Chapter 2 Relational Data Model-part 2

RELATIONAL DATA MODEL
PART 2
(Additional Notes)

DFC2033 Database System

Course Learning Outcome
¨  CLO1 : Explain the fundamentals concepts of database management
and relational data model to create a database based on an
organization’s requirements.
¨  CLO3 : Solve an organization’s requirements by selecting the correct
database query formulation using an appropriate commercial
Database Management System (DBMS).
FP 304 – Database System

Learning Outcome
¨  Use operators of relational algebra.
¨  Identify the fundamental operators used to retrieve information from
a relational database.
¨  Describe the purpose and input of each of the operators.
¨  Use the operators to write the expressions based on given relational
tables.
¨  Show the output of the fundamental operators based on a given
database.
¨  Define the traditional set of operators for relational tables.
¨  Draw the Venn diagrams for traditional set operators.
¨  Define union compatibility.
¨  Apply the union, intersect, and difference set operators to two given
relational tables.

Relational Algebra
Relational Algebra is :
¨  The formal description of how a relational database operates
¨  An interface to the data stored in the database itself
¨  The mathematics which underpin SQL operations
¨  Operators in relational algebra are not necessarily the same as SQL
operators, even if they have the same name. For example, the SELECT
statement exists in SQL, and also exists in relational algebra. These two uses
of SELECT are not the same.
¨  The DBMS must take whatever SQL statements the user types in and translate
them into relational algebra operations before applying them to the
database.

Restrict (select)
¨  SELECT operation is used to select a subset of the tuples from a relation that
satisfy a selection condition.
¨  It is a filter that keeps only those tuples that satisfy a qualifying condition –
those satisfying the condition are selected while others are discarded.
¨  Symbol :
¤  σ (sigma) used to denote the SELECT operator
¤  (R) denote relation name.
¨  Syntax :
¤  σ<selection condition > ( R )
¤  Normally combine with {=,<,>, <=, >=, =}

Restrict (select)
¨  Symbol :
¤  σ (sigma) used to denote the SELECT operator
¤  (R) denote relation name.
¨  Syntax :
¤ σ<selection condition>( R )
¤  Normally combine with {=,<,>, <=, >=}
¨  May combine with Boolean Operator:
¤  AND
¤  OR
¤  NOT

Restrict (select)
¨  Example:
¤  To select the EMPLOYEE tuples whose department
number is four

¤  Select salary is greater than $30,000 the following
notation is used:
σDNO = 4 (EMPLOYEE)
σSALARY > 30,000 (EMPLOYEE)

¨  Select the tuples for all employees who either work
in department 4 and make over RM2500 per year,
or work in department 1 and make over RM3000.
Restrict (select)
σ(Dno=4 AND Salary>2500) OR (Dno=1 AND Salary>3000)(EMPLOYEE)

Example
Table : EMP_RESULT
EMP_RESULT ß σ(Dno=4 AND Salary>2500) OR (Dno=1 AND Salary>3000)(EMPLOYEE)

Project
¨  Project operation selects certain columns from the
table and discards the other columns.
¨  The PROJECT creates a vertical partitioning – one
with the needed columns (attributes) containing
results of the operation and other containing the
discarded Columns.
¨  Symbol -: Л (pi)
¨  Syntax : Л <attribute list> (R)


Example
¨  List each employee’s staff number first, last name and salary.
STAFF_NEW ß Л staffNo,fname,lname,salary(STAFF)

Example
Table : STAFF_NEW

Project and select operators
¨  We can combine project with select operators when
we want to select certain column that specify
specific conditions.
¨  Example:
¤  Select student name and address for people who live in
Seremban.
¤  First : Select from temporary table who live in
Seremban
¤  Select : List name and address à temporary table

Example
Retrieve the first name, last name, salary and branch number of all employees
who work in branch B003.
The sequence is :
TEM_STAFF ßσbranchNo=B003(STAFF)
RESULT ß ЛFname,Lname,Salary,branchNo(TEMP_STAFF)

Example
TEM_STAFF ßσbranchNo=B003(STAFF)
RESULT ß ЛFname,Lname,Salary,branchNo(TEMP_STAFF)
You can also combine the operation as below:
ЛFname,Lname,Salary,branchNo(σbranchNo=B003(STAFF))

Exercise
¨  Using relational algebra
¤  Select Employee whose test score is greater than 91.
¤  List all the employee number, test code and score for test record.
¤  List all the test number, test code for employee number 110.
Table : Employee

Cross product
¨  This operation is used to combine tuples from two
relations in a combinatorial fashion.
¨  Concatenation of every tuple of relation R with
every tuple of relation S.
¨  Denoted by X
¨  R X S
¨  Syntax: (Л <attributelist>(R))X (Л <attributelist>(S))

