Master Thesis - ICS

Computer Science Department
Antonis Misargopoulos
Figure 4.2: Relation
Q = R * S
The natural join operation can be written as
R ∗ S = π R >< ],
( a b −s(
a))
[
r(
a)
s(
b)
S
i j
=
where a and b are the attributes in relations R and S, respectively. The result relation Q is
given by
Q = { t | t = ( rs − s(
a))
∧ r ∈ R ∧ s ∈ S ∧ r(
a)
= s(
b)}
.
The result of
R ∗ S on the payscale attribute is the relation Q in figure 4.2.
• Semi-Join
In the conventional execution of the join operation, the resulting relation has all the
attributes of both input relations. Sometimes it is required that only the attributes of one
of the relations be present in the output relation. The semi-join operation is designed to
perform such a join [109]. It has also been defined as an operation that selects a set of
tuples from one relation that relate to one or more tuples in another relation. The
relationship is defined by the join condition. It is equivalent to the join of the two
relations followed by a project operation that results in the attributes of the second
relation being dropped from the output relation. The initial join itself may be performed
by any of the join techniques. The semi-join operation is written as
R >p
r( a)
ϑs(
b)
S = π
a
[ R ><
r(
a)
s(
b)
S]
i ϑ
,
and the result relation Q is given by
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