1. Database Systems The Basic (Flat) Relational Model

2. Relational Model Concepts (1)
Table is called relation
Row (record) is called tuple
Column header is called attribute
Students
SSN Name Age GPA
John
Mary
Bill
Name of the relation
Attributes
head
tuples (rows)
columns

3. Relational Model Concepts (2)
Given a tuple t and an attribute A in a relation R,
t[A] represents the value of t under A in R
Example: If t is the second tuple in Students
t[Name] = Mary
t[Age] = 18
t[Name, Age] = (Mary, 18)

4. Domain of an Attribute Definition:
The set of values that an attribute can take on is the domain of the attribute
dom(A) --- the domain of attribute A
A domain is usually represented by a type
Examples:
SSN char(9) --- character string of length 9
Name varchar(30) --- character string of variable length up to 30 characters
Age number --- a number

5. Relational Model Concepts (3)
Two aspects of a relation:
Schema --- the set of attributes of R.
State (or contents) --- the CURRENT set of tuples of R (denoted by r(R))
Schema of a relation rarely changes.
Some possible changes are:
Rename an attribute
Delete an attribute
Add an attribute
Delete the schema

6. Relational Model Concepts (4)
The state of a relation may change frequently. Some possible changes are:
Modify some attribute values
Delete an existing tuple
Insert a new tuple
A given schema may have different states at different times.

7. An Example Database Students Departments
SSN Name Major GPA Name Location Chairperson
Jeff CS CS N18 EB Aggarwal
Mary Math EE Q4 EB Sackman
Bob CS Math LN Hanson
Wang EE Biology S Smith
Courses Sections
Name Course# CreditHours Dept Course# Section# Semester Instructor
Database CS CS CS Fall Meng
Database CS CS CS Fall Meng
Dis. Math Math Math Math Fall Hanson
Lin. Alg Math Math Math Spring Brown

8. Relation Schema A relation schema is used to describe a relation
Denoted by R(A1, A2, A3, …, An), where
R: Relation schema name
A1, …, An: attributes of R
The degree of a table/relation is the number of attributes in a relation schema

9. Examples STUDENT(Name, SSN, HomePhone, Address, OfficePhone, Age, GPA)
Degree(STUDENT) = 7
dom(Name) = all names which consists of at most 30 characters.
dom (SSN) is the set of valid 9-digit social security numbers.
dom(HomePhone): local phone numbers.

10. Relation Instance (1)
A relation (or relation instance) r of the relation schema R(A1, A2, …, An), denoted by r(R), is a set of n-tuples
r = {t1, t2, …, tm)
each n-tuple ti is an ordered list of n values,
ti = <v1, v2, …, vn) where
each value vi, 1  i  n, is an element of dom(Ai) or a special null value
The Cartesian product of two sets is all combination of elements with the first from set one and the second from set two.

11. Relation Instance (2)
A relation r(R) is a mathematical relation of degree n on the domains dom(A1), dom(A2), …, and dom(An), which is a subset of the Cartesian product of the domains that define R:
r(R)  dom(A1)  dom(A2)  …  dom(An)
We denote the number of values or cardinality of a domain D by D
The total number of tuples in the Cartesian product is
dom(A1) * dom(A2) * … * dom(An)

12. Characteristics of Relations
A relation has a name that is distinct from all other relation names
Each cell of the relation contains exactly one atomic (single) value
Each attribute has a distinct name (unique)
All values of an attribute (single column) are from the same domain (same type and meaning)

13. Characteristics of Relations
Ordering of attributes in a relation schema R (and of values within each tuple):
We will consider the attributes in R(A1, A2, ..., An) and the values in t=<v1, v2, ..., vn> to be ordered .
(However, a more general alternative definition of relation does not require this ordering).
Each tuple is distinct; there are no duplicate tuples
The order of tuples has no significance, theoretically (efficiency)

14. Relational Model Constraints
Domain Constraint
No multi-valued attributes are allowed in a table
That is, for any tuple t and attribute A in a table, t[A] must be a single atomic value
entries in the table are single-valued (atomic). Therefore composite and multi-valued attributes are not directly represented in the relational model
Attribute data should match its data type

