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Database Normalization
MIS 520 – Database Theory
Fall 2001 (Day)
Lecture 4/5/6

? This is the process which allows you to winnow out
redundant data within your database.
? This involves restructuring the tables to successively
meeting higher forms of Normalization.
? A properly normalized database should have the
following characteristics
– Scalar values in each fields
– Absence of redundancy.
– Minimal use of null values.
– Minimal loss of information.
Definition

? Levels of normalization based on the amount of
redundancy in the database.
? Various levels of normalization are:
– First Normal Form (1NF)
– Second Normal Form (2NF)
– Third Normal Form (3NF)
– Boyce-Codd Normal Form (BCNF)
– Fourth Normal Form (4NF)
– Fifth Normal Form (5NF)
– Domain Key Normal Form (DKNF)
Levels of Normalization
Redundancy
Number
of
Tables
Most databases should be 3NF or BCNF in order to avoid
the database anomalies.
Complexity

Levels of Normalization
Each higher level is a subset of the lower level
DKNF
1NF
2NF
3NF
4NF
5NF

A table is considered to be in 1NF if all the fields contain
only scalar values (as opposed to list of values).
Example (Not 1NF)
First Normal Form (1NF)
Author and AuPhone columns are not scalar
0-321-32132-1 Balloon Sleepy,
Snoopy,
Grumpy
321-321-1111,
232-234-1234,
665-235-6532
Small House 714-000-0000 $34.00
0-55-123456-9 Main Street Jones,
Smith
123-333-3333,
654-223-3455
Small House 714-000-0000 $22.95
0-123-45678-0 Ulysses Joyce 666-666-6666 Alpha Press 999-999-9999 $34.00
1-22-233700-0 Visual
Basic
Roman 444-444-4444 Big House 123-456-7890 $25.00
ISBN Title AuName AuPhone PubName PubPhone Price

1. Place all items that appear in the repeating group in a new
table
2. Designate a primary key for each new table produced.
3. Duplicate in the new table the primary key of the table from
which the repeating group was extracted or vice versa.
Example (1NF)
1NF - Decomposition
0-321-32132-1 Balloon Small House 714-000-0000 $34.00
0-55-123456-9 Main Street Small House 714-000-0000 $22.95
0-123-45678-0 Ulysses Alpha Press 999-999-9999 $34.00
1-22-233700-0 Visual
Basic
Big House 123-456-7890 $25.00
ISBN Title PubName PubPhone Price
ISBN AuName AuPhone
0-123-45678-0 Joyce 666-666-6666
1-22-233700-0 Roman 444-444-4444
0-55-123456-9 Smith 654-223-3455
0-55-123456-9 Jones 123-333-3333
0-321-32132-1 Grumpy 665-235-6532
0-321-32132-1 Snoopy 232-234-1234
0-321-32132-1 Sleepy 321-321-1111

1. If one set of attributes in a table determines another
set of attributes in the table, then the second set of
attributes is said to be functionally dependent on the
first set of attributes.
Example 1
Functional Dependencies
0-321-32132-1 Balloon $34.00
0-55-123456-9 Main Street $22.95
0-123-45678-0 Ulysses $34.00
1-22-233700-0 Visual
Basic
$25.00
ISBN Title Price Table Scheme: {ISBN, Title, Price}
Functional Dependencies: {ISBN} ? {Title}
{ISBN} ? {Price}

Example 2
1 Big House 999-999-9999
2 Small House 123-456-7890
3 Alpha Press 111-111-1111
PubID PubName PubPhone Table Scheme: {PubID, PubName, PubPhone}
Functional Dependencies: {PubId} ? {PubPhone}
{PubId} ? {PubName}
{PubName, PubPhone} ? {PubID}
AuID AuName AuPhone
6 Joyce 666-666-6666
7 Roman 444-444-4444
5 Smith 654-223-3455
4 Jones 123-333-3333
3 Grumpy 665-235-6532
2 Snoopy 232-234-1234
1 Sleepy 321-321-1111
Example 3
Table Scheme: {AuID, AuName, AuPhone}
Functional Dependencies: {AuId} ? {AuPhone}
{AuId} ? {AuName}
{AuName, AuPhone} ? {AuID}

