Chapter 7

NormalizationNormalization

Chapter 13 in Textbook

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How to produce a good relation How to produce a good relation schema?schema?

1. Start with a set of relation

2. Define the functional dependencies for the relation to specify the PK

3. Transform relations to normal form

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Data RedundancyData Redundancy

SL21

SG37

SG14

SA9

SG5

StaffNo

John

Ann

David

Mary

Susan

FName

White

Beech

Ford

Howe

Brand

LName position

Manager

Assistant

Supervisor

Assistant

Manager

Salary

30000

12000

18000

9000

24000

BrnNo

B005

B003

B003

B007

B003

City

London

Glasgow

Glasgow

Aberdeen

Glasgow

SL41 Julie Lee Assistant 9000 B005 London

Address

22 Deer Rd

163 Main St

16 Arglly St

22 Deer Rd

163 Main St

163 Main St

Relations that have redundant data may have update anomalies (insert, modify, delete)

STAFFBRANCH

B003 Glasgow163 Main St

B003 Glasgow163 Main St

B003 Glasgow163 Main St

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SL21

SG37

SG14

SA9

SG5

StaffNo

John

Ann

David

Mary

Susan

FName

White

Beech

Ford

Howe

Brand

LName position

Manager

Assistant

Supervisor

Assistant

Manager

Salary

30000

12000

18000

9000

24000

SL41 Julie Lee Assistant 9000

BrnNo

B005

B003

B007

City

London

Glasgow

Aberdeen

Address

22 Deer Rd

163 Main St

16 Arglly St

STAFF

BRANCH

BrnNo

B005

B005

B003

B003

B003

B007

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Functional Dependencies

Example

AStaffNo

Bposition

B is functionallydependent on A

position StaffNoStaffNo is NOT functionally

dependent on position

SL21 Manager

Manager SL21 SG5

1:1 or M:1 relationship

between attributes in a

relation

1:M relationship

between attributes in a

relation

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StaffBranch ExampleStaffBranch ExampleFunctional dependencies on StaffBranch relation

StaffNo FName, Lname, position, salary, brnNo, Address, city

BranchNo Address, city

Address, city BranchNo

BranchNo, position salary

Address, city, position salary

Determinants:

StaffNo, BranchNo, (Address, city), (branchNo, position), and (address, city, position)

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The purpose of NormalizationThe purpose of NormalizationNormalization is a bottom-up approach to database design that begins by examining

the relationships between attributes. It is performed as a serious of tests on a relation

to determine whether it satisfies or violates the requirements of a given normal form.

Purpose:

Guarantees no redundancy due to FDs

Normal Forms:

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)

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The Process of NormalizationThe Process of Normalization

5NF

4NF

BCNF

3NF

2NF

1NF

Higher Normal Form

Strong

er in

form

at

Less

vulne

rable

to u

pdat

e an

omali

es

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First Normal Form (1NF)First Normal Form (1NF)

Unnormalized form (UNF): A relation that contains one or more repeating groups

First normal form (1NF): A relation in which the intersection of each row and

column contains one & only one value

Unnormalized relation

ClientNo

CR76

PropertyNo

PG4

Name

John Key

CLIENT_PROPERTY

PG16

PG4PG36

PG16

CR56 Aline Stewart

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UNF 1NFUNF 1NFApproach 1Approach 1

Expand the key so that there will be a separate tuple in the original relation for each

repeated attribute(s). Primary key becomes the combination of primary key and

redundant value

1NF relation

Disadvantage: introduce redundancy in the relation

ClientNo

CR76

PropertyNo

PG4

Name

John Key

CLIENT_PROPERTY

PG16

PG4PG36

PG16

CR56 Aline Stewart

CR76 John Key

CR56 Aline Stewart

CR56 Aline Stewart

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If the maximum number of values is known for the attribute, replace repeated

attribute (PropertyNo) with a number of atomic attributes (PropertyNo1,

PropertyNo2, PropertyNo3)

1NF relation

Disadvantage: introduce NULL values in the relation

UNF 1NFUNF 1NFApproach 2Approach 2

ClientNo

CR76

PropertyNo1

PG4

Name

John Key

CLIENT_PROPERTY

PG16

PG4 PG36CR56 Aline Stewart

PropertyNo2 PropertyNo3

NULL

PG16

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UNF 1NFUNF 1NFApproach 3Approach 3

Remove the attribute that violates the 1NF and place it in a separate relation along

with the primary key

ClientNo

CR76

Name

John Key

CLIENT

CR56 Aline Stewart

ClientNo

CR76

PropertyNo

PG4

PROPERTY

PG16

PG4PG36

PG16

CR56

CR76

CR56CR56

1NF relation

1NF relation

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Full Functional DependencyFull Functional Dependency

If A and B are attributes of a relation

B is fully functionally dependent on A if B is functionally dependent on A, but not

on any proper set of A

B is partial functional dependent on A if some attributes can be removed from A

& the dependency still holds

StaffNo, Sname BranchNo Partial dependency

ClientNo, PropertyNo RentDate Full dependency

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Second Normal Form (2NF)Second Normal Form (2NF)

Second normal form (2NF): A 1NF relation in which every attribute is fully

nontrivial functionally dependent on the PK.non-prime attributes fully dependent on

PK.

