Improving Expressive Power in Modeling Data Warehouse and OLAP Applications - Evolving Application Domains of Data Warehousing and Mining - page 26

Simple Hierarchies For example, the Product groups hierarchy is

represented as snowflake schema in Figure 2
composed of the tables DimProduct , DimProd-
uctSubcategory , and DimProductCategory .
Note that there are more attributes in the Dim-
Product table that can be used for forming
hierarchies, e.g., Color , Size , SizeRange . In
the MultiDim level if the attribute is used for
aggregation purposes, it should be represented
as a separate level, as shown for the Product
colors hierarchy in Figure 3. If the attribute is
not represented as a hierarchy level, this indi-
cates that the user is not interested in using it
for aggregation purposes.
SSAS uses the same representation for all kinds
of hierarchies (except recursive as we will see
later) as shown for the Sales Territory hierarchy
in Figure 7a.
From the above mentioned example, we see
that the balanced hierarchies are distinguishable
at the conceptual as well as at the logical and
implementation levels. The logical level requires
the snowflake representation since otherwise users
would need to deduce the structure of a hierarchy
considering the names of attributes found in a
dimension.

Simple hierarchies represent hierarchies where
the relationship between their members can be
represented as a tree, if all its parent-child relation-
ships are one-to-many (Malinowski & Zimányi,
2008). These hierarchies include only one criterion
for analysis. Moreover, simple hierarchies are
divided into balanced, unbalanced, and general-
ized hierarchies.

Balanced Hierarchies

A balanced hierarchy is a simple hierarchy that
has only one path at the schema level, e.g., the
Product groups hierarchy in Figure 5a (also seen
in Figure 3) composed by the Product , SubCat-
egory , and Category levels. Since the parent-child
cardinality is many-to-one, at the instance level,
the members form a tree where all the branches
have the same length, i.e., all parent members have
at least one child member and a child member
belongs to only one parent member as can be
seen in Figure 5b.
Balanced hierarchies are the most common
kind of hierarchies. Their mapping to the re-
lational model gives a snowflake schema that
can be later denormalized into a star schema.

Figure 6. An unbalanced hierarchy: a) schema and b) examples of instances