FD – Example
Database to track reviews of papers submitted to an academic
conference. Prospective authors submit papers for review and
possible acceptance in the published conference proceedings.
Details of the entities
– Author information includes a unique author number, a name, a mailing
address, and a unique (optional) email address.
– Paper information includes the primary author, the paper number, the
title, the abstract, and review status (pending, accepted,rejected)
– Reviewer information includes the reviewer number, the name, the
mailing address, and a unique (optional) email address
– A completed review includes the reviewer number, the date, the paper
number, comments to the authors, comments to the program
chairperson, and ratings (overall, originality, correctness, style, clarity)

FD – Example
– AuthNo ? AuthName, AuthEmail, AuthAddress
– AuthEmail ? AuthNo
– PaperNo ? Primary-AuthNo, Title, Abstract, Status
– RevNo ? RevName, RevEmail, RevAddress
– RevEmail ? RevNo
– RevNo, PaperNo ? AuthComm, Prog-Comm, Date,
Rating1, Rating2, Rating3, Rating4, Rating5

For a table to be in 2NF, there are two requirements
– The database is in first normal form
– All nonkey attributes in the table must be functionally dependent on the
entire primary key
Note: Remember that we are dealing with non-key attributes
Example 1 (Not 2NF)
Scheme ? {Title, PubId, AuId, Price, AuAddress}
1. Key ? {Title, PubId, AuId}
2. {Title, PubId, AuID} ? {Price}
3. {AuID} ? {AuAddress}
4. AuAddress does not belong to a key
5. AuAddress functionally depends on AuId which is a subset of a key
Second Normal Form (2NF)

Example 2 (Not 2NF)
Scheme ? {City, Street, HouseNumber, HouseColor, CityPopulation}
1. key ? {City, Street, HouseNumber}
2. {City, Street, HouseNumber} ? {HouseColor}
3. {City} ? {CityPopulation}
4. CityPopulation does not belong to any key.
5. CityPopulation is functionally dependent on the City which is a proper subset of the
key
Example 3 (Not 2NF)
Scheme ? {studio, movie, budget, studio_city}
1. Key ? {studio, movie}
2. {studio, movie} ? {budget}
3. {studio} ? {studio_city}
4. studio_city is not a part of a key
5. studio_city functionally depends on studio which is a proper subset of the key
Second Normal Form (2NF)

1. If a data item is fully functionally dependent on only a part of the
primary key, move that data item and that part of the primary key
to a new table.
2. If other data items are functionally dependent on the same part of
the key, place them in the new table also
3. Make the partial primary key copied from the original table the
primary key for the new table. Place all items that appear in the
repeating group in a new table
Example 1 (Convert to 2NF)
Old Scheme ? {Title, PubId, AuId, Price, AuAddress}
New Scheme ? {Title, PubId, AuId, Price}
New Scheme ? {AuId, AuAddress}
2NF - Decomposition

Old Scheme ? {Studio, Movie, Budget, StudioCity}
New Scheme ? {Movie, Studio, Budget}
New Scheme ? {Studio, City}
Old Scheme ? {City, Street, HouseNumber, HouseColor, CityPopulation}
New Scheme ? {City, Street, HouseNumber, HouseColor}
New Scheme ? {City, CityPopulation}
2NF - Decomposition

? Concepts of Database Management
– Chapter 5 - Problems 9 & 11
Home Work #2 (Normalization)

? Lecture 7 & Lecture 9 in CETL to work on Access
? Project guidelines are provided
– Students should start the design of their database
Announcement

This form dictates that all non-key attributes of a table must be functionally
dependent on a candidate key i.e. there can be no interdependencies
among non-key attributes.
For a table to be in 3NF, there are two requirements
– The table should be second normal form
– No attribute is transitively dependent on the primary key
Example (Not in 3NF)
Scheme ? {Title, PubID, PageCount, Price }
1. Key ? {Title, PubId}
2. {Title, PubId} ? {PageCount}
3. {PageCount} ? {Price}
4. Both Price and PageCount depend on a key hence 2NF
5. Transitively {Title, PubID} ? {Price} hence not in 3NF
Third Normal Form (3NF)

