1. CS 3630 Database Design and Implementation

2. Retrieving Data From Database
Relational Algebra
Procedural
How to get the data
Relational Calculus
Non-Procedural
What data to retrieve
We use Relational Algebra
Could have more materials

3. Relational Algebra Operations
Selection
Projection
Union
Set difference
Intersection
Cartesian product
Join

4. Relational Algebra Operations
Applied to relation instances (tables)
The result is still a relation (table)
Syntax

5. Selection  (predicate) (R) R is a relation
The result is a subset of relation R

6. Selection (II) Relation Schema: R (Att1, Att2, Att3) Relation Instancex y x
 (att1 < 100) (R) y
(att1 < 100) (R) = {(90, 20, y)}
The result is still a relation (table).

7. Selection (III)  ((att1 >= 100 and att2 <= 20) or att3  x) (R)
Table Schema
R (Att1, Att2, Att3)
Table Instance
Att1 Att2 Att3 x y x
 ((att1 >= 100 and att2 <= 20) or att3  x) (R)
= {(100, 10, x), (90, 20, y)}
As a table
Att1 Att2 Att3 x y

8. Notations ((att1 >= 100 and att2 <= 20) or att3  x) (R)
Correct!
 ((att1 >= 100  att2 <= 20)  att3  x) (R)
Incorrect!
 ((att1 >= 100 && att2 <= 20) || att3  x) (R)

9. Projection Att1, Att3 (R) R is a relation
The result is a relation with specified attributes
all or some attributes
same or different order
The schema of the result is usually different
No equivalent set operation
No duplicates

10. Projection (II) (Att1, Att3) (R) Att1 Att2 Att3 100 10 x 90 20 y

11. Projection (III) (Att3, Att1) (R) (Att1, Att3) (R)
Order of Attributes
(Att3, Att1) (R)
(Att1, Att3) (R)

12. Projection (IV) All attributes: all records * (R)
(Att1, Att2, Att3) (R)
(Att1, Att3, Att2) (R)

13. Union R (Att1, Att2, Att3) S (Att1, Att2, Att4)
Att1 Att2 Att Att1 Att2 Att4
x x
y y x
R S
Union compatible (Same schema)
T (Att1, Att2, Att4, Att5)
R T ?

14. Union (II) R (Att1, Att2, Att3) S (Att1, Att2, Att4)
Att1 Att2 Att Att1 Att2 Att4
x x
y y x
R S
Att1 Att2 Att4(Att3) x y x x

15. Set Difference R - S Union compatible (same schema)
Att1 Att2 Att Att1 Att2 Att4
x x
y y x
Att1 Att2 Att3 x x

16. Intersection R S Union compatible (same schema)
Att1 Att2 Att Att1 Att2 Att4
x x
y y x
Att1 Att2 Att4(Att3) y

17. Cartesian Product R S Cardinality: |R S| = |R| * |S|
Degree : (Degree of R) + (Degree of S)
R (Att1, Att2, Att3)
Att1 Att2 Att3 x y z
S (Att2, Att4)
Att2 Att4 a b
R S
Att R.Att Att S.Att Att4
x a
x b
y a
y b
z a
z b

18. Theta Join Based on Cartesian Product R p S =  (p) (R S)
R (R.Att2 >= S.Att2) S =  (R.Att2 >= S.Att2) (R S)
R: Att1 Att2 Att3 x y z
S: Att2 Att4 a b
Att1 R.Att2 Att3 S.Att2 Att4
x a
x b
y a
y b
z a
z b 
Att1 R.Att2 Att3 S.Att2 Att4
y a
y b
z b

19. Natural Join R: Att1 Att2 Att3 S: Att2 Att4 100 10 x 20 a 90 20 y 15 bz
Common attribute Att2
R S
=  (Att1, R.Att2, Att3, Att4)  (R.Att2 = S.Att2) (R S)  
Att1 R.Att2 Att3 S.Att2 Att4
x a
x b
y a
y b
z a
z b 
Att1 R.Att2 Att3 S.Att2 Att4
y a
z b 
Att1 R.Att2 Att3 Att4
y a
z b 

20. Natural Join
R S =  (Att1, R.Att2, Att3, Att4)  (R.Att2 = S.Att2) (R S)  
Att1 Att2 Att Att2 Att4
x a
y b z
Att1 R.Att2 Att3 S.Att2 Att Att1 R.Att2 Att3 S.Att2 Att4
x a z b
x b y a
y a
y b Att1 R.Att2 Att3 Att4
z a z b
z b  y a
Remove the common attribute of the 2nd table
Keep all attributes in the original order

21. Outer Join R S Left Outer-Join Keep non-matching tuples of R
(Natural unless otherwise stated)
Att1 Att2 Att Att2 Att4
x a
y b z
Att1 R.Att2 Att3 Att4
x null
y a
z b 

22. Left Outer Join (II) R S How to implement it? For each r of R
Joined = False
For each s of S
If (Same value on common attribute)
Generate a tuple
Joined = True
If Not Joined
Generate a tuple from r with null values

23. Other Joins
Right Outer Join
Full Outer Join
Semi-Join

24. Exercise: Natural Join
R S  
Att1 Att2 Att Att2 Att4
x a
y b
z b
w c d
Att1 R.Att2 Att3 Att4
(first record of R does not join with any record of S)
y a
y b
z b
z c
w d

25. Exercise: Left Outer Join
R S  
Att1 Att2 Att Att2 Att4
x a
y b
z b
w c d
Att1 R.Att2 Att3 Att4
x null (does not join)
y a
y b
z b
z c
w d

26. Exercise: Right Outer Join
R S  
Att1 Att2 Att Att2 Att4
x a
y b
z b
w c
y d
Att1 R.Att2 Att3 Att4
y a
y a
z b
y b
y b
z c
w d

27. Aggregation
COUNT
SUM
AVG
MIN
MAX

28. Grouping

29. Relational Calculus

30. Assignment 1 Due Wednesday (week 2), Jan 31, at 5 pm D2L
It will be late after 5:00 pm

31. Due Wednesday (week 3), Feb 7
Assignment 2
Due Wednesday (week 3), Feb 7