Improving Expressive Power in Modeling Data Warehouse and OLAP Applications - Evolving Application Domains of Data Warehousing and Mining - page 18

formed by the City , County , and State attributes.
However, the schema in Figure 1 does not reflect
the real situation about the geographical division
of a country where some states do not divide
themselves in counties. In addition, the Sales terri-
tory table includes a hierarchy composed of Sales
territory region , Sales territory country , and Sales
territory group ; nevertheless, the schema in Figure
1 does not represent the hierarchy clearly since
some countries are not partitioned into regions,
i.e., this attribute will have a null value for those
countries that do not have regions. .
A similar situation has occurred with different
kinds of dimensions. They have been proposed
mainly by practitioners and implemented in
some commercial tools due to a growing interest
in having DW and OLAP systems in different
application areas. Nevertheless, these different
kinds of dimensions are difficult to represent
using models of current DW and OLAP systems
and the proposed implementation solutions are
not clear for non-experienced users. An example
is the so-called role-playing dimension (the Time
table in Figure 1) which participates in the fact
table several times playing different roles, i.e., in
the figure indicating a date of requesting a product
and paying for it.
The above-mentioned problems have brought
on since the necessity of building DW systems
that fulfill user expectations was ahead of formal
approaches such as the ones we had for opera-
tional databases (List, Bruckner, Machaczek &
Schiefer, 2002). In particular, even though DWs
are databases dedicated to analytical purposes, the
traditional design phases used in operational data-
bases (i.e., requirements specification, conceptual,
logical, and physical modeling) are not applied
to the DW design. The latter process typically
starts at a logical level skipping the conceptual
level design. This situation occurs since currently
there is no a well-established conceptual model
for multidimensional data, even though several
proposals have been emerged.

The advantage of using a conceptual model
for database design has been acknowledged for
several decades. Conceptual schemas are typically
expressed using the ER model or the Unified
Modeling Language (UML). They facilitate com-
munication between users and designers, given
that they do not require knowledge about specific
features of the underlying implementation system.
The conceptual schemas are also more stable due
to the fact that they focus on user requirements
and do not change when the target implementation
platform changes.
Further, operational databases are usually de-
veloped using a relational model that has a strong
formalism and many years of accumulated experi-
ence in their development. On the other hand, the
multidimensional model was proposed in response
to complex aggregation queries with little scien-
tific support for establishing the correctness of
such a model.Although some scientific works have
formally approached the multidimensional model
by proposing, among others, aggregation operators
(e.g., Gray et al., 1998), summarizability condi-
tions (Lenz & Shoshani, 1997), multidimensional
normal forms (e.g., Lehner,Albrecht & Wedekind,
1998; J. Lechtenbörger & G. Vossen, 2003), and
conditions for handling structural heterogeneity
in hierarchies (Hurtado & Gutierrez, 2007), the
usual practice in multidimensional modeling is to
use “intuition” or application-ready solutions, such
as proposed by Kimball and Ross (2002).
Therefore, the situation is twofold: on the one
hand, there is a lack of a well-accepted conceptual
multidimensional model as well as a formality
and standardization of concepts related to mul-
tidimensional model; on the other hand, there
is the major influence of practitioners that are
proposing specific solutions for developing DWs
in different application areas and of commercial
tools that include solutions for managing different
multidimensional elements.
In this chapter we refer to different kinds of
hierarchies and dimensions already classified in