A simple presentation on Relational Algebra
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Relational algebra is a procedural query language used for manipulating relations in databases, providing the theoretical foundation for relational databases and SQL. It comprises basic operations such as selection, projection, and union, allowing for expressive and composed queries. While advantageous due to its solid mathematical basis, it has limitations, including the inability to express certain operators like the transitive closure of a relation.
![What is Relational Algebra?
Relational Algebra is procedural query language, which takes Relation as input and generate relation
as output. Relational algebra mainly provides theoretical foundation for relational databases and
SQL.
[ 1 ]](https://image.slidesharecdn.com/relationalalgebra-191028180219/85/A-simple-presentation-on-Relational-Algebra-2-320.jpg)
![Why Relational Algebra?
Once we have the data in a database, we want to access it.
Relational algebra supports expressive queries by composing fairly simple operators.
Only few operators needed.
We need to know the operators for the schema refinement discussion.
[ 2 ]](https://image.slidesharecdn.com/relationalalgebra-191028180219/85/A-simple-presentation-on-Relational-Algebra-3-320.jpg)
![How to use Relational Algebra?
Basic operations:
Selection ( ): Selects a subset of rows from relation.
Projection ( ): Deletes columns from relation.
Cross-product ( ): Allows us to combine two relations.
Rename Operation ( ρ ): Allows us to rename the output relation.
Set-difference ( ): Tuples in relation 1, but not in relation 2.
Union ( ): Tuples in relation 1 and in relation 2.
Additional operations:
Intersection, join, division, renaming: Not essential, but (very) useful.
Since each operation returns a relation, operations can be composed (Algebra is “closed”)
[ 3 ]](https://image.slidesharecdn.com/relationalalgebra-191028180219/85/A-simple-presentation-on-Relational-Algebra-4-320.jpg)
![Advantages of Relational Algebra
The relational algebra has solid mathematical background.
The mathematical background of relational algebra is the basis of many interesting developments
and theorems.
If we have two expressions for the same operation and if the expressions are proved to be
equivalent, then a query optimizer can automatically substitute the more efficient form.
[ 4 ]](https://image.slidesharecdn.com/relationalalgebra-191028180219/85/A-simple-presentation-on-Relational-Algebra-11-320.jpg)
![Limitations of Relational Algebra
Although relational algebra seems powerful enough for most practical purposes, there are some
simple and natural operators on relations which cannot be expressed by relational algebra. The
transitive closure of a binary relation is one of them.
[ 5 ]](https://image.slidesharecdn.com/relationalalgebra-191028180219/85/A-simple-presentation-on-Relational-Algebra-12-320.jpg)
![References:
[ 1 ] https://www.geeksforgeeks.org/database-management-system-relational-algebra/
[ 2 ] http://www.ccs.neu.edu/home/mirek/classes/2010-F-CS3200/Slides/Ch4_Algebra.pdf
[ 3 ] http://www.cs.cornell.edu/projects/btr/bioinformaticsschool/slides/gehrke.pdf
[ 4 ] https://www.scribd.com/presentation/63853016/Advantages-of-Relational-Algebra
[ 5 ] http://studylib.net/doc/9870912/limitations-of-relational-algebra](https://image.slidesharecdn.com/relationalalgebra-191028180219/85/A-simple-presentation-on-Relational-Algebra-13-320.jpg)
A simple presentation on Relational Algebra
- 1. Relational Algebra What? Why? How? Presentation By: Arman Hossain CSE 11th Batch, SMUCT, Dhaka
- 2. What is Relational Algebra? Relational Algebra is procedural query language, which takes Relation as input and generate relation as output. Relational algebra mainly provides theoretical foundation for relational databases and SQL. [ 1 ]
- 3. Why Relational Algebra? Once we have the data in a database, we want to access it. Relational algebra supports expressive queries by composing fairly simple operators. Only few operators needed. We need to know the operators for the schema refinement discussion. [ 2 ]
- 4. How to use Relational Algebra? Basic operations: Selection ( ): Selects a subset of rows from relation. Projection ( ): Deletes columns from relation. Cross-product ( ): Allows us to combine two relations. Rename Operation ( ρ ): Allows us to rename the output relation. Set-difference ( ): Tuples in relation 1, but not in relation 2. Union ( ): Tuples in relation 1 and in relation 2. Additional operations: Intersection, join, division, renaming: Not essential, but (very) useful. Since each operation returns a relation, operations can be composed (Algebra is “closed”) [ 3 ]
- 5. Select Operation ( σ ) ID Name Age 1 John 21 2 Samuel 19 3 Michael 17 Person σ Age > 17 (Person) ID Name Age 1 John 21 2 Samuel 19 Relational AlgebraSource Result
- 6. Projection ( ) ID Name Mark 54 Frank 86 67 Ron 76 77 Jane 63 Student ID, Name (Student) ID Name 54 Frank 67 Ron 77 Jane Relational AlgebraSource Result
- 7. Union Operation ( ∪ ) ID Name Jailed 1 Alan Burk 2 2 Lev Denz 4 3 Sam Stew 1 Criminal Name (Criminal) ∪ Name (Victim) Relational AlgebraSource Result Name Sam Stew Lev Denz Victim ID Name Loss 1 Den Sen 2200 2 Sam Stew 5800 3 Mark Nez 1000 4 Lev Denz 500
- 8. Set-Difference ( ) Name (Criminal) Name (Victim) Relational AlgebraSource Result Name Alan Burk ID Name Jailed 1 Alan Burk 2 2 Lev Denz 4 3 Sam Stew 1 Criminal Victim ID Name Loss 1 Den Sen 2200 2 Sam Stew 5800 3 Mark Nez 1000 4 Lev Denz 500
- 9. Cross-product ( ) ID Name Salary 13 Jefferson 6500 16 Richard 9000 19 Paronios 8100 Alpha σ Salary > 8000 (Alpha Beta) Relational AlgebraSource Result Beta ID Name Salary 25 Dustinov 8500 36 Izinowa 4800 41 Denzikova 6700 ID Name Salary 16 Richard 9000 19 Paronios 8100 25 Dustinov 8500
- 10. Translation of Relational Algebra to SQL ID, Name (Student) Relational Algebra Equivalent SQL SELECT ID, Name FROM Student σ Age > 17 (Person) SELECT * FROM Person WHERE Age > 17 ID, Name σ Age > 17 (Person) SELECT ID, Name FROM Person WHERE Age > 17
- 11. Advantages of Relational Algebra The relational algebra has solid mathematical background. The mathematical background of relational algebra is the basis of many interesting developments and theorems. If we have two expressions for the same operation and if the expressions are proved to be equivalent, then a query optimizer can automatically substitute the more efficient form. [ 4 ]
- 12. Limitations of Relational Algebra Although relational algebra seems powerful enough for most practical purposes, there are some simple and natural operators on relations which cannot be expressed by relational algebra. The transitive closure of a binary relation is one of them. [ 5 ]
- 13. References: [ 1 ] https://www.geeksforgeeks.org/database-management-system-relational-algebra/ [ 2 ] http://www.ccs.neu.edu/home/mirek/classes/2010-F-CS3200/Slides/Ch4_Algebra.pdf [ 3 ] http://www.cs.cornell.edu/projects/btr/bioinformaticsschool/slides/gehrke.pdf [ 4 ] https://www.scribd.com/presentation/63853016/Advantages-of-Relational-Algebra [ 5 ] http://studylib.net/doc/9870912/limitations-of-relational-algebra