Applies to relations with composite primary keys & partial dependencies

1NF relation

ClientNo cNamePropertyNo

CLIENT_RENTAL

Address RentStart RentFinish Rent OwnerNo OName

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1NF 2NF1NF 2NF

1. Start with 1NF relation

2. Find the FDs of a relation

3. Test the FDs whose determinant attribute is part of the PK

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ClientNo cNamePropertyNo

CLIENT_RENTAL

pAddress RentStart RentFinish Rent OwnerNo OName

(ClientNo, PropertyNo) PKClientNo, PropertyNo RentStart, RentFinish Full DependencyClientNo CName Partial DependencyPropertyNo Paddress, Rent, OwnerNo, Oname Partial Dependency

ClientNo, RentStart PropertyNo, pAddress, RentFinish, Rent, OwnerNo, OnamePropertyNo, RentStart ClientNo, cName, RentFinish

1NF 2NF1NF 2NF

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1NF 2NF1NF 2NF

3. Remove partial dependencies by placing the functionally dependent attributes in

a new relation along with a copy of their determinants

2NF relation 2NF relation

2NF relation

ClientNo cName

CLIENTClientNo PropertyNo RentStart RentFinish

RENTAL

PropertyNo

PROPERTY_OWNER

pAddress Rent OwnerNo OName

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Transitive DependencyTransitive Dependency

A, B, C are attributes of a relation, such that

If A B and B C, then C is transitively dependent on A via B

Provided A is NOT functionally dependent on B or C (nontrivial FD)

Example

StaffNo BranchNo , BranchNo Address

StaffNo Address

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Third Normal Form (3NF)Third Normal Form (3NF)

Third normal form (3NF): A 2NF relation in which NO non-prime attribute is

transitively dependent on the PK

3NF relation 3NF relation

2NF relation

ClientNo cName

CLIENTClientNo PropertyNo RentStart RentFinish

RENTAL

PropertyNo

PROPERTY_OWNER

pAddress Rent OwnerNo OName

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2NF 3NF2NF 3NF

1. Identify the PK in the 2NF relation

2. Identify FDs in this relation

3. If transitive dependencies exist, place transitively dependent attributes in a new

relation along with a copy of their determinants

3NF relation 3NF relation

OwnerNo OName

OWNER

PropertyNo pAddress rent OwnerNo

PROPERTY_FOR_RENT

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General Definition of 2NF & 3NFGeneral Definition of 2NF & 3NF

Second normal form (2NF): A 1NF relation in which every non-primary-key

attribute is fully functionally dependent on the CK

Third normal form (3NF): A 2NF relation in which NO non-primary-key attribute in

a nontrivial FD is transitively dependent on the CK

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Boyce-Codd Normal Form Boyce-Codd Normal Form (BCNF)(BCNF)

Boyce-Codd normal form (3NF): A 3NF relation in which every determinant in a

nontrivial FD is a CK

Difference between 3NF & BCNF: A B

• 3NF allows A NOT CK

• BCNF insists on A is a CK

Potential to violate BCNF may occur in a relation that:

• Contain two (or more) composite CKs

• CKs overlap. (at least one attribute in common)

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Boyce-Codd Normal Form Boyce-Codd Normal Form (BCNF)(BCNF)

A B C D

3NF but not BCNF

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ClientNo

CLIENT_INTERVIEW

Int_Date Int_Time StaffNo RoomNo

3NF BCNF3NF BCNF

ClientNo, Int_Date Int_Time, StaffNo, RoomNoStaffNo, Int_Date, Int_Time ClientNoRoomNo, Int_Date, Int_Time StaffNo, ClientNoStaffNo, Int_Date RoomNo

