Relational Model 2: Relational Algebra

Transcription

1 Yufei Tao Department of Computer Science and Engineering Chinese University of Hong Kong

2 The relational model defines: 1 the format by which data should be stored; 2 the operations for querying the data. We will focus on the second aspect in this lecture.

3 Relational Algebra Relational algebra is a language for issuing queries on the data stored in a relation database. Its core consists of 6 fundamental operations: Rename ρ Selection σ Projection Π Set union Set difference Cartesian product

4 Rename Denoted by ρ s (T ) where T is a table, and s is a string. The output of the operation is a table T that is exactly the same as T, but is named s.

5 ρ LECT (PROF) returns: PROF p1 Adam CS asst 6000 p6 Frank CS full 9000 LECT p1 Adam CS asst 6000 p6 Frank CS full 9000

6 Selection Denoted by σ P (T ) where T is a table, and P is a predicate on the tuples of T. The output is a table T such that T has the same schema as T. T includes all and only the tuples in T satisfying P. Each predicate can be a comparison using the following operators: =,, <,, >,. multiple comparisons connected by (and), (or) and (not).

7 σ name= Bob (PROF) returns: PROF p1 Adam CS asst 6000 p6 Frank CS full 9000

8 PROF p1 Adam CS asst 6000 p6 Frank CS full 9000 σ dept= EE sal > 7000 (PROF) returns:

9 Projection Denoted by Π A (T ) where T is a table, and A is a set of attributes in T. The output of the operation is a table T such that T has all and only the attributes in A. T contains all the tuples of T after trimming the attributes not in A. All duplicates (resulting from the trimming) are removed.

10 Π dept (PROF) returns: PROF p1 Adam CS asst 6000 p6 Frank CS full 9000 dept CS EE

11 Π dept, rank (PROF) returns: PROF p1 Adam CS asst 6000 p6 Frank CS full 9000 dept CS EE CS EE rank asst asso full asst

12 Union Denoted by T 1 T 2 where T 1 and T 2 are tables with the same schema. The output of the operation is a table T such that T has the same schema as T 1 (and hence, T 2 ). T contains all the tuples of T 1 and T 2, after removing duplicates.

13 PROF p1 Adam CS asst 6000 p6 Frank CS full 9000 σ sal 5000 (PROF) σ sal (PROF) returns: PROF

14 Set difference Denoted by T 1 T 2 where T 1 and T 2 are tables with the same schema. The output of the operation is a table T such that T has the same schema as T 1 (and hence, T 2 ). T contains all the tuples that appear in T 1 but not in T 2.

15 PROF p1 Adam CS asst 6000 p6 Frank CS full 9000 Π rank (σ sal 8000 (PROF)) Π rank (σ sal 9000 (PROF)) returns: rank asso

16 Cartesian product Denoted by T 1 T 2 where T 1 and T 2 are tables. The output of the operation is a table T such that The schema of T includes all the attributes in T 1 and T 2 (if an attribute in T 1 has the same name as an attribute in T 2, they are treated as different attributes in T ). For every tuple t 1 T 1 and t 2 T 2, T contains a tuple t whose values are the same as t 1 (t 2 ) on the attributes from T 1 (T 2 ).

17 PROF p1 Adam CS asst 6000 TEACH pid cid year p1 c p2 c p1 c PROF TEACH returns the table in the next slide.

18 pid cid year p1 Adam CS asst 6000 p 1 c p 1 c p 1 c p 1 c p 1 c p1 Adam CS asst 6000 p 2 c p 2 c p 2 c p 2 c p 2 c p1 Adam CS asst 6000 p 1 c p 1 c p 1 c p 1 c p 1 c