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type in the ER model, for every measure an
attribute is included in a relation.
eralized hierarchies.Also, unbalanced hierarchies
are further specialized in recursive hierarchies,
while generalized hierarchies include the special
case of non-covering hierarchies. For each of
these simple hierarchies, another specialization
can be applied, making them strict or non-strict.
Non-strict hierarchies relax the usual one-to-many
cardinality between parent and child levels and
allow the inclusion of child members belonging
to several parent members, i.e., the many-to-many
cardinalities. All these hierarchies are handled
as individual hierarchies with only one analysis
criterion. Finally, several individual hierarchies
may be attached to the same dimension. Depend-
ing on whether they share common levels or not,
they are called parallel dependent and parallel
independent, respectively.
However, even though many of these hierar-
chies are already implemented in commercial tools,
such as in SSAS, they are difficult to distinguish
and the proposed implementation solutions are
hard to understand. In this section, we will discuss
different kinds of hierarchies and dimensions at
the conceptual level using the MultiDim model
as described above and the conceptual schema in
Figure 3. We also include logical representation
using relational tables, and cube representation
using SSAS. We will show the expressiveness
of the conceptual multidimensional model over
other types of representations.
In Malinowski and Zimányi (2008) some
modifications were proposed to this mapping that
are irrelevant for the content of this chapter.
dIfferent kIndS of
hIerArchIeS: theIr
rePreSentAtIon And
IMPleMentAtIon
Hierarchies are very important elements in analyti-
cal processing, since they allow decision-making
users to see quantified data, i.e., measures, at
different levels of detail. However, even though
in real-world applications users need to manage
different kinds of hierarchies, the current situa-
tion is that either significant programming effort
is required in order to manage these hierarchies
or logical models are used that make difficult the
distinction of these hierarchies.
In Malinowski and Zimányi (2008) we
proposed a classification of different kinds of
hierarchies as is shown in Figure 4, where we
distinguish simple and alternative hierarchies. The
latter hierarchies are composed of two or more
simple hierarchies. Simple hierarchies include
additional types: balanced, unbalanced, and gen-
Figure 5. A balanced hierarchy: a) schema and b) examples of instances as included in Adventure-
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