In this definition, “Fast”
refers to the expectation of response times that are within a few seconds—such response times
enable interactive, or on-line, data analysis; “Analysis” refers to the need for easy-to-use support
for business logic and statistical analyses; “Shared” suggests a need for security mechanisms and
concurrency control for multiple users; “Multidimensional” refers to the expectation that a data
model with hierarchical dimensions is used; and “Information” suggests that the system must be able
to manage all the required data as well as derived information.
Third, data mining, where the aim is to (semi-)automatically discover hitherto unknown
knowledge in large databases, is increasingly being applied to multidimensional data. Indeed, it
turns out that a multidimensional organization of data is also particularly well suited for the queries
posed by data mining tools.
In summary, the multidimensional data model is very powerful for data analysis. It is widely
used in industry, and (at least basic) knowledge of it is needed if one wants to analyze and understand
large amounts of data.
1.2 MULTIDIMENSIONAL HISTORY
Multidimensional databases do not have their origin in database technology, but they stem from
multidimensional matrix algebra, which has been used for (manual) data analyses since the late 19th
century.
During the late 1960s, two companies, IRI and Comshare, independently began the devel-
opment of systems that later turned into multidimensional database systems. The IRI Express tool
became very popular in the marketing analysis area in the late 1970s and early 1980s; it later turned
into a market-leading OLAP tool and was acquired by Oracle. Concurrently, the Comshare system
developed into System W, which was used heavily for financial planning, analysis, and reporting
during the 1980s.
In 1991,Arbor was formed with the specific purpose of creating“a multiuser,multidimensional
database server,” which resulted in the Essbase system. Arbor, now Hyperion, later licensed a basic
version of Essbase to IBM for integration into DB2. It was Arbor and Codd that in 1993 coined
the term OLAP [13].
Another significant development in the early 1990s was the advent of large data ware-
houses [48], which were typically based on relational star or snowflake schemas (see Section 2.5),
an approach to implementing multidimensional databases using relational database technology.
In 1998, Microsoft first shipped its MS OLAP Server, which was the first multidimensional
system aimed at the mass market. This led to the current situation where multidimensional systems