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Relation algebra (1).ppt
- 1. Relational Algebra V.Deepa M.Sc.,M.Phil., AssistantProfessor Department of Computer Science Sri Ramakrishna College of Arts and Science
- 2. Relational Algebra • Fiveoperators: • Union: • Difference: - • Selection: s • Projection: P • Cartesian Product: • Derived operators: • Intersection, complement • Joins (natural,equi-join, theta join, semi-join) • Renaming: r
- 3. DBMS • Database ManagementSystem or DBMS in short refers to the technology of storing and retrieving users data.
- 4. What is dataand Information?
- 5. How relational algebrarelated to DBMS? • Relational algebra mainly provides theoretical foundation for relational databases
- 7. Introduction to RelationAlgebra • It was introduction by 1970 • By EF Code who is the father of DBMS. • It is called procedural or formal query language.
- 8. Relational Algebra • Framefor creating new relations from existing ones • Its place in the big picture: Declartive query language Algebra Implementation SQL, relational calculus Relational algebra Executable code
- 9. 1. Union and2. Difference • R1 R2 • Example: • ActiveEmployees RetiredEmployees • R1 – R2 • Example: • AllEmployees -- RetiredEmployees
- 10. What about Intersection? • It is a derived operator • R1 R2 = R1 – (R1 – R2) • Also expressed as a join (will see later) • Example • UnionizedEmployees RetiredEmployees
- 11. 3. Selection • Returnsall tuples which satisfy a condition • Notation: sc(R) • Examples • sSalary > 40000 (Employee) • sname = “Smith” (Employee) • The condition c can be =, <, , >, , <>
- 12. sSalary > 40000(Employee) SSN Name Salary 1234545 John 200000 5423341 Smith 600000 4352342 Fred 500000 SSN Name Salary 5423341 Smith 600000 4352342 Fred 500000
- 13. 4. Projection • Eliminatescolumns, then removes duplicates • Notation: P A1,…,An (R) • Example: project social-security number and names: • P SSN, Name (Employee) • Output schema: Answer(SSN, Name)
- 14. P Name,Salary (Employee) SSNName Salary 1234545 John 200000 5423341 John 600000 4352342 John 200000 Name Salary John 20000 John 60000
- 15. 5. Cartesian Product •Each tuple in R1 with each tuple in R2 • Notation: R1 R2 • Example: • Employee Dependents • Very rare in practice; mainly used to express joins
- 16. Cartesian Product Example Employee NameSSN John 999999999 Tony 777777777 Dependents EmployeeSSN Dname 999999999 Emily 777777777 Joe Employee x Dependents Name SSN EmployeeSSN Dname John 999999999 999999999 Emily John 999999999 777777777 Joe Tony 777777777 999999999 Emily Tony 777777777 777777777 Joe
- 17. Relational Algebra • Fiveoperators: • Union: • Difference: - • Selection: s • Projection: P • Cartesian Product: • Derived or auxiliary operators: • Intersection, complement • Joins (natural,equi-join, theta join, semi-join) • Renaming: r
- 18. Operations on Bags Abag = a set with repeated elements All operations need to be defined carefully on bags • {a,b,b,c}{a,b,b,b,e,f,f}={a,a,b,b,b,b,b,c,e,f,f} • {a,b,b,b,c,c} – {b,c,c,c,d} = {a,b,b,c,d} • sC(R): preserve the number of occurrences • PA(R): no duplicate elimination • Cartesian product, join: no duplicate elimination Important ! Relational Engines work on bags, not sets !
- 19. Joins • Joins isa combinatio of Cartesian product by a selection process. • Inner Joins: Theta join EQUI join Natural join • Outer joins: Left outer join Right outer join Full outer join
- 20. • Also knownas conditional join. • Used when you want to join two or more relation based on some conditions.
- 21. • Is aspecial case of conditional join. • When a theta join uses only equivalence condition, it become a equi join • As value of two attributes will be equal in result of equaijoin, only one attribute will be appeared in result.
- 22.