Example 2 (Not in 3NF)
Scheme ? {Studio, StudioCity, CityTemp}
1. Primary Key ? {Studio}
2. {Studio} ? {StudioCity}
3. {StudioCity} ? {CityTemp}
4. {Studio} ? {CityTemp}
5. Both StudioCity and CityTemp depend on the entire key hence 2NF
6. CityTemp transitively depends on Studio hence violates 3NF
Scheme ? {BuildingID, Contractor, Fee}
1. Primary Key ? {BuildingID}
2. {BuildingID} ? {Contractor}
3. {Contractor} ? {Fee}
4. {BuildingID} ? {Fee}
5. Fee transitively depends on the BuildingID
6. Both Contractor and Fee depend on the entire key hence 2NF
Third Normal Form (3NF)
BuildingID Contractor Fee
100 Randolph 1200
150 Ingersoll 1100
200 Randolph 1200
250 Pitkin 1100
300 Randolph 1200

1. Move all items involved in transitive dependencies to a new entity.
2. Identify a primary key for the new entity.
3. Place the primary key for the new entity as a foreign key on the
original entity.
Old Scheme ? {Title, PubID, PageCount, Price }
New Scheme ? {PubID, PageCount, Price}
New Scheme ? {Title, PubID, PageCount}
3NF - Decomposition

Old Scheme ? {Studio, StudioCity, CityTemp}
New Scheme ? {Studio, StudioCity}
New Scheme ? {StudioCity, CityTemp}
Old Scheme ? {BuildingID, Contractor, Fee}
New Scheme ? {BuildingID, Contractor}
New Scheme ? {Contractor, Fee}
3NF - Decomposition
BuildingID Contractor
100 Randolph
150 Ingersoll
200 Randolph
250 Pitkin
300 Randolph
Contractor Fee
Randolph 1200
Ingersoll 1100
Pitkin 1100

? BCNF does not allow dependencies between attributes that belong to candidate keys.
? BCNF is a refinement of the third normal form in which it drops the restriction of a non-key
attribute from the 3rd normal form.
? Third normal form and BCNF are not same if the following conditions are true:
– The table has two or more candidate keys
– At least two of the candidate keys are composed of more than one attribute
– The keys are not disjoint i.e. The composite candidate keys share some attributes
Example 1 - Address (Not in BCNF)
Scheme ? {City, Street, ZipCode }
1. Key1 ? {City, Street }
2. Key2 ? {ZipCode, Street}
3. No non-key attribute hence 3NF
4. {City, Street} ? {ZipCode}
5. {ZipCode} ? {City}
6. Dependency between attributes belonging to a key
Boyce-Codd Normal Form (BCNF)

Example 2 - Movie (Not in BCNF)
Scheme ? {MovieTitle, MovieID, PersonName, Role, Payment }
1. Key1 ? {MovieTitle, PersonName}
2. Key2 ? {MovieID, PersonName}
3. Both role and payment functionally depend on both candidate keys thus 3NF
4. {MovieID} ? {MovieTitle}
5. Dependency between MovieID & MovieTitle Violates BCNF
Example 3 - Consulting (Not in BCNF)
Scheme ? {Client, Problem, Consultant}
1. Key1 ? {Client, Problem}
2. Key2 ? {Client, Consultant}
3. No non-key attribute hence 3NF
4. {Client, Problem} ? {Consultant}
5. {Client, Consultant} ? {Problem}
6. Dependency between attributess belonging to keys violates BCNF
Boyce Codd Normal Form (BCNF)

1. Place the two candidate primary keys in separate
entities
2. Place each of the remaining data items in one of the
resulting entities according to its dependency on the
primary key.
Example 1 (Convert to BCNF)
Old Scheme ? {City, Street, ZipCode }
New Scheme1 ? {ZipCode, Street}
New Scheme2 ? {City, Street}
? Loss of relation {ZipCode} ? {City}
Alternate New Scheme1 ? {ZipCode, Street }
Alternate New Scheme2 ? {ZipCode, City}
BCNF - Decomposition

