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are composed of several hierarchies accounting for different analysis criteria.
When parallel hierarchies share a level, they are called dependent; otherwise,
they are called independent. All the above hierarchies can be either strict
or nonstrict, depending on whether they contain many-to-many relationships
between parent and child levels. Nonstrict hierarchies define graphs at the
instance level. We then presented advanced modeling aspects, namely, facts
with multiple granularities and many-to-many dimensions. These often arise
in practice but are frequently overlooked in the data warehouse literature.
In Chap.
5
, we will study how all these concepts can be implemented at the
logical level. We concluded showing how the OLAP operations introduced in
Chap.
3
can be applied over the conceptual model, using as example a set of
queries over the Northwind data cube.
4.6 Bibliographic Notes
Conceptual data warehouse design was first introduced by Golfarelli et al.
[
65
]. A detailed description of conceptual multidimensional models can be
found in [
203
]. Many multidimensional models have been proposed in the
literature. Some of them provide graphical representations based on the ER
model (e.g., [
184
,
205
]), as is the case of the MultiDim model, while others
are based on UML (e.g., [
1
,
120
,
204
]). Other models propose new notations
(e.g., [
67
,
88
,
207
]), while others do not refer to a graphical representation
(e.g., [
86
,
160
,
166
]). There is great variation in the kinds of hierarchies
supported by current multidimensional models. A detailed comparison of
how the various multidimensional models cope with hierarchies is given in
[
126
,
158
]. Multidimensional normal forms were defined in [
113
,
114
].
The Object Management Group (OMG) has proposed the Common Ware-
house Model (CWM)
1
as a standard for representing data warehouse and
OLAP systems. This model provides a framework for representing metadata
about data sources, data targets, transformations, and analysis, in addition
to processes and operations for the creation and management of warehouse
data. The CWM model is represented as a layered structure consisting of
a number of submodels. One of these submodels, the resource layer, defines
models that can be used for representing data in data warehouses and includes
the relational model as one of them. Further, the analysis layer presents a
metamodel for OLAP, which includes the concepts of a dimension and a
hierarchy. In the CWM, it is possible to represent all of the kinds of hierarchies
presented in this chapter.
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