Introduction of Relational Algebra in DBMS
Relational Algebra is a procedural query language, which takes Relation as input and generates relation as output. Relational algebra mainly provides a theoretical foundation for relational databases and SQL.
Operators in Relational Algebra
Projection (π)
Projection is used to project required column data from a relation.
Example :
Suppose we want column A and B from Relation R.
R (A B C) ---------- 1 2 4 2 2 3 3 2 3 4 3 4
π B,C(R) will show following columns. B C ----- 2 4 2 3 3 4
Note: By Default, projection removes duplicate data.
Selection (σ)
Selection is used to select required tuples of the relations.
for the above relation
σ (c>3)R
will select the tuples which have c more than 3.
Note: selection operator only selects the required tuples but does not display them. For display, the data projection operator is used.
For the above-selected tuples, to display we need to use projection also.
π (σ (c>3)R ) will show following tuples. A B C ------- 1 2 4 4 3 4
Union (U)
Union operation in relational algebra is the same as union operation in set theory, the only constraint is for the union of two relations both relations must have the same set of Attributes.
Set Difference (-)
Set Difference in relational algebra is the same set difference operation as in set theory with the constraint that both relations should have the same set of attributes.
Rename (ρ)
Rename is a unary operation used for renaming attributes of a relation. ρ (a/b)R will rename the attribute ‘b’ of the relation by ‘a’.
Cross Product (X)
Cross product between two relations let’s say A and B, so cross product between A X B will result in all the attributes of A followed by each attribute of B. Each record of A will pair with every record of B.
below is the example
A B
(Name Age Sex ) (Id Course)
------------------ -------------
Ram 14 M 1 DS
Sona 15 F 2 DBMS
kim 20 M
A X B
Name Age Sex Id Course
---------------------------------
Ram 14 M 1 DS
Ram 14 M 2 DBMS
Sona 15 F 1 DS
Sona 15 F 2 DBMS
Kim 20 M 1 DS
Kim 20 M 2 DBMS
Note: if A has ‘n’ tuples and B has ‘m’ tuples then A X B will have ‘n*m’ tuples.
Natural Join (⋈)
Natural join is a binary operator. Natural join between two or more relations will result set of all combinations of tuples where they have an equal common attribute.
Let us see the below example
Emp Dep
(Name Id Dept_name ) (Dept_name Manager)
------------------------ ---------------------
A 120 IT Sale Y
B 125 HR Prod Z
C 110 Sale IT A
D 111 IT
Emp ⋈ Dep
Name Id Dept_name Manager
-------------------------------
A 120 IT A
C 110 Sale Y
D 111 IT A
Conditional Join
Conditional join works similarly to natural join. In natural join, by default condition is equal between common attributes while in conditional join we can specify any condition such as greater than, less than, or not equal
Let us see the below example
R S (ID Sex Marks) (ID Sex Marks) ------------------ -------------------- 1 F 45 10 M 20 2 F 55 11 M 22 3 F 60 12 M 59 Join between R And S with condition R.marks >= S.marks R.ID R.Sex R.Marks S.ID S.Sex S.Marks ----------------------------------------------- 1 F 45 10 M 20 1 F 45 11 M 22 2 F 55 10 M 20 2 F 55 11 M 22 3 F 60 10 M 20 3 F 60 11 M 22 3 F 60 12 M 59
In-depth articles:
Basic-operators-in-relational-algebra
Extended Relational Algebra Operators
Following are Previous Year Gate Question
https://www.geeksforgeeks.org/gate-gate-cs-2012-question-50/
https://www.geeksforgeeks.org/gate-gate-cs-2012-question-43/
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