15. Examples of Multi-valued Attributes
Employees
SSN Name Age Dependents
Bob Allen, Ann
Mary Kathy
Bill Mike, Susan, David
Other examples:
Attribute Authors of relation Books
Attribute Reference_Books of relation Courses
Attribute of Hobbies of relation Employees

16. Key Constraints All tuples in a relation must be distinct
No two rows in the same table can be identical at any given time. That is, each tuple in a table is unique
This rule comes from the mathematical definition that a relation is a set of tuples and the fact that a set never contains two identical elements
This rule has serious implications on the performance of relational database systems.
When a new tuple is inserted to a relation, the system has to make sure that the new tuple is different from all existing tuples in the relation

17. Superkey (1)
Definition:
A superkey (SK) of a relation is a set of one or more attributes whose values uniquely identify every tuple of the relation
Superkey: a subset of attributes whose values are distinct for each tuple in R
Superkeys may contain redundant (extra) attributes
Examples:
Attribute SSN is a SK of relation Students
{SSN, Name} is also a SK
The set of attributes {Name, Birthdate, Home_Address} is a SK of Students

18. Superkey (2)
Is the set of all attributes of a relation a superkey of the relation?
In the following relation, is attribute A a superkey?
How about {B, C}?
A B C D
a b c1 d1
a b c2 d1
a b c1 d1
a b c2 d1

19. Superkey (3) Some claims: Every relation has at least one superkey
Any superset of a superkey is a superkey
From a given state of a relation, we may determine whether a set of attributes of the relation does not form a superkey, but we can not determine if a set of attributes forms a superkey

20. Key (1)
Key: a subset of attributes in R whose values are unique for each tuple in r(R), but with no redundant (extra) attributes.
Definition: A set of attributes is a key of a relation if
(1) it is a superkey of the relation, and
(2) no proper subset of it is a superkey of the relation
A Key of any relation is a minimal superkey
Student ID is candidate key for Student, since it is a superkey, and no subset of it is a superkey.

21. Key (2)
If any attribute is removed from a key, then the remaining attributes no longer form a key (minimality property)
Example:
Students(SSN, Name, Home_Address, Birthdate, GPA),
SSN is a key.
{SSN, Name} is a superkey but not a key
{Name, Home_Address, Birthdate} is also a key

22. Key (3)
Every relation has at least one key
A relation may have more than one key
Keys of a relation are also known as candidate keys of the relation.
Candidate keys: a subset of attributes which can be used as a key
Customer-id is candidate key of customer
account-number is candidate key of account

23. Candidate Key
Example: Find all possible candidate keys for the following relation based on its current tuples.
A B C D
a b c d1
a b c d1
a b c d1
a b c d1
Answer: {A, B}, {A, C}, {B, C}
Although several candidate keys may exist, one of the candidate keys is selected to be the primary key

24. Primary Key (1) Definition:
A primary key of a relation is the candidate key chosen by the database designer for a particular application.
The primary key of each relation is chosen and declared at the time when the relation is defined Once chosen, it cannot be changed
The primary key is usually chosen to be the candidate key that has the smallest number of attributes to improve both storage efficiency and query processing efficiency

25. Primary Key (2)
With the primary key defined, only the values under the attributes in the primary key need to be checked for identifying duplicate when new tuples are inserted (index is often used)
The primary key of a relation is often used in references from other relations

26. Example STUDENT(ST-NO, SSN, Name, Age, GPA, … ) Superkey:
{ST-No, Name}
{SSN, Age, Address}
Candidate keys:
SSN
ST-NO
Primary Key:

27. Null Value
For a given tuple t and a given attribute A of a relation R, the following cases may occur when t is to be inserted into R.
t[A] is unknown
t[A] is yet to be assigned
t[A] is inapplicable
When one of the above cases occurs, assign a null value to t[A]:
t[A] = null

28. Constraints on Null Entity Integrity Constraint
No attribute in the primary key can take on null values
Note: A null value is different from either a 0 or a space
No primary key value can be null
i.e. null is not allowed as a value for a primary key

29. Foreign Key (1) Definition:
A set of attributes of relation R1 is a foreign key FK in R1 if it satisfies the following two conditions:
There is a relation R2 with the primary key PK such that FK and PK have the same number of attributes with compatible domains
For any tuple ti in R1, either there exists a tuple tj in R2 such that ti[FK] = tj[PK] or ti[FK] is null

