1 / 22

Relational Algebra

Relational Algebra. Eugene Sheng Computer Science Department NIU. Introduction . one of the two formal query languages of the relational model collection of operators for manipulating relations Operators: two types of operators

lixue
Download Presentation

Relational Algebra

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Relational Algebra Eugene Sheng Computer Science Department NIU

  2. Introduction • one of the two formal query languages of the relational model • collection of operators for manipulating relations • Operators: two types of operators • Set Operators: Union(),Intersection(), Difference(-), Cartesian Product (x) • New Operators: Select (), Project (), Join (⋈)

  3. Introduction – cont’d • A Relational Algebra Expression: a sequence of relational algebra operators and operands (relations), formed according to a set of rules. • The result of evaluating a relational algebra expression is a relation.

  4. Selection • Denoted by c(R) • Selects the tuples (rows) from a relation R that satisfy a certain selection condition c. • It is a unary operator • The resulting relation has the same attributes as those in R.

  5. Example 1: S: • state=‘IL’(S)

  6. Example 2: • CREDIT  3(C) C:

  7. Example 3 SNO=‘S1’and CNO=‘C1’(E) E:

  8. Selection - Properties • Selection Operator is commutative C1(C2 (R)) = C2(C1 (R)) • The Selection is an unary operator, it cannot be used to select tuples from more than one relations.

  9. Projection • Denoted by L(R), where L is list of attribute names and R is a relation name or some other relational algebra expression. • The resulting relation has only those attributes of R specified in L. • The projection is also an unary operation. •  Duplication is removed from the result.

  10. Projection - Example • Example 1: STATE (S)

  11. Projection - Example Example 2: CNAME, DEPT(C)

  12. Projection - Example Example 3: S#(STATE=‘NY'(S))

  13. SET Operations • UNION: R1 R2 • INTERSECTION: R1 R2 • DIFFERENCE: R1 - R2 • CARTESIAN PRODUCT: R1 R2

  14. Union Compatibility • For operators , , -, the operand relations R1(A1, A2, ..., An) and R2(B1, B2, ..., Bn) must have the same number of attributes, and the domains of the corresponding attributes must be compatible; that is, dom(Ai)=dom(Bi) for i=1,2,...,n. • The resulting relation for , , or - has the same attribute names as the first operand relation R1 (by convention).

  15. Union Compatibility - Examples • Are S(SNO, SNAME, AGE, STATE) and C(CNO, CNAME, CREDIT, DEPT) union compatible? • Are S(S#, SNAME, AGE, STATE) and C(CNO, CNAME, CREDIT_HOURS, DEPT_NAME) union compatible?

  16. Union, Intersection, Difference • T= R U S : A tuple t is in relation T if and only if t is in relation R or t is in relation S • T = R  S: A tuple t is in relation T if and only if t is in both relations R and S • T= R - S :A tuple t is in relation T if and only if t is in R but not in S

  17. Examples R S

  18. Examples R  S R S R - S S - R

  19. Cartesian Product • R(A1, A2, ..., Am) and S(B1, B2, ... , Bn) • T(A1, A2, ... , Am, B1, B2, ..., Bn) = R(A1, A2, ..., Am) X S(B1, B2, ..., Bn) • A tuple t is in T if and only if t[A1,A2, ... ,Am] is in R and t[B1, B2, ..., Bn] is in S. - If R has N1 tuples and S has N2 tuples, then T will have N1*N2 tuples.

  20. Cartesian Product R Rx S S

  21. Question • Compute S x C • Compute S x E

  22. A Sample DB: student-course-enrollment S: E: C:

More Related