1. Database Design Dr. M.E. Fayad, Professor
5/9/2019
Database Design
Dr. M.E. Fayad, Professor
Computer Engineering Department, Room #283I
College of Engineering
San José State University
One Washington Square
San José, CA
© M.E. Fayad
SJSU -- CmpE

2. Relational Algebra and SQL
5/9/2019
Lesson 06:
Relational Algebra and SQL 2
© M.E. Fayad
SJSU – CmpE M.E. Fayad

3. 5/9/2019
Lesson Objectives
Understand Two Different Query Languages: Relational Algebra and SQL
Learn how to deal with:
Relational Algebra Operators
Relational Algebra Queries
The Benefits of Query Composition
Illustrated Examples
Explore SQL with examples 3
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SJSU – CmpE M.E. Fayad

4. Two Different Query Languages for Relational Database (1)
5/9/2019
Two Different Query Languages for Relational Database (1)
Relational Algebra
Has a small set of well-defined operators that can be composed to form query expressions.
It is a procedural language, because the sequence of operators and the operators themselves can be evaluated using well-defined procedures
Relational Algebra is a useful theoretical language that serves to define more complex languages. 4
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SJSU – CmpE M.E. Fayad

5. Two Different Query Languages for Relational Database (2)
5/9/2019
Two Different Query Languages for Relational Database (2)
Structured Query Language (SQL)
It is a practical language that allows a high level expression of queries.
A user of SQL does not need to think procedurally about queries
But can rely on the meaning of higher-level keywords provided by SQL.
However, most SQL queries can be translated to relational algebra queries to understand the precise meaning of a SQL query. 5
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SJSU – CmpE M.E. Fayad

6. Relational Algebra Operators
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Relational Algebra Operators
Relational Algebra is a query language composed of a number of operators.
Each take relations as arguments and return a single relation as result. 6
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SJSU – CmpE M.E. Fayad

7. 5/9/2019
Intersection
The intersection of two relations A and B, denoted A  B
Results: the set of points belongs to both A and B
The intersection operator can be applied only to operands that have the same set and order of attributes. 7
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SJSU – CmpE M.E. Fayad

8. 8 Union The union of two relations A and B, denoted A  B
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Union
The union of two relations A and B, denoted A  B
Results: the set of points belongs to A or B or both.
The union operator can be applied only to operands that have the same set and order of attributes. 8
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SJSU – CmpE M.E. Fayad

9. 9 Difference The difference of two relations, denoted A \ B
5/9/2019
Difference
The difference of two relations, denoted A \ B
Results: the set of points belongs to A but do not belongs to B.
The difference operator can be applied only to operands that have the same set and order of attributes. 9
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SJSU – CmpE M.E. Fayad

10. 5/9/2019
Product
The product operator applied to an n-dimensional relation A and an m-dimensional relation B, denoted A x B
Results: a relation that contains all (n + m) dimensional points whose first n components belong to A and last m components belong to B.
The product operator can be applied only to operands that have no common attributes. 10
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SJSU – CmpE M.E. Fayad

11. 5/9/2019
Project
The project is used to reorder the columns of a relation or to eliminate some columns of a relation.
The project operator from a relation A is denoted πL A, where L is a list of [l1, ….., lk] that specifies an ordering of a subset of the attributes of A.
The project operator creates a new relation that contains in its ith column the column of A corresponding to attribute li. 11
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SJSU – CmpE M.E. Fayad

12. 5/9/2019
Select
The select operator is used to select a relation A those points that satisfy a certain logical formula F.
The select operator has the form σF A. The logical formula F is a constraint formula.
Constraint formula – Chapter 2 12
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SJSU – CmpE M.E. Fayad

13. 5/9/2019
Rename
The rename operator ρB(X1/Y1, …., Xn/Yn)A for any n ≥ 1, changes the name of relation A to B and changes the attribute Xi to Yi.
If we only want to change the name of the relation, then the form ρBA can be used. 13
© M.E. Fayad
SJSU – CmpE M.E. Fayad

14. 5/9/2019
Natural Join
The natural join operator applied to an n-dimensional relation A and an m-dimensional relation B that have k attributes in common is denoted A B.
The natural join operator returns a relation that contains all (n + m – k)-dimensional points whose projection onto attributes of A belong to A and whose projection onto the attributes of B belong to B. 14
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SJSU – CmpE M.E. Fayad

15. Which Operators can be applied?
5/9/2019
Which Operators can be applied?
A and B
Two sets of points: A(x, y) and B (x, y) are 2-dimensional
Operators that can be applied:
Intersection
Union
Difference 15
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SJSU – CmpE M.E. Fayad

16. How to read set of points
5/9/2019
How to read set of points
Example:
Let the following relations describe point sets:
A(x, y), B(x, y), J(x, y) D points in the plane
H(x, y, z), I(x, y, z) D points in space
F(z) line on the z-axis
K(y,z) D points in (y, z) plane 16
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SJSU – CmpE M.E. Fayad