Example
ClientNo fName lname
CR76 John Kay
CR56 Aline Stewart
CR74 Mike Ritchie
CR62 Mary Tregear
ClientNo propertyNo comment
CR56 PA14 Too small
CR76 PG4 Too remote
CR56 PG4
CR62 PA14 No dining room
CR56 PG36
TABLE: CLIENT TABLE: VIEWING
TABLE: RESULT

TABLE: RESULT
RESULT ß(Л clientNo, fName, lName(Client)) X ((Л clientNo, propertyNo, comment (Viewing))
RESULT

Join
¨  Two relations R and S over all common attributes.
¨  One occurrence of each common attribute is eliminated from
the result.
¨  Symbol :
¨  Syntax:(Л <attributelist>(R)) (Л <attributlist> (R))
¨  Types of Join:
¤  Inner Join
¤  Outer Join
¤  Theta Join
¤  Natural Join
¤  Equi Join
¤  Semi Join
Please Find the definition

Inner join
¨  An INNER JOIN produces a result table containing
composite rows created by combining rows from two
tables where some join condition evaluates to true.
¨  Rows that do not satisfy the join condition will not
appear in the result table of an inner join.
¨  The inner join is the default join type, therefore the
keyword INNER is optional and may be omitted.

ClientNo fName lname
CR76 John Kay
CR56 Aline Stewart
CR74 Mike Ritchie
CR62 Mary Tregear
ClientNo propertyNo comment
CR56 PA14 Too small
CR76 PG4 Too remote
CR56 PG4
CR62 PA14 No dining room
CR56 PG36
TABLE: client TABLE: VIEWING
Example

Example
Client.ClientNo fname lname comment.ClientNo propertyNo comment
CR76 John Kay CR76 PG4 Too remote
CR56 Aline Stewart CR56 PA14 Too small
CR56 Aline Stewart CR56 PG4
CR56 Aline Stewart CR56 PG36
CR62 Mary Tregear CR62 PA14 No dining room
Result ß (Л clientNo, fName, lName(Client)) (Л clientNo, propertyNo, comment (Viewing))
TABLE: Result
Viewing.

Outer join
¨  There are two types of outer join:
¤  Left Outer Join
¤  Right Outer Join

Left outer join
¡  The left outer join operation keeps every tuple in the first
or left relation R in R and S;
¡  If no matching tuple is found in S, then the attributes of S
in the join result are filled with null values.
¡  Symbol :

Left outer join
Result ß (Л P.PROJNO, PPROJNAME, DEPNO(Project)) Department
NullNull

Right outer join
¡  A similar operation with left outer join, right outer join,
keeps every tuple in the second or right relation S in the
result of R and S.
¨  Symbol :

Right outer join
Result ß (Л P.PROJNO, PPROJNAME, DEPNO(Project)) Department)
NullNullNull

Traditional set operator from set theory
¨  There are 3 traditional set operator :
¤  Union
¤  Intersection
¤  Difference

Union
¨  Relation that includes all tuples that are either in R
or in S or in both R and S.
¨  Table must have the same number of attribute.
¨  Duplicate tuples are eliminated.
¨  Symbol : ∪
¨  Syntax :
Л <attribute list>(R) ∪ Л <attribute list>(R)

Union

Union
List all cities where there is in branch office or in property for rent.
Result1 ß Л city(Branch)
Result2 ß Л city(PropertyForRent)
Result_Union ß Result1 ∪ Result2

Result_Union ß
Л city(Branch) ∪ Л city(PropertyForRent)
Result

Union compatibility
¡  The operand relations R1(A1, A2, ..., An) and R2(B1, B2, ...,
Bn) must have the same number of attributes, and the
domains of corresponding attributes must be compatible;
that is, dom(Ai)=dom(Bi) for i=1, 2, ..., n.
¡  In other words, two relations are union compatibles if they
have the same degree and the
¡  same number attribute
¡  and domains

Union compatibility
¨  The relations below is said to be union compatibility
relation

Intersection
¨  Only those tuples that appear in both of the named
relation are given as an output result.
¨  The two operand must be type compatible.
¨  Symbol : ∩
¨  R ∩ S
¨  Syntax: Л <attributelist>(R) ∩ Л <attributelist>(R)

Intersection

Intersection
¨  List all cities where there is both a branch office and at least
one property for rent.
¨  Л city(Branch) ∩ Л city(PropertyForRent)

Difference
¨  Subtracts from the first named relation those tuples
that appear in the second named relation and
create a new relation.
¨  The two operand must be type compatible.
¨  Symbol : - (minus)
¨  Syntax: Л <attributelist>(R) – Л<attributelist>(R)

Difference

Difference
¨  List all cities where there is a branch office but no properties for rent.

Л city(Branch) – Лcity(PropertyForRent)

Chapter 2 Relational Data Model-part 2

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Chapter 2 Relational Data Model-part 2