the relational modelcourses.cs.vt.edu/.../lecture-02-intro-relational-model.pdf · 2010. 9. 2. ·...

The Relational Model

T. M. Murali

August 25, 2010

T. M. Murali August 25, 2010 CS4604: The Relational Model

Course Outline

I Weeks 1–5, 13: Query/Manipulation Languages

I The relational modelI Relational AlgebraI SQLI Data definitionI Programming with SQL

I Weeks 6–8: Data Modelling

I Weeks 9–13: Relational Design

I Week 14–15: Students’ choice


What is a Data Model?

I Data model: notation for describing data or information.

I Structure of the data: models in databases are conceptual as opposedto physical.

I Operations on the data: databases data models allow limited set ofqueries and modifications.

I Constraints on the data: database data models support specificationsof constraints on the data.

I Examples of Data Models:

1. Relational data model.2. Semi-structured data model (e.g., XML).3. Object-relational models.


What is a Data Model?

I Data model: notation for describing data or information.I Structure of the data: models in databases are conceptual as opposed

to physical.I Operations on the data: databases data models allow limited set of

queries and modifications.I Constraints on the data: database data models support specifications

of constraints on the data.

I Examples of Data Models:

1. Relational data model.2. Semi-structured data model (e.g., XML).3. Object-relational models.


The Relational Model

CoursesTakenStudent Course Grade

Hermione Grainger Potions A-

Draco Malfoy Potions B

Harry Potter Potions A

Ron Weasley Potions C

I Structure: Table (like an array of structs)

I Operations: Relational algebra (selection, projection, conditions, etc.)

I Constraints: E.g., grades can be from a fixed list.


The Semi-structured Model<CoursesTaken>

<Student>Hermione Grainger</Student>

<Course>Potions</Course>

<Grade>A-</Grade>

<Student>Draco Malfoy</Student>

<Course>Potions</Course>

<Grade>B</Grade>

...

</CoursesTaken>

I Structure: Trees or graphs, tags define role played by different piecesof data.

I Operations: Follow paths in the implied tree from one element toanother.

I Constraints: Can express limitations on data types.


Comparison of Models

I Flexibility:

XML models can represent graphs.I Limitations of relational model:

1. Simple, limited approach to structuring data.2. Limited but useful set of operations on the data.

I Ease of use: SQL enables programmer to express wishes at high level.

I Efficiency of access/modifications: Dramatic query optimisationspossible.



I Flexibility: XML models can represent graphs.

I Limitations of relational model:






I Flexibility: XML models can represent graphs.I Limitations of relational model:





What is the Relational Model?

I Built around a single concept for modelling data: the relation or table.

I Supports high-level programming language (SQL).

I Has an elegant mathematical design theory.

I Most current DBMS are relational.


The Relation

I A relation is a two-dimensional table:I Relation ≡ table.I Attribute ≡ column name.I Tuple ≡ row (not the header row).

I Database ≡ collection of relations.







The Schema






I The schema of a relation is the name of the relation followed by aparanthetised list of attributes.

CoursesTaken(Student, Course, Grade)

I A design in a relational model consists of a set of schemas.I Such a set of schemas is called a relational database schema.


Equivalent Representations of a Relation






I A relation is a set of tuples and not a list of tuples.I Order in which we present the tuples does not matter.

I The attributes in a schema are a set (not a list).I Schema is the same irrespective of order of attributes.I We specify a “standard” order when we introduce a schema.I If we reorder attributes, we must also reorder tuples.

I How many equivalent representations are there for a relation with mattributes and n tuples?

m!n!.


Equivalent Representations of a Relation






I A relation is a set of tuples and not a list of tuples.I Order in which we present the tuples does not matter.

I The attributes in a schema are a set (not a list).I Schema is the same irrespective of order of attributes.I We specify a “standard” order when we introduce a schema.I If we reorder attributes, we must also reorder tuples.

I How many equivalent representations are there for a relation with mattributes and n tuples? m!n!.


Schema vs. Instance






I Schema of a relation rarely changes.

I Instance of a relation is the set of tuples in it.

I Relation instances can and are expected to change over time.

I A conventional database maintains the “current” instances of therelations in it.


Keys of Relations

I A set of attributes forms a key if we forbid any pair of tuples in aninstance from having the same values for the attributes in the key.

I Indicate the attributes in the key by underlining them.

I What is the key for CoursesTaken?

I Just Student if the relation stores information for only one course.I The pair (Student, Course) if the relation stores information for many

courses.I If a student can take the same course many times,

add Semester andYear as attributes of the relation and include both in the key.







Keys of Relations



I What is the key for CoursesTaken?I Just Student if the relation stores information for only one course.

I The pair (Student, Course) if the relation stores information for manycourses.

I If a student can take the same course many times,








Keys of Relations



I What is the key for CoursesTaken?I Just Student if the relation stores information for only one course.I The pair (Student, Course) if the relation stores information for many

courses.

I If a student can take the same course many times,








Keys of Relations




courses.I If a student can take the same course many times,








Keys of Relations




courses.I If a student can take the same course many times, add Semester and

Year as attributes of the relation and include both in the key.







Example: Class Enrollments in a Single Semester

1. Student: a name, a unique PID, and an address.

2. Professor: a name, a unique PID, and belongs to a department. Alsorecord the age and office of the professor.

3. Course: a name, a number, an offering department, a classroom, andan enrollment. (No CRNs.) Each department offers only one coursewith each number.

4. Department: a unique name, ≤ 1 chairperson. Each chairperson canbe the head of at most one department.

5. At most one professor teaches each course. Each student receives agrade in each course. Each student evaluates the professor teachingthe course.

6. Each course can have ≥ 0 pre-requisites, excluding itself. A studentenrolled in a course must have enrolled in all its pre-requisites.


Relational Design for the Example

I What should the keys be?

Students(PID: string, Name: string, Address: string)

Professors(PID: string, Name: string, Office: string,

Age: integer, DepartmentName: string)

Courses(Number: integer, DeptName: string,

CourseName: string, Classroom: string, Enrollment:

integer)

Departments(Name: string, ChairPID: string)

Take(StudentPID: string, Number: integer, DeptName:

string, Grade: string, ProfessorEvaluation: integer)

Teach(ProfessorPID: string, Number: integer, DeptName:

string)

PreReq(Number: integer, DeptName: string,

PreReqNumber: integer, PreReqDeptName: string)


Relational Design for the Example

I What should the keys be?

Students(PID: string, Name: string, Address: string)

Professors(PID: string, Name: string, Office:

string, Age: integer, DepartmentName: string)

Courses(Number: integer, DeptName: string,

CourseName: string, Classroom: string, Enrollment:

integer)

Departments(Name: string, ChairPID: string)

Take(StudentPID: string, Number: integer, DeptName:

string, Grade: string, ProfessorEvaluation: integer)

Teach(ProfessorPID: string, Number: integer, DeptName:

string)

PreReq(Number: integer, DeptName: string,

PreReqNumber: integer, PreReqDeptName: string)


Issues to Consider in the Design

I Can we merge Courses and Teach since each course is taught by atmost one professor?

I Do we need a separate relation to store evaluations?

I How can we handle pre-requisites that are “or”s, e.g., you can takeCS 4604 if you have taken either CS 2604 or CS 2606?

I What should we do if more than one professor can teach the samecourse?

I How do we generalise this schema to handle data over more than onesemester?

I How do we handle the situation when a student is allowed to re-takea course?


the relational modelcourses.cs.vt.edu/.../lecture-02-intro-relational-model.pdf · 2010. 9. 2. ·...

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