17. Relation algebra operators (1)
5/9/2019
Relation algebra operators (1)
A and B
A  B = C 5
A  B = D
A \ B = E
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SJSU – CmpE M.E. Fayad

18. Relation algebra operators (2)
5/9/2019
Relation algebra operators (2)
Let F(z) be a relation that contains all points on the z-axis between z = 5 and z = 15.
Then the product A(x, y) X F(z) = G(x, y, z), where G is the polyhedron, as shown in the figure.
A  F
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SJSU – CmpE M.E. Fayad

19. Relation algebra operators (3)
5/9/2019
Relation algebra operators (3)
 y,z H
Consider H(x, y, z) is the polyhedron in the shown figure.
The projection  x,y H is the shaded rectangle in the (x, y) plane, while  y,z H is the shaded rectangle in (y, z) plane.
 x,y H
Projection from H
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SJSU – CmpE M.E. Fayad

20. Relation algebra operators (4)
5/9/2019
Relation algebra operators (4)
Consider the rectangular body l(x, y, z), shown in the figure.
The shaded rectangle that lies in the plane defined by the equation 2x + z = 0 cuts l into two.
The selection operation  2x+z ≤0 I returns the part of l that lies below the shaded rectangle
 2x+z = 0 I
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SJSU – CmpE M.E. Fayad

21. Relation algebra operators (5)
5/9/2019
Relation algebra operators (5)
The natural join of the shaded rectangle J(x, y) and the shaded circle K(y, z) is the cylinder L(x, y, z).
This can be written as
J(x, y) K(y, z) = L(x, y, z)
J K
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SJSU – CmpE M.E. Fayad

22. Relational Algebra Queries (1)
5/9/2019
Relational Algebra Queries (1)
Because the result of each operation is a relation, the operators can be composed to form queries
The relational algebra query language is defined recursively as following: 22
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SJSU – CmpE M.E. Fayad

23. Relational Algebra Queries (2)
5/9/2019
Relational Algebra Queries (2)
Each relation name Ri is a relational algebra expression. (This will just return the relation Ri as a result.)
If e1 and e2 are relational algebra expressions that result in relations that have the same set and order of attributes, then (e1  e2), (e1  e2), (e1 \ e2) are also relational algebra expressions. 23
© M.E. Fayad
SJSU – CmpE M.E. Fayad

24. Relational Algebra Queries (3)
5/9/2019
Relational Algebra Queries (3)
If e1 and e2 are relational algebra expressions that result in relations with no common attributes, then (e1 x e2) is also relational algebra expression.
If e1 and e2 are relational algebra expressions, then (e e2) is also relational algebra expression. 24
© M.E. Fayad
SJSU – CmpE M.E. Fayad

25. Relational Algebra Queries (4)
5/9/2019
Relational Algebra Queries (4)
If e1 is a relational algebra expression, then πL (e1), where L is a subset of the attributes of the resulting relation σF (e1), where F is a selection condition, and ρC(e1), where C is a renaming specification, are also relational algebra expressions.
No other expressions are relational algebra expressions. 25
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SJSU – CmpE M.E. Fayad

26. Relational Algebra Queries (5)
5/9/2019
Relational Algebra Queries (5)
Example: Consider the relations Taxrecord and Taxable – Chapter 1. Find the SSN and tax for each person.
πSSN,Tax σwages+interest+capital_gain = income Taxrecord × Taxtable
Means: if there is a tuple t in Taxrecord and a tuple s in Taxable, such that the sum of the last three attributes value of t equals the first attribute value of s, then print out the first attribute value of t and the second attribute value of s.
© M.E. Fayad
SJSU – CmpE M.E. Fayad

27. Relational Algebra Queries (6)
5/9/2019
Relational Algebra Queries (6)
Example: Assume for now that the point of origin in both town and the broadcast maps in the same. The following query finds the area of Lincoln reached by a radio station.
( πX,Y ( σName=“Lincoln” Town ) )  ( πX,Y Broadcast )
The part before  selects the points of town and the part after  selects the points belong to at least one radio station broadcast area.
© M.E. Fayad
SJSU – CmpE M.E. Fayad

28. 28 SQL (1) SQL stands for Structured Query Language
5/9/2019
SQL (1)
SQL stands for Structured Query Language
SQL is a popular query language for relational database systems.
It is a complex language with many functions and options
SQL is an ANSI standard language for accessing databases!
SQL can execute queries against a database 28
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SJSU – CmpE M.E. Fayad

29. 29 SQL (2) SQL can retrieve data from a database
5/9/2019
SQL (2)
SQL can retrieve data from a database
SQL can insert new records in a database
SQL can delete records from a database
SQL can update records in a database
SQL is easy to learn 29
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SJSU – CmpE M.E. Fayad

