S., while it is false for most European
countries where no decomposition in states is defined (see Figure 6).
Definition 13: A ragged (or incomplete) hierarchy is a hierarchy where, for some
instances, the values of one or more attributes are missing (since undefined or unknown).
A ragged hierarchy is graphically denoted by marking with a dash the attributes
whose values may be missing.
As stated by Niemi (2001), within a ragged hierarchy each aggregation level has
precise and consistent semantics, but the different hierarchy instances may have
different length since one or more levels are missing, making the interlevel relationships
not uniform (the father of ???San Francisco??? belongs to level state, the father
of ???Rome??? to level nat on).
There is a noticeable difference between a ragged hierarchy and an optional arc. In
the first case we model the fact that, for some hierarchy instances, there is no value
for one or more attributes in any position of the hierarchy. Conversely, through an
Figure 6. Ragged geographic hierarchies
Conceptual Modeling Solutions for the Data Warehouse
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optional arc we model the fact that there is no value for an attribute and for all of
its descendents.
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