30. Foreign Key (2) R1(PK1, A1, A2, …, An, FK) R2(PK2, B1, B2, …, Bm)
FK is called a foreign key iff:
Attributes in FK have the same domain as PK2
A value of FK in a tuple ti of R1 either occurs as a value of PK2 for some tuple tj in R2 or null:
ti[FK] = tj[PK2]
we say that ti refers to (references) tj
R1 and R2 in the definition could be the same relation
Employees(SSN, Age, Salary, Position, Manager_SSN)

31. Foreign Key (3) Employee SSN Name Age Dept-Name
John Sales
Mary Service
Bob null
Department Name Location Manager
Sales Binghamton Bill
Inventory Vestal Charles
Service Vestal Maria
Dept_Name of Employee is a foreign key referencing Name of Department

32. Foreign Key (4) Referential Integrity Constraint
No relation is allowed to contain unmatched foreign key values
States that a tuple in one relation which refers to another relation must refer to an existing tuple in that relation
Using a foreign key of a relation to reference the (primary) key of another relation is THE WAY used by the relational data model to establish relationships among different relations

33. Foreign Key (5) CSNO Ruba 123 cs111 Ali 222 cs210 CSNO Name Hrs
STNO
CSNO
Name
Ruba cs111
Ali cs210
CSNO Name Hrs
Cs Intro to com
Cs C programming 3

34. Semantic Integrity Constraints
GPA: grater than or equal to 0 and less than or equal to 4
Age: greater than 0
Grade: greater than or equal 35 and less than or equal 100

35. Update Operations on Relations
Updates
insert, or
delete, or
Modify
Retrievals
Queries

36. Populated database state for COMPANY

37. The Insert Operation
Provides a list of attribute values for a new tuple (t) which is to be inserted into a relation r(R)
When inserting a new tuple in r(R), we should make sure that the values preserve all constraint types we studied before
May violate all types of constraint
Insert<‘Cecilia’, ‘F’, ‘Kolonsky’, null, ‘ ’,’3rd Street, Katy, TX’, F, 28000, null, 4> into EMPLOYEE >
Rejected, Primary Key is null (Entity Integrity Constraint)

38. The Insert Operation
Insert<‘Cecilia’, ‘F’, ‘Kolonsky’, ‘ ’, ‘ ’,’3rd Street, Katy, TX’, F, 28000, null, 4> into EMPLOYEE >
Rejected, Primary Key is duplicate (Key Constraint)
Insert<‘Cecilia’, ‘F’, ‘Kolonsky’, ‘ , ‘ ’,’3rd Street, Katy, TX’, F, 28000, null, 7> into EMPLOYEE >
Rejected, DEPARTMENT # 7 does not exist. (Referential Integrity Constraint)
Insert<‘Cecilia’, ‘F’, ‘Kolonsky’, ‘ , ‘ ’,’3rd Street, Katy, TX’, F, 28000, null, 4> into EMPLOYEE >
Accepted

39. The Delete Operation Deletes a tuple or tuples from r(R)
It can only violate referential integrity constraint.
“Delete from WORKS_ON where ESSN = ‘ ’ and PNO = 10”
Accepted
“Delete from EMPLOYEE where SSN = ‘ ’”
Rejected. Tuples in WORK_ON refer to this tuple, if the tuple is deleted, referential integrity violations will result

40. The Delete Operation “Delete from EMPLOYEE where SSN = ‘333445555’”
Rejected. Tuples in EMPLOYEE, DEPARTMENT, WORK_ON, and DEPENDENT refer to this tuple, if the tuple is deleted, referential integrity violations will result

41. The Modify Operation
It is used to change the values of one or more attributes in a tuple or more of some relation r(R)
May violate all constraints
“Update EMPLOYEE, set Salary = where SSN = ‘ ’”
Accepted
“Update EMPLOYEE, set DNO = 1 where SSN = ‘ ’”

42. The Modify Operation
“Update EMPLOYEE, set DNO = 7 where SSN = ‘ ’”
Rejected, it violates referential integrity constraint
“Update EMPLOYEE, set SSN = ‘ ’ where SSN = ‘ ’”
“Update EMPLOYEE, set SSN = ‘ ’ where SSN = ‘ ’”
Rejected, it violates unique row (key) and referential integrity constraints