1. Fundamental of Database Systems 1401312-3By
Dr Abdullah Alzahrani د. عبدالله الزهراني
Part 2

2. Assessment توزيع الدرجات
20% Mid-Term written exam
10% Mid-Term practical exam
20% Project
50% Final Exam
20% اختبار نصفي نظري
10% اختبار نصفي عملي
20% مشروع
50% اختبار نهائي
Dr Abdullah Alzahrani.
Fundamental of Database Systems
9/20/2016

3. Reference الكتاب المرجع
Fundamentals of Database Systems, 5th ed., by Elmasri and Navathe, Pearson International Edition,
Dr Abdullah Alzahrani.
Fundamental of Database Systems
9/20/2016

4. Relational Algebra Relational algebra Introduction Operations
Unary Operations
SELECT
PROJECT
Rename
Binary Operations
JOIN and Cartesian product
DIVISION
Relational Algebra Operations from Set Theory
Some important terms
relations, tuples, attributes, relation schema
Dr Abdullah Alzahrani.
Fundamental of Database Systems
9/20/2016

5. Relational Algebra
Relational algebra is a query language for manipulating relations. It takes instances of relations as input and produces instances of relations as output. It uses operators to perform queries. An operator can be either unary or binary.
The relational algebra is often considered to be an primary part of the relational data model
It provides a set of operations that allow creation and manipulation of relation.
What is an expression in relational algebra ?
A sequence of relational algebra operations
The relational algebra is very important for several reasons:
formal language
It provides a formal foundation for relational model operations.
it is used as a basis for implementing and optimizing queries in the query processing and optimization
some of its concepts are incorporated into the SQL standard query language.
Relational algebra operations {σ,π, ρ,⨝, ×,  , ∪, ∩,–}
Dr Abdullah Alzahrani.
Fundamental of Database Systems
9/20/2016

6. Relational Algebra
Some types of operations that, in general, cannot be specified in the basic original relational algebra:
Recursive closure.
Aggregate functions
Dr Abdullah Alzahrani.
Fundamental of Database Systems
9/20/2016

7. Relational Algebra Operations
The fundamental operations of relational algebra are as follows −
Unary Relational Operations:
SELECT
PROJECT
Rename
Binary Relational Operations:
JOIN and Cartesian product
DIVISION
Relational Algebra Operations from Set Theory:
The UNION, INTERSECTION, and MINUS (SET DIFFERENCE) Operations
Dr Abdullah Alzahrani.
Fundamental of Database Systems
9/20/2016

8. Relational Algebra SELECT operation
Unary Relational Operations
SELECT operation
The SELECT operation is used to choose a subset of the tuples from a relation that satisfies a selection condition
symbol σ (sigma)
In general, the SELECT operation is denoted by
σ <selection condition>(R)
where the symbol σ(sigma) is used to denote the SELECT operator and the selection condition is a Boolean expression (condition) specified on the attributes of relation R. Notice that R is generally a relational algebra expression whose result is a relation
Examples:
Dr Abdullah Alzahrani.
Fundamental of Database Systems
9/20/2016

9. Relational Algebra PROJECT operation
Unary Relational Operations
PROJECT operation
If we think of a relation as a table, the SELECT operation chooses some of the rows from the table while discarding other rows. The PROJECT operation, on the other hand, selects certain columns from the table and discards the other columns
symbol π (pi)
In general, the PROJECT operation is denoted by
π <attribute list> (R)
where π(pi) is the symbol used to represent the PROJECT operation, and <attribute list> is the desired sublist of attributes from the attributes of relation R.
Examples:
π Bdate, Salary (EMPLOYEE)
Dr Abdullah Alzahrani.
Fundamental of Database Systems
9/20/2016

10. Relational Algebra
Unary Relational Operations
OK, How do we get Only the Bdate of employees whose Dno = 5?
Answer:
π Bdate(σ Dno=5( EMPLOYEE)) in-line expression or
DEP5_EMPS ← σ Dno=5 (EMPLOYEE) sequence of operations
RESULT ← π Bdate(DEP5_EMPS)
Dr Abdullah Alzahrani.
Fundamental of Database Systems
9/20/2016

11. Relational Algebra RENAME operation
Unary Relational Operations
RENAME operation
can RENAME either the relation name or the attribute names, or both
symbol ρ(rho)
In general, the RENAME operation is denoted by
or or
where S is the new relation name, and B1, B2, ..., Bn are the new attribute names. The first expression renames both the relation and its attributes, the second renames the relation only, and the third renames the attributes only. If the attributes of R are (A1,A2, ...,An) in that order, then each Ai is renamed as Bi.
Dr Abdullah Alzahrani.
Fundamental of Database Systems
9/20/2016

12. Relational Algebra Examples: What are the results of the above?
Unary Relational Operations
Examples:
ρ Empl_table(EMPLOYEE)
ρ DoB, Sal_Monthly(π Bdate, Salary (EMPLOYEE))
ρ Empl_table(DoB, Sal_Monthly)(π Bdate, Salary (EMPLOYEE))
What are the results of the above?
Dr Abdullah Alzahrani.
Fundamental of Database Systems
9/20/2016

