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to the schema that the designer had in mind to create, i.e., the intended integrated
schema. The relationship can be measured in terms like the amount of information
in the source schema that is also described in the integrated schema, the differ-
ence in the schema structures, etc. Three metrics have been recently proposed: the
completeness
,
minimality
,and
structurality
.
Completeness.
Let
Si
tool
represent the target schema generated by the mapping tool
and
Si
int
the intended target schema that models the integration. The notation
is
used to refer to the number of elements in a schema
S
.The
completeness
[
Batista
and Salgado
2007
] is a metric in the range of 0 to 1, which intuitively measures
how many of the concepts that can be modeled by the source schema(s) can also be
modeled by the target schema, i.e., the integration. More formally,
j
S
j
j
S
tool
\
S
int
j
Completeness
D
j
S
int
j
Minimality.
The
minimality
[
Batista and Salgado 2007
] is another metric also in the
range of 0 to 1, which indicates the redundancy that may appear in the integrated
schema. The higher the minimality, the lower the redundancy. Minimality is defined
by the following expression, which basically calculates the percentage of extra ele-
ments in the integrated schema produced by the mapping tool with respect to the
intended instance. In particular:
j
S
tool
jj
S
tool
\
S
int
j
Minimality
D
1
j
S
int
j
Structurality.
The
structurality
has been introduced [
Duchateau 2009
] to intuitively
measure the
qualities of the structure an object possesses
.
6
In the case of schemas,
this notion is translated to the set of ancestors of a schema structure. In other words,
the structurality measures whether the elements of the generated and the intended
schema contain the same set of ancestors. To compute structurality, the schemas
are viewed as trees. Let
S
int
and
S
gen
denote the intended and the generated target
schema, respectively. Assume also that in the tree representation of a schema
S
,
P
S
.e/
is the set of elements in the path from the root to the element
e
, exclusively.
The structurality of an element
e
is defined as follows:
max
0;
˛
j
P
S
int
.e/
\
P
S
gen
.e/
j
.
j
P
S
gen
.e/
jj
P
S
int
.e/
\
P
S
gen
.e/
j
/
Structurality
.e/
D
˛
j
P
S
int
.e/
j
Intuitively, the formula checks that an element shares most ancestors both in
the generated and intended integrated schemas. Besides, it takes into account the
insertion of incorrect ancestors in the generated integrated schema. Note that the
6
http://en.wiktionary.org/wiki/structurality.
