Relational Algebra
SELECT(σ)
Projection(π)
Rename (ρ)
Union operation (υ)
Set Difference (-)
Intersection
Cartesian product(X)
Join Operations
Inner Join:
Theta Join:
EQUI join:
NATURAL JOIN (⋈)
OUTER JOIN
Left Outer Join(A B)
Right Outer Join: ( A B )
Full Outer Join: ( A B)
Basic SQL Relational Algebra Operations
Relational Algebra devided in various groups
Unary Relational Operations
SELECT (symbol: σ) PROJECT (symbol: π) RENAME (symbol: ρ)
Relational Algebra Operations From Set Theory
UNION (υ) INTERSECTION ( ), DIFFERENCE (-) CARTESIAN PRODUCT ( x )
Binary Relational Operations
JOIN DIVISION
Let’s study them in detail with solutions:
SELECT (σ)
The SELECT operation is used for selecting a subset of the tuples according to a given selection condition. Sigma(σ)Symbol denotes it. It is used as an expression to choose tuples which meet the selection condition. Select operator selects tuples that satisfy a given predicate. σp(r) σ is the predicate r stands for relation which is the name of the table p is prepositional logic Example 1 Output – Selects tuples from Tutorials where topic = ‘Database’. Example 2 Output – Selects tuples from Tutorials where the topic is ‘Database’ and ‘author’ is guru99. Example 3
Projection(π)
The projection eliminates all attributes of the input relation but those mentioned in the projection list. The projection method defines a relation that contains a vertical subset of Relation. This helps to extract the values of specified attributes to eliminates duplicate values. (pi) symbol is used to choose attributes from a relation. This operator helps you to keep specific columns from a relation and discards the other columns. Example of Projection: Consider the following table Here, the projection of CustomerName and status will give
Rename (ρ)
Rename is a unary operation used for renaming attributes of a relation. ρ (a/b)R will rename the attribute ‘b’ of relation by ‘a’.
Union operation (υ)
UNION is symbolized by ∪ symbol. It includes all tuples that are in tables A or in B. It also eliminates duplicate tuples. So, set A UNION set B would be expressed as: The result <- A ∪ B For a union operation to be valid, the following conditions must hold –
R and S must be the same number of attributes. Attribute domains need to be compatible. Duplicate tuples should be automatically removed.
Example Consider the following tables. A ∪ B gives
Set Difference (-)
– Symbol denotes it. The result of A – B, is a relation which includes all tuples that are in A but not in B.
The attribute name of A has to match with the attribute name in B. The two-operand relations A and B should be either compatible or Union compatible. It should be defined relation consisting of the tuples that are in relation A, but not in B.
Example
Intersection
An intersection is defined by the symbol ∩ A ∩ B Defines a relation consisting of a set of all tuple that are in both A and B. However, A and B must be union-compatible.
Example: Example – Cartesian product σ column 2 = ‘1’ (A X B) Output – The above example shows all rows from relation A and B whose column 2 has value 1
Join Operations
Join operation is essentially a cartesian product followed by a selection criterion. Join operation denoted by ⋈. JOIN operation also allows joining variously related tuples from different relations. Types of JOIN: Various forms of join operation are: Inner Joins:
Theta join EQUI join Natural join
Outer join:
Left Outer Join Right Outer Join Full Outer Join
Inner Join:
In an inner join, only those tuples that satisfy the matching criteria are included, while the rest are excluded. Let’s study various types of Inner Joins:
Theta Join:
The general case of JOIN operation is called a Theta join. It is denoted by symbol θ Example Theta join can use any conditions in the selection criteria. For example:
EQUI join:
When a theta join uses only equivalence condition, it becomes a equi join. For example: EQUI join is the most difficult operations to implement efficiently using SQL in an RDBMS and one reason why RDBMS have essential performance problems.
NATURAL JOIN (⋈)
Natural join can only be performed if there is a common attribute (column) between the relations. The name and type of the attribute must be same. Example Consider the following two tables
OUTER JOIN
In an outer join, along with tuples that satisfy the matching criteria, we also include some or all tuples that do not match the criteria.
Left Outer Join(A B)
In the left outer join, operation allows keeping all tuple in the left relation. However, if there is no matching tuple is found in right relation, then the attributes of right relation in the join result are filled with null values.
Consider the following 2 Tables
Right Outer Join: ( A B )
In the right outer join, operation allows keeping all tuple in the right relation. However, if there is no matching tuple is found in the left relation, then the attributes of the left relation in the join result are filled with null values.
Full Outer Join: ( A B)
In a full outer join, all tuples from both relations are included in the result, irrespective of the matching condition.
