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data by exploring it from different perspectives, at different level of generaliza-
tions, and in an interactive manner. Popular architectures of OLAP systems
include
ROLAP
(relational OLAP) and
MOLAP
(multidimensional OLAP).
ROLAP provides a front-end tool that translates multidimensional queries
into corresponding SQL queries to be processed by the relational backend.
MOLAP does not rely on the relational model but instead materializes the
multidimensional views. Using MOLAP for dense parts of the data and RO-
LAP for the others leads to a hybrid architecture, namely, the
HOLAP
or
hybrid OLAP.
As a component of decision support systems, OLAP interacts with other
components, such as data mining, to assist analysts in making business de-
cisions. While data mining algorithms automatically produce knowledge in a
pre-defined form, such as association rule or classification. OLAP does not
directly generate such knowledge, but instead relies on human analysts to ob-
serve it by interpreting the query results. On the other hand, OLAP is more
flexible than data mining in the sense that analysts may obtain all kinds of
patterns and trends rather than only knowledge of fixed forms. OLAP and
data mining can also be combined to enable analysts in obtaining data mining
results from different portion of the data and at different level of generaliza-
tion [17]. The requirements on OLAP systems have been defined differently,
such as the FASMI (Fast Analysis of Shared Multidimensional Information)
test [23] and the Codd rules [9]. Some of the requirements are especially rel-
evant to this chapter. First, to make OLAP analysis an interactive process,
the OLAP system must be highly ecient in answering queries. OLAP sys-
tems usually rely on extensive pre-computations, indexing, and specialized
storage to improve the performance. Second, to allow analysts to explore the
data from different perspectives and at different level of generalization, OLAP
organizes and generalizes data along multiple dimensions and dimension hi-
erarchies. The data cube model we shall address shortly is one of the most
popular abstract models for this purpose.
Data cube was proposed as a SQL operator to support common OLAP
tasks like histograms and sub-totals [15]. Even though such tasks are usually
possible with standard SQL queries, the queries may become very complex.
The number of needed unions is exponential in the number of dimensions of
the
base
table. Such a complex query may result in many scans of the base
table, leading to poor performance. Because sub-totals are very common in
OLAP queries, it is desired to define a new operator for the collection of such
sub-totals, namely,
data cube
.
Figure 1 depicts a fictitious
data cube
. It has two
dimensions
:
time
and
organization
with three and four
attributes
, respectively. We regard
all
as a
special attribute having one attribute value
ALL
, which depends on all other
attribute values. The attributes of each dimension are partially ordered by
the
dependency relation
into a
dependency lattice
[18],thatis,
quarter
year
all
. The product of
the two lattices gives the dependency lattice of cuboids. Each element of
all
and
employee
department
branch