1. If decomposition does not cause any loss of information it is called
a lossless decomposition.
2. If a decomposition does not cause any dependencies to be lost it is
called a dependency-preserving decomposition.
3. Any table scheme can be decomposed in a lossless way into a
collection of smaller schemas that are in BCNF form. However the
dependency preservation is not guaranteed.
4. Any table can be decomposed in a lossless way into 3rd normal form
that also preserves the dependencies.
? 3NF may be better than BCNF in some cases
Decomposition – Loss of
Information
Use your own judgment when decomposing schemas

Old Scheme ? {MovieTitle, MovieID, PersonName, Role, Payment }
New Scheme ? {MovieID, PersonName, Role, Payment}
New Scheme ? {MovieTitle, PersonName}
? Loss of relation {MovieID} ? {MovieTitle}
New Scheme ? {MovieID, PersonName, Role, Payment}
New Scheme ? {MovieID, MovieTitle}
? We got the {MovieID} ? {MovieTitle} relationship back
Old Scheme ? {Client, Problem, Consultant}
New Scheme ? {Client, Consultant}
New Scheme ? {Client, Problem}
BCNF - Decomposition

? Fourth normal form eliminates independent many-to-one relationships
between columns.
? To be in Fourth Normal Form,
– a relation must first be in Boyce-Codd Normal Form.
– a given relation may not contain more than one multi-valued attribute.
Example (Not in 4NF)
Scheme ? {MovieName, ScreeningCity, Genre)
Primary Key: {MovieName, ScreeningCity, Genre)
1. All columns are a part of the only candidate key, hence BCNF
2. Many Movies can have the same Genre
3. Many Cities can have the same movie
4. Violates 4NF
Fourth Normal Form (4NF)
Movie ScreeningCity Genre
Hard Code Los Angles Comedy
Hard Code New York Comedy
Bill Durham Santa Cruz Drama
Bill Durham Durham Drama
The Code Warrier New York Horror

Scheme ? {Manager, Child, Employee}
1. Primary Key ? {Manager, Child, Employee}
2. Each manager can have more than one child
3. Each manager can supervise more than one employee
4. 4NF Violated
Scheme ? {Employee, Skill, ForeignLanguage}
1. Primary Key ? {Employee, Skill, Language }
2. Each employee can speak multiple languages
3. Each employee can have multiple skills
4. Thus violates 4NF
Fourth Normal Form (4NF)
Manager Child Employee
Jim Beth Alice
Mary Bob Jane
Mary NULL Adam
Employee Skill Language
1234 Cooking French
1234 Cooking German
1453 Carpentry Spanish
1453 Cooking Spanish
2345 Cooking Spanish

1. Move the two multi-valued relations to separate tables
2. Identify a primary key for each of the new entity.
Old Scheme ? {MovieName, ScreeningCity, Genre}
New Scheme ? {MovieName, ScreeningCity}
New Scheme ? {MovieName, Genre}
4NF - Decomposition
Movie Genre
Hard Code Comedy
Bill Durham Drama
The Code Warrier Horror
Movie ScreeningCity
Hard Code Los Angles
Hard Code New York
Bill Durham Santa Cruz
Bill Durham Durham
The Code Warrier New York

Old Scheme ? {Manager, Child, Employee}
New Scheme ? {Manager, Child}
New Scheme ? {Manager, Employee}
Old Scheme ? {Employee, Skill, ForeignLanguage}
New Scheme ? {Employee, Skill}
New Scheme ? {Employee, ForeignLanguage}
4NF - Decomposition
Manager Child
Jim Beth
Mary Bob
Manager Employee
Jim Alice
Mary Jane
Mary Adam
Employee Language
1234 French
1234 German
1453 Spanish
2345 Spanish
Employee Skill
1234 Cooking
1453 Carpentry
1453 Cooking
2345 Cooking

? Fifth normal form is satisfied when all tables are broken into
as many tables as possible in order to avoid redundancy.
Once it is in fifth normal form it cannot be broken into
smaller relations without changing the facts or the meaning.
Fifth Normal Form (5NF)

? The relation is in DKNF when there can be no insertion or
deletion anomalies in the database.
Domain Key Normal Form (DKNF)

? Make Teams
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