13. Relational Algebra Binary Relational Operations JOIN operation
is used to combine related tuples from two relations into single “longer” tuples
The sequence of Cartesian product followed by select is used quite commonly to identify and select related tuples from two relations.
It is denoted by a
Symbol ⨝
This operation is very important for any relational database with more than a single relation, because it allows us to process relationships among relations.
The general form of a join operation on two relations R(A1, A2, . . ., An) and S(B1, B2, . . ., Bm) is:
R ⨝ <join condition>S
where R and S can be any relations that result from general relational algebra expressions.
Dr Abdullah Alzahrani.
Fundamental of Database Systems
9/20/2016

14. Relational Algebra JOIN operation example Binary Relational Operations
Dr Abdullah Alzahrani.
Fundamental of Database Systems
9/20/2016

15. Relational Algebra Binary Relational Operations
CARTESIAN (or cross product) Operation
This operation is used to combine tuples from two relations in a combinatorial fashion. In general, the result of R(A1, A2, . . ., An) x S(B1, B2, . . ., Bm) is a relation Q with degree n + m attributes Q(A1, A2, . . ., An, B1, B2, . . ., Bm), in that order. The resulting relation Q has one tuple for each combination of tuples—one from R and one from S.
Hence, if R has nR tuples (denoted as |R| = nR ), and S has nS tuples, then
| R × S | will have nR * nS tuples.
The two operands do NOT have to be "type compatible”
In JOIN, only combinations of tuples satisfying the join condition appear in the result, whereas in the CARTESIAN PRODUCT all combinations of tuples are included in the result.
Example:
FEMALE_EMPS   SEX=’F’(EMPLOYEE)
EMPNAMES   FNAME, LNAME, SSN (FEMALE_EMPS)
EMP_DEPENDENTS  EMPNAMES × DEPENDENT
Dr Abdullah Alzahrani.
Fundamental of Database Systems
9/20/2016

16. Relational Algebra CARTESIAN example Binary Relational Operations
Dr Abdullah Alzahrani.
Fundamental of Database Systems
9/20/2016

17. Relational Algebra CARTESIAN example Binary Relational Operations
Dr Abdullah Alzahrani.
Fundamental of Database Systems
9/20/2016

18. Relational Algebra CARTESIAN example Binary Relational Operations
Dr Abdullah Alzahrani.
Fundamental of Database Systems
9/20/2016

19. Relational Algebra In slide 15
CARTESIAN example
Binary Relational Operations
In slide 15
What was the required action (Questions) for the aforementioned results?
Explain each operation?
Dr Abdullah Alzahrani.
Fundamental of Database Systems
9/20/2016

20. Relational Algebra DIVISION Operation
Binary Relational Operations
DIVISION Operation
The division operation is applied to two relations
R(Z)  S(X), where X subset Z. Let Y = Z - X (and hence Z = X  Y); that is, let Y be the set of attributes of R that are not attributes of S.
The result of DIVISION is a relation T(Y) that includes a tuple t if tuples tR appear in R with tR [Y] = t, and with
tR [X] = ts for every tuple ts in S.
For a tuple t to appear in the result T of the DIVISION, the values in t must appear in R in combination with every tuple in S.
Dr Abdullah Alzahrani.
Fundamental of Database Systems
9/20/2016

21. Relational Algebra DIVISION example Binary Relational Operations
Dr Abdullah Alzahrani.
Fundamental of Database Systems
9/20/2016

22. Relational Algebra
Relational Algebra Operations from Set Theory:
We can define the three operations UNION,INTERSECTION, and SET DIFFERENCE on two union-compatible relations R and S as follows:
UNION (∪): The result of this operation, denoted by R∪S, is a relation that includes all tuples that are either in R or in S or in both R and S. Duplicate tuples are eliminated.
INTERSECTION (∩): The result of this operation, denoted by R∩S, is a relation that includes all tuples that are in both Rand S.
SET DIFFERENCE (or MINUS): The result of this operation, denoted by R–S, is a relation that includes all tuples that are in R but not in S.
Dr Abdullah Alzahrani.
Fundamental of Database Systems
9/20/2016

23. Relational Algebra Some examples
Relational Algebra Operations from Set Theory: ∩
Dr Abdullah Alzahrani.
Fundamental of Database Systems
9/20/2016

24. Relational Algebra Use of the Functional operator ℱ
Additional Relational Operations
Use of the Functional operator ℱ
ℱMAX Salary (Employee) retrieves the maximum salary value from the Employee relation
ℱMIN Salary (Employee) retrieves the minimum Salary value from the Employee relation
ℱSUM Salary (Employee) retrieves the sum of the Salary from the Employee relation
Dr Abdullah Alzahrani.
Fundamental of Database Systems
9/20/2016

25. Relational Algebra Examples of Queries in Relational Algebra
Note: all needed relations (tables) are in slide 14 and 16
Q1: Retrieve the name and address of all employees who work for the ‘Research’ department.
Q2: Retrieve the names of employees who have no dependents.
Rename attribute
Dr Abdullah Alzahrani.
Fundamental of Database Systems
9/20/2016

26. Relational Algebra Some important terms: Relation: Attribute: Tuple:
is defined to be a set of tuples in the formal relational model
Attribute:
represents a same property of a same data type for all entities.
Tuple:
represents a set of properties of different data types for a specific entity
Relation schema:
Dr Abdullah Alzahrani.
Fundamental of Database Systems
9/20/2016

27. End Relational Algebra Dr Abdullah Alzahrani. aahzahrani@uqu.edu.sa
Fundamental of Database Systems
9/20/2016