.., bm be its children attributes connected by optional arcs:
??? The coverage is total if each value of a always corresponds to a value for at
least one of its children; conversely, if some values of a exist for which all of
its children are undefined, the coverage is said to be partial.
??? The coverage is disjoint if each value of a corresponds to a value for, at most,
one of its children; conversely, if some values of a exist that correspond to
values for two or more children, the coverage is said to be overlapped.
Thus, overall, there are four possible coverages, denoted by T-D, T-O, P-D, and P-O.
Figure 4 shows an example of optionality annotated with its coverage. We assume
that products can have three types: food, clothing, and household, since expiration
date and size are defined only for, respectively, food and clothing, the coverage is
partial and disjoint.
Multiple.Arcs
In most cases, as already said, hierarchies include attributes related by many-to-one
associations. On the other hand, in some situations it is necessary to include also attributes
that, for a single value taken by their father attribute, take several values.
Definition 12: A multiple arc is an arc, within a hierarchy, modeling a
many-to-many association between the two dimension attributes it connects.
Graphically, it is denoted by doubling the line that represents the arc.
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