The Relational Model

Transcription

1 The Relational Model T. M. Murali August 26, 2009

2 Course Outline Weeks 1 5, 13: Query/Manipulation Languages The relational model Relational Algebra SQL Data definition Programming with SQL Weeks 6 8: Data Modelling Weeks 9 13: Relational Design Week 14 15: Students choice

3 What is a Data Model? Data model: notation for describing data or information.

4 What is a Data Model? Data model: notation for describing data or information. Structure of the data: models in databases are conceptual as opposed to physical. Operations on the data: databases data models allow limited set of queries and modifications. Constraints on the data: database data models support specifications of constraints on the data.

5 What is a Data Model? Data model: notation for describing data or information. Structure of the data: models in databases are conceptual as opposed to physical. Operations on the data: databases data models allow limited set of queries and modifications. Constraints on the data: database data models support specifications of constraints on the data. Examples of Data Models: 1. Relational data model. 2. Semi-structured data model (e.g., XML). 3. Object-relational models.

6 The Relational Model CoursesTaken Student Course Grade Hermione Grainger Potions A- Draco Malfoy Potions B Harry Potter Potions A Ron Weasley Potions C Structure: Table (like an array of structs) Operations: Relational algebra (selection, projection, conditions, etc.) Constraints: E.g., grades can be from a fixed list.

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8 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> Structure: Trees or graphs, tags define role played by different pieces of data. Operations: Follow paths in the implied tree from one element to another. Constraints: Can express limitations on data types.

9 Comparison of Models Flexibility:

10 Comparison of Models Flexibility: XML models can represent graphs.

11 Comparison of Models Flexibility: XML models can represent graphs. Limitations of relational model: 1. Simple, limited approach to structuring data. 2. Limited but useful set of operations on the data.

12 Comparison of Models Flexibility: XML models can represent graphs. Limitations of relational model: 1. Simple, limited approach to structuring data. 2. Limited but useful set of operations on the data. Ease of use: SQL enables programmer to express wishes at high level.

13 Comparison of Models Flexibility: XML models can represent graphs. Limitations of relational model: 1. Simple, limited approach to structuring data. 2. Limited but useful set of operations on the data. Ease of use: SQL enables programmer to express wishes at high level. Efficiency of access/modifications: Dramatic query optimisations possible.

14 What is the Relational Model? Built around a single concept for modelling data: the relation or table. Supports high-level programming language (SQL). Has an elegant mathematical design theory. Most current DBMS are relational.

15 The Relation A relation is a two-dimensional table: Relation table. Attribute column name. Tuple row (not the header row). Database collection of relations. CoursesTaken Student Course Grade Hermione Grainger Potions A- Draco Malfoy Potions B Harry Potter Potions A Ron Weasley Potions C

16 The Schema CoursesTaken Student Course Grade Hermione Grainger Potions A- Draco Malfoy Potions B Harry Potter Potions A Ron Weasley Potions C The schema of a relation is the name of the relation followed by a paranthetised list of attributes. CoursesTaken(Student, Course, Grade) A design in a relational model consists of a set of schemas. Such a set of schemas is called a relational database schema.

17 Equivalent Representations of a Relation CoursesTaken Student Course Grade Hermione Grainger Potions A- Draco Malfoy Potions B Harry Potter Potions A Ron Weasley Potions C A relation is a set of tuples and not a list of tuples. Order in which we present the tuples does not matter. The attributes in a schema are a set (not a list). Schema is the same irrespective of order of attributes. We specify a standard order when we introduce a schema. If we reorder attributes, we must also reorder tuples.

18 Equivalent Representations of a Relation CoursesTaken Student Course Grade Hermione Grainger Potions A- Draco Malfoy Potions B Harry Potter Potions A Ron Weasley Potions C A relation is a set of tuples and not a list of tuples. Order in which we present the tuples does not matter. The attributes in a schema are a set (not a list). Schema is the same irrespective of order of attributes. We specify a standard order when we introduce a schema. If we reorder attributes, we must also reorder tuples. How many equivalent representations are there for a relation with m attributes and n tuples?

19 Equivalent Representations of a Relation CoursesTaken Student Course Grade Hermione Grainger Potions A- Draco Malfoy Potions B Harry Potter Potions A Ron Weasley Potions C A relation is a set of tuples and not a list of tuples. Order in which we present the tuples does not matter. The attributes in a schema are a set (not a list). Schema is the same irrespective of order of attributes. We specify a standard order when we introduce a schema. If we reorder attributes, we must also reorder tuples. How many equivalent representations are there for a relation with m attributes and n tuples? m!n!.