1. Examine FDs for a relation2. If determinant is NOT a CK, decompose relation into 2 relations

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3NF BCNF3NF BCNF

3. Remove non-CK dependencies by placing the functionally dependent attributes

in a new relation

BCNF relation BCNF relation

Int_Date RoomNo

STAFF_ROOMClientNo Int_date Int_time StaffNo

INTERVIEW

ClientNo

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Review Example

PG4

PG16

Pno pAddress

18-Oct-00

22-Apr-01

1-Oct-01

22-Apr-01

24-Oct-01

iDate iTime

10:00

09:00

12:00

13:00

14:00

comments

Replace crockery

Good order

Damp rot

Replace carpet

Good condition

StaffNo

SG37

SG14

SG14

SG14

SG37

CarReg

M23JGR

M53HDR

N72HFR

M53HDR

N72HFR

Lawrence St,

Glasgow

5 Novar Dr.,

Glasgow

sName

Ann

David

David

David

Ann

STAFF_PROPERTY_INSPECTION

Unnormalized relation

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UNF 1NF

PG4

PG4

PG4

PG16

PG16

Pno pAddress

18-Oct-00

22-Apr-01

1-Oct-01

22-Apr-01

24-Oct-01

iDate iTime

10:00

09:00

12:00

13:00

14:00

comments

Replace crockery

Good order

Damp rot

Replace carpet

Good condition

StaffNo

SG37

SG14

SG14

SG14

SG37

CarReg

M23JGR

M53HDR

N72HFR

M53HDR

N72HFR

Lawrence St, Glasgow

Lawrence St,Glasgow

5 Novar Dr., Glasgow

5 Novar Dr., Glasgow

5 Novar Dr., Glasgow

sName

Ann

David

David

David

Ann

STAFF_PROPERTY_INSPECTION

1NF

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1NF 2NF

Pno pAddressiDate iTime comments StaffNo CarRegsName

STAFF_PROPERTY_INSPECTION

Pno, iDate iTime, comments, StaffNo, Sname, CarRegPno pAddress Partial DependencyStaffNo SnameiDate, StaffNo CarRegiDate, iTime, CarReg Pno, pAddress, comments, StaffNo, SnameiDate, iTime, StaffNo Pno, pAddress, Comments

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1NF 2NF

Pno iDate iTime comments StaffNo CarRegsName

PROPERTY_INSPECTION

Pno, iDate iTime, comments, StaffNo, Sname, CarRegStaffNo Sname Transitive DependencyiDate, StaffNo CarRegiDate, iTime, CarReg Pno, comments, StaffNo, SnameiDate, iTime, StaffNo Pno, comments

Pno pAddress

PROPERTY

2NF

2NF

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2NF 3NF

Pno iDate iTime comments StaffNo CarReg

PROPERTY_INSPECTION

StaffNo sName

STAFF

3NF

PROPERTY(Pno, pAddres)STAFF(StaffNo, sName)PROPERTY_INSPECT(Pno, iDate, iTime, comments, staffNo, CarReg)

3NF

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3NF BCNF

Pno iDate iTime comments StaffNo CarReg

PROPERTY_INSPECTION

Pno, iDate iTime, comments, staffNo, CarReg)StaffNo, iDate carRegCarReg, iDate, iTime pno, comments, staffNoStaffNo, iDate, iTime pno, comments

STAFF_CAR(StaffNo, iDate, CarReg)PROPERTY_INSPECT(pno, iDate, iTime, comments, StaffNo, CarReg)

3NF

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Multi-Valued Dependency (MVD)

Represents a dependency between attributes A, B, C in a relation, such that for

each value of A, there is a set of values for B and a set of values of values for C.

However, the set of values for B & C are independent of each others.

Denoted by: A B, A C

Example

BranchNo SName, BranchNo OName

SName OName

BRANCH_STAFF_OWNER

BranchNo

B003B003B003B003

AnnDavidAnnDavid

CarolCarolTinaTina

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Trivial MVD

A B trivial MVD if:

B A

OR

A B = R

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Fourth Normal Form (4NF)

Fourth normal form (4NF): A BCNF relation with NO nontrivial MVD

BCNF relation

SName OName

BRANCH_STAFF_OWNER

BranchNo

B003B003B003B003

AnnDavidAnnDavid

CarolCarolTinaTina

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BCNF 4NF

1. Start with a BCNF relation2. Examine FDs for a relation3. If nontrivial MVD exists, remove the MVD by placing the attributes in a new

relation along with a copy of their determinant

4NF 4NF

SName

BRANCH_STAFF

BranchNo

B003B003

AnnDavid

OName

BRANCH_OWNER

BranchNo

B003B003

CarolTina

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Lossless-Join Dependency

A property of decompostion, which ensures that no spurious tuples are generated

when relations are reunited through a natural join operation

Objectives:

Preserve all the data in the original relation

Does not result in the creation of additional spurious tuples

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Join Dependency

A, B, .., Z attributes in relation R satisfies join dependency if

Every legal value of R is equal to the join of its projections on A, B, .., Z

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Fifth Normal Form (5NF)

Fifth normal form (5NF): A relation with no join dependency

Description SupplierNo

PROPERTY_ITEM_SUPPLIER

PropertyNo

PG4PG4PG16

BedChairBed

S1S2S2

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4NF 5NF

Description

PROPERTY_ITEM

PropertyNo

PG4PG4PG16

BedChairBed

SupplierNo

ITEM_SUPPLIER

Description

BedChairBed

S1S2S2

SupplierNo

PROPERTY_ITEM

PropertyNo

PG4PