1. COP 6726: New Directions in Database Systems
Normalization

2. Outline
Goal:
Measure the quality of the logical model
Normalization
First Normal Form (1NF)
Second Normal Form (2NF)
Third Normal Form (3NF)
Boyce-Codd Normal Form (BCNF)

3. What is problem? z-no name address c-id c-name c-loc grade z1 James
5th st 1
Database
CM128 A 2
Data mining
CM25 3
Graph theory
CM100 A+ 4
Optimization
CM21 C z2
Paul
11th ave B 5
Network
EE221 z3
Jin
9th st D

4. What is problem? z-no name address c-id c-name c-loc grade z1 James
5th st 1
Database
CM128 A 2
Data mining
CM25 3
Graph theory
CM100 A+ 4
Optimization
CM21 C z2
Paul
11th ave B 5
Network
EE221 z3
Jin
9th st D

5. Normalization
Normalization is the process of decomposing large tables into smaller tables in order to eliminate redundant data and duplicate data and to avoid problems with inserting, deleting, or updating data.
Goal:
Information preservation
Minimum redundancy.

6. Top Down Approach z-no name address c-id c-name c-loc grade z-no name

7. Semantics of attributes is clear.
Informal Guideline
Semantics of attributes is clear.
Reducing redundant information in tuples.
Reducing NULL values in tuples.
Disallowing the possibility of generating spurious tuples

9. Insertion Anomalies Insert a new employee
Employee works for ‘Research’ Department.
Employee does not work for any department.
Insert a new department tuple
Department without an employee

10. Deletion Anomalies
Delete a department.
‘Research’ department

11. Update Anomalies Update a department.
Update manager in ‘Research’ department

12. Functional Dependency (FD)
Given two tuples t1 and t2 ,and
two attributes (or columns) X and Y,
If t1[X] = t2 [X], then t1 [Y] = t2 [Y]
Notation: X  Y
Ssn  {Ename, Bdate, Address, Dnumber}
Dnumber  {Dname, Dmgr_ssn}
{SSN Pnumber}  {Hour}
Ssn  Ename
Pnumber  {Pname, Plocatoin}

13. Functional Dependency (FD)
If X is a candidate key in a relation R, then X  R
If X  Y in R, then we cannot say Y  X
Ssn  {Ename, Bdate, Address, Dnumber}
Dnumber  {Dname, Dmgr_ssn}
{SSN Pnumber}  {Hour}
Ssn  Ename
Pnumber  {Pname, Plocatoin}

14. Functional Dependency (FD)
A functional dependency is a property of the semantics or meaning of the attributes.
Ssn  Ename
: Ssn uniquely determines the employee name.
Pnumber  {Pname, Plocation}
: Project’s number uniquely determines the project names and location.
{Ssn, Pnumber}  Hours
: Ssn and Pnumber uniquely determines the number of hours.

15. Normalization
Normalization process takes a relation schema though a series of tests to certify whether it satisfies a certain normal form.
Minimize redundancy
Minimize the insertion, deletion, and update anomalies.
Normal Form (NF)
1 NF, 2NF, 3NF, Boyce-Codd normal form (BCNF)

16. Normalization Non-addictive Join (or lossless join) property
Spurious tuples generation problem does not occurs after decomposition.
Dependency property
Each functional dependency is preserved after decomposition.

17. Basic Concept Super key Candidate key Primary key
Prime attribute is a member of some candidate key.
Non-prime attribute is not a prime attribute.

18. Basic Concept Dependency Preservation Property
Every functional dependency should be preserved after decomposition.
Non-addictive Join (or lossless Join) Property

19. First Normal Form
An attribute is single atomic value.

20. First Normal Form

21. Second Normal Form FD1 : {Ssn, Pnumber}  Hours FD2 : Ssn  Ename
Every non-prime attribute is full functionally dependent on any key.
FD1 : {Ssn, Pnumber}  Hours
FD2 : Ssn  Ename
FD3 : Pnumber  {Pname, Plocation}

22. Second Normal Form
Every non-prime attribute is full functionally dependent on any key.
FD1 : {Ssn, Pnumber}  Hours
FD2 : Ssn  Ename
FD3 : Pnumber  {Pname, Plocation}

23. Third Normal Form Given FD X  A,
(a) X is a superkey or (b) A is a prime attribute
Transitive dependency
FD1 : Ssn  {Ename, Bdate, Address, Dnumber}
FD2 : Dnumber {Dname, Dmgr_ssn}

24. Third Normal Form Given FD X  A,
(a) X is a superkey or (b) A is a prime attribute

25. 1 NF, 2NF, 3NF

26. Example
FD1 : Property_id#  {Country_name, Lot#, Area, Price, Tax_rate}
FD2 : {County_name, Lot#} {Property_id#, Area, Price, Tax_rate}
FD3 : County_name  Tax_rate
FD4 : Area  Price

27. Example
FD1 : Property_id#  {Country_name, Lot#, Area, Price, Tax_rate}
FD2 : {County_name, Lot#} {Property_id#, Area, Price, Tax_rate}
FD3 : County_name  Tax_rate
FD4 : Area  Price

28. Example
FD1 : Property_id#  {Country_name, Lot#, Area, Price, Tax_rate}
FD2 : {County_name, Lot#} {Property_id#, Area, Price, Tax_rate}
FD3 : County_name  Tax_rate
FD4 : Area  Price

29. Normalization (Top Down Approach)

30. BCNF (Boyce Codd Normal Form)
Given FD X  A, X is always a super key
FD1 : Property_id#  {Country_name, Lot#, Area}
FD2 : {County_name, Lot#} {Property_id#, Area}
FD5 : Area  Country_name
Third Normal Form
Given FD X  A, (a) X is a superkey or (b) A is a prime attribute.

31. BCNF (Boyce Codd Normal Form)
FD1 : Property_id#  {Country_name, Lot#, Area}
FD2 : {County_name, Lot#} {Property_id#, Area}
FD5 : Area  Country_name

32. Take Home Message
Functional Dependency (FD)
Non-addictive join property
Dependency preservation property
Normalization
First Normal Form (1NF)
Second Normal Form (2NF)
Third Normal Form (3NF)
Boyce-Codd Normal Form (BCNF)