20 Schema vs. Instance CoursesTaken Student Course Grade Hermione Grainger Potions A- Draco Malfoy Potions B Harry Potter Potions A Ron Weasley Potions C Schema of a relation rarely changes. Instance of a relation is the set of tuples in it. Relation instances can and are expected to change over time. A conventional database maintains the current instances of the relations in it.

21 Keys of Relations A set of attributes forms a key if we forbid any pair of tuples in an instance from having the same values for the attributes in the key. Indicate the attributes in the key by underlining them. CoursesTaken Student Course Grade Hermione Grainger Potions A- Draco Malfoy Potions B Harry Potter Potions A Ron Weasley Potions C

22 Keys of Relations A set of attributes forms a key if we forbid any pair of tuples in an instance from having the same values for the attributes in the key. Indicate the attributes in the key by underlining them. What is the key for CoursesTaken? CoursesTaken Student Course Grade Hermione Grainger Potions A- Draco Malfoy Potions B Harry Potter Potions A Ron Weasley Potions C

23 Keys of Relations A set of attributes forms a key if we forbid any pair of tuples in an instance from having the same values for the attributes in the key. Indicate the attributes in the key by underlining them. What is the key for CoursesTaken? Just Student if the relation stores information for only one course. CoursesTaken Student Course Grade Hermione Grainger Potions A- Draco Malfoy Potions B Harry Potter Potions A Ron Weasley Potions C

24 Keys of Relations A set of attributes forms a key if we forbid any pair of tuples in an instance from having the same values for the attributes in the key. Indicate the attributes in the key by underlining them. What is the key for CoursesTaken? Just Student if the relation stores information for only one course. The pair (Student, Course) if the relation stores information for many courses. CoursesTaken Student Course Grade Hermione Grainger Potions A- Draco Malfoy Potions B Harry Potter Potions A Ron Weasley Potions C

25 Keys of Relations A set of attributes forms a key if we forbid any pair of tuples in an instance from having the same values for the attributes in the key. Indicate the attributes in the key by underlining them. What is the key for CoursesTaken? Just Student if the relation stores information for only one course. The pair (Student, Course) if the relation stores information for many courses. If a student can take the same course many times, CoursesTaken Student Course Grade Hermione Grainger Potions A- Draco Malfoy Potions B Harry Potter Potions A Ron Weasley Potions C

26 Keys of Relations A set of attributes forms a key if we forbid any pair of tuples in an instance from having the same values for the attributes in the key. Indicate the attributes in the key by underlining them. What is the key for CoursesTaken? Just Student if the relation stores information for only one course. The pair (Student, Course) if the relation stores information for many courses. 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. CoursesTaken Student Course Grade Hermione Grainger Potions A- Draco Malfoy Potions B Harry Potter Potions A Ron Weasley Potions C

27 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. Also record the age and office of the professor. 3. Course: a name, a number, an offering department, a classroom, and an enrollment. (No CRNs.) Each department offers only one course with each number. 4. Department: a unique name, 1 chairperson. Each chairperson can be the head of at most one department. 5. At most one professor teaches each course. Each student receives a grade in each course. Each student evaluates the professor teaching the course. 6. Each course can have 0 pre-requisites, excluding itself. A student enrolled in a course must have enrolled in all its pre-requisites.

28 Relational Design for the Example 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, ChairmanPID: string) Take(StudentPID: string, Number: integer, DeptName: string, Grade: string, ProfessorEvaluation: integer) Teach(ProfessorPID: string, Number: string) integer, DeptName: PreReq(Number: integer, DeptName: string, PreReqNumber: integer, PreReqDeptName: string)

29 Relational Design for the Example 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, ChairmanPID: string) Take(StudentPID: string, Number: integer, DeptName: string, Grade: string, ProfessorEvaluation: integer) Teach(ProfessorPID: string, Number: string) integer, DeptName: PreReq(Number: integer, DeptName: string, PreReqNumber: integer, PreReqDeptName: string)

30 Relational Design for the Example 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, ChairmanPID: 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)

31 Issues to Consider in the Design Can we merge Courses and Teach since each course is taught by at most one professor? Do we need a separate relation to store evaluations? How can we handle pre-requisites that are or s, e.g., you can take CS 4604 if you have taken either CS 2604 or CS 2606? What should we do if more than one professor can teach the same course? How do we handle the situation when a student is allowed to re-take a course? How do we generalise this schema to handle data over more than one semester? What modifications does the schema need if more than one professor can teach a course?