1. Database Design The Relational Model Text Ch5
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2. In the relational model, data are organized into tables.
A table corresponds to the mathematical concept of a relation (come back shortly).
The table must have a name (a.k.a the relation name).
Each column must have a name, known as an attribute.
Each row (not including the table heading row) is called a tuple. If the tuple has n elements then it is called an n-tuple.
The number of columns (resp. rows) is called the degree or arity (resp. cardinality) of the relation.
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3. Table (Relation) Example 1
A Student table in a university database
studentNo
Name
City
Phone
Barbara
Brisbane
David
Sydney
Darren
Melbourne
Johnson
Gold Coast
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4. Relation Schema and Instance
Let R be the name of a relation, and A1,…, An be the attributes. Then R(A1,…, An ) is called the schema of the relation.
Each attribute of a relation must have a fixed set from which to obtain values. Eg,
Name : the set of all possible names
Age: {0, 1, 2,…, 150}
The set corresponding to attribute Ai is called the domain of Ai , denoted dom(Ai ).
At different times, the relation may contain different tuples. Each possible set of tuples is called a state (or an instance) of the relation.
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5. Relational Database Schema and Instance
A relational database – a collection of relations.
The schemas of the relations collectively (together with a set of integrity constraints – see slide 13) is called the relational database schema.
The relations in a database should have distinct names.
Attributes within the same relation should have distinct names.
A database (instance) consists of the instances (one for each relation) of the relations.
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6. Atomic value in each cell
Data Inside a Relation
Atomic value in each cell
The data item in each table cell must be atomic
can not be divided into smaller components
Atomicity is a relative concept, it depends on the application.
A special value NULL can appear in any cell
represents unknown value or non-existent value
eg, in Student table, a student may have no phone number, or his phone number may be unknown. In such cases, the corresponding value is NULL
If t is a tuple, and A is an attribute, then the value of attribute A in t is denoted t[A]. Similarly t[A1, A3] denotes the subtuple of values of the attributes A1 and A3, and so forth.
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7. Mathematical Definition of Relations
Formally, given sets D1, D2, …. Dn a relation r is a subset of D1 x D2 x … x Dn Thus a relation is a set of n-tuples (a1, a2, …, an) where ai  Di
Example: if
student_number = set of 6 digit numbers
student_name = {Jones, Smith, Curry, Lindsay} student_city = {Sydney, Brisbane, Melbourne, GoldCoast}
Then r = { (100001, Jones, Brisbane), (100002, Curry, GoldCoast), (100003, Lindsay, Brisbane), (100004, Smith, Sydney)} is a relation over student_number x student_name x student_city
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8. Properties of Relations
No duplicate tuples within a relation
By definition sets do not contain duplicate elements, hence no tuples should appear more than once.
Ordering of tuples has no significance
elements in a set has no ordering
also in the sense that no information is lost or added when different orders are used.
but it may affect performance!
Ordering of attributes
has no significance in the sense that no information is lost or added if the attributes are ordered differently.
BUT it is important when a tuple is considered an ordered list - for easy presentation.
Alternative definition of tuple can make the ordering unimportant – a tuple is a mapping from attributes to values.
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9. In each tuple of R, values of K uniquely identify that tuple.
Relational Keys
Superkey
An attribute, or a set of attributes, that can uniquely identify a tuple within a relation.
Every relation has at least one superkey -- all attributes of the relation
Key (Candidate Key)
Superkey (K) such that no proper subset is a superkey within the relation.
In each tuple of R, values of K uniquely identify that tuple.
Removing any attribute from K, K will no longer be a superkey.
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10. Candidate keys that are not selected to be primary key.
Relational Keys
Primary Key (PK)
Candidate key selected to identify tuples uniquely within relation. PK attributes will be underlined.
Alternate Keys
Candidate keys that are not selected to be primary key.
Foreign Key (FK)
Attribute, or set of attributes, within one relation that matches candidate key of some (possibly same) relation.
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11. Subjects(subjNo, subjName, points) Students(studNo, Name, Addr, Phone)
Foreign Keys
Example
Subjects(subjNo, subjName, points)
Students(studNo, Name, Addr, Phone)
Enrollment(studNo, subjNo, semester, grade)
In enrollment,
studNo is a FK which references Students
subjNo is a FK which references Subjects
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12. Another Example of FKs
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13. Relational Constraints
Domain constraints
Specify the possible values an attribute can take
Null-value constraints
Specify whether Null value is allowed in an attribute
Key constraints
PK, AK
Entity integrity
No PK value can be NULL
Referential integrity
FK values must either be NULL or appear in corresponding attribute(s) of referenced relation.
Data dependencies, Enterprise rules (later)
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14. Example
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15. Diagram Representation of FKs
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16. Alternative Schema Diagram
Department
Dept_locations
DNAME
DNUMBER
MGRSSN
MGRSTARTDATE
Project
DNUMBER
DLOCATION
PNAME
PNUMBER
PLOCATION
DNUM
Employee
Dependent
FNAME
MINT
LNAME
SSN
BDATE
ADDRESS
SEX
SALARY
SUPERSSN
DNO
ESSN
DEPDENT_NAME
SEX
BDATE
RELATIONSHIP
Works_on
ESSN
PNO
HOURS
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