Master Thesis - ICS

Computer Science Department
Antonis Misargopoulos
As such, the result of joining two relations is a subset, proper or otherwise, of the
Cartesian product of the two relations. The tuples of either relation that do not participate
in the join are called dangling tuples [108]. The result of joining relations R and S with n
and m attributes, respectively, is a relation Q with n+m attributes. The relation Q has one
tuple for each pair of tuples from R and S that satisfies the join condition. The result
relation Q may then be defined as
Q = { t | t = rs ∧ r ∈ R ∧ s ∈ S ∧ t(
a)
ϑt(
b)}
.
The join operator is time-consuming and data-intensive operations. In the most
naive implementation, each tuple in one relation must be compared to every tuple in the
other relation. Therefore, the complexity of the operation for relations with n tuples each
is Ο ( n
2 ) . Further, the comparison of tuples requires a large number of I/O operations.
Many algorithms have been devised to execute joins intending to reduce the number of
comparisons, reduce the amount of I/O, or both.
4.2 Types of Join
Several other types of joins have been defined. Some are direct derivatives of the thetajoin;
others are combinations of the theta-join and other relational operations such as
projection. Some have been implemented as primitive operations in database
management systems, whereas others are currently found only in the database literature.
Variations of the join operation seen in database management systems and in the
literature are discussed below.
• Equi-Join
The most commonly used theta operator is the equality operator; in these cases, the join is
called an equi-join. For all other theta operators the join is called a non equi-join. The
result relation Q is defined as follows:
36