Database Reference
In-Depth Information
It is easy to show, based on the case 3 of Example
34
and Definition
49
, that this
atomic transition
α
∗
===
OP
BA
⇒
M
α
1
, which represents the deleting of tuples
t
i
⊆
t
i
in the
database
B
(based on deletion of
n
of its views,
(V
i
,t
i
)
∈S
B
for
i
=
1
,...,n
)of
k
different relations
r
1
,...,r
k
∈
B
by the deleting operations 'DELETE FROM
r
i
WHERE
C
i
',
i
1
,...,k
, can be represented in the
DB
category as the morphisms
f
D
=
η
P
n
◦···◦
P
1
(
B
)
:
α
∗
(
B
)
→
α
1
(
B
)
.
This morphism in
DB
is represented as a horizontal arrow from the instance
database
B
=
α
∗
(
)
in the diagram on the left ellipse, which represents the image
of the data mapping graph
G
for the initial interpretation
α
∗
, into the new updated
instance
α
1
(
=
B
in the diagram on the right ellipse (which represents
the image of the data mapping graph
G
for the resulting interpretation
α
1
).
B
)
of a schema
B
Note that enlarged horizontal arrows represent the satisfied morphisms in
DB
while the enlarged vertical arrow is a satisfied arrow of a database mapping graph
G
if
t
i
=
1
,...,n
.This
backward propagation
is denoted
by the cone of ingoing arrows into the node (schema)
t
i
for all
(V
i
,t
i
)
∈S
B
for
i
=
A
in the diagram above).
7.2.2 Insertion by Minimal Side-Effects
α
∗
(
In an insertion minimization, the input is a database
B
=
B
)
, a model of a schema
B
B
, and a set of tuples to be inserted
t
.
The view side-effect minimization is an algorithm for providing a set
=
, a query
q
B
i
(
x
i
)
,aview
V
q
B
i
(
x
i
)
B
⊆
B
in
order to minimize
|
V
|
such that for the same query executed over updated database
B
=
∪
B
B
B
(which is another model of database schema
) the obtained view is
V
t)
. In other words, we wish to find a set of tuples in
B
whose addition
will insert
t
while minimizing the number of other tuples inserted into the view
V
.
We can define this
view insertion translation
(VIT) as follows:
∪
(
V
∪