30. 30 SQL (3) SELECT a1, ..., an FROM R1, R2, …, Rm WHERE Con1, …,Conk
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SQL (3)
SELECT a1, ..., an
FROM R1, R2, …, Rm
WHERE Con1, …,Conk
Ri for 1 ≤ I ≤ m are relation names, an (attribute names)
Coni are atomic constraints
This means:
π a1, ..., an( σ Con1( … (σ Conk ( R1 × R2 × … × Rm))…)) 30
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SJSU – CmpE M.E. Fayad

31. 31 SQL: Example Find the SSN and tax for each person. SELECT SSN, Tax
5/9/2019
SQL: Example
Find the SSN and tax for each person.
SELECT SSN, Tax
FROM Taxrecord, Taxtable
WHERE wages+interest+capital_gain = income 31
© M.E. Fayad
SJSU – CmpE M.E. Fayad

32. AS – keyword used to rename relations (1)
5/9/2019
AS – keyword used to rename relations (1)
Two SQL expressions can be combined by:
INTERSECT
UNION
MINUS – set difference
Which has the form:
SQL Query Q1
SQL Query Q2 32
© M.E. Fayad
SJSU – CmpE M.E. Fayad

33. AS – keyword used to rename relations (2)
5/9/2019
AS – keyword used to rename relations (2)
AS keyword can be used for renaming attribute names in the SELECT clause and relation names in the FROM clause of basic queries.
AS keyword is also useful for making multiple copies of a relation.
For example, to rename an attribute A by B and to declare S and T to be copies of the relation R in SQL, we write
SELECT A AS B
FROM R A, R AS T
WHERE …. 33
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SJSU – CmpE M.E. Fayad

34. AS – keyword used to rename relations (3)
5/9/2019
AS – keyword used to rename relations (3)
Example: Find the names of the streets that intersect.
SELECT S.NAME, T.NAME
FROM Streets AS S, Streets AS T
WHERE S.X = T.X and S.Y = T.Y 34
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SJSU – CmpE M.E. Fayad

35. 35 Another Example Example: Assume we have the relations:
5/9/2019
Another Example
Example: Assume we have the relations:
Broadcast ( Radio, X , Y )
Town ( Name, X, Y )
Find the parts of Lincoln, NE that can be reached by at least one Radio station.
SELECT X, Y
FROM Town
WHERE Name = “Lincoln”
INTERSECT
SELECT X, Y
FROM Broadcast 35
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SJSU – CmpE M.E. Fayad

36. Another way of connecting SQL expressions is using the IN keyword.
5/9/2019
Another way of connecting SQL expressions is using the IN keyword.
SELECT ……..
FROM ……..
WHERE a IN ( SELECT b
FROM …..
WHERE ….. ) 36
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SJSU – CmpE M.E. Fayad

37. 37 SQL with Aggregation SELECT aggregate_function FROM ……. WHERE ……
5/9/2019
SQL with Aggregation
SELECT aggregate_function
FROM …….
WHERE ……
Aggregate_function –
Max (c1a1 + ……..+ cnan) where ai are attributes
Min (c1a1 + ……..+ cnan) and ci are constants
Sum(a) where a is an attribute that is
Avg(a) constant in each constraint tuple
Count(a) 37
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SJSU – CmpE M.E. Fayad

38. 38 Example Find the total postage of all packages sent from Omaha.
5/9/2019
Example
Package(Serial_No, From, Destination, Weight)
Postage (Weight , Fee)
Find the total postage of all packages sent
from Omaha.
SELECT Sum(Fee)
FROM Package, Postage
WHERE Package.Weight = Postage.Weight
AND Package.From = “ Omaha “ 38
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SJSU – CmpE M.E. Fayad

39. 39 GROUP BY SELECT a1, …, an, aggregate_function FROM ….. WHERE ……
5/9/2019
GROUP BY
SELECT a1, …, an, aggregate_function
FROM …..
WHERE ……
GROUP BY a1, ..., ak
Evaluates basic SQL query
Groups the tuples according to different values of a1,..,ak
Applies the aggregate function to each group separately
{a1, …, ak}  {a1, …, an} 39
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SJSU – CmpE M.E. Fayad

40. 40 GROUP BY: Example Find the total postage sent out from each city.
5/9/2019
GROUP BY: Example
Find the total postage sent out from each city.
SELECT Package.From, Sum(Postage.Fee)
FROM Package, Postage
WHERE Package.Weight = Postage.Weight
GROUP BY Package.From 40
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SJSU – CmpE M.E. Fayad

41. Solution for Exercise # 3.1
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Solution for Exercise # 3.1
??? 41
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SJSU – CmpE M.E. Fayad

42. 42 Discussion Questions T/F
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Discussion Questions
T/F
The operands of intersection, union, and difference relational algebra operators have no common attributes
Product operands have to be the same set and order of attributes.
Intersection is denoted by A  B.
The difference operator is denoted by A / B.
product is denoted by A x B.
A "projection"of a table is a choice of some or all of its columns. 42
© M.E. Fayad
SJSU – CmpE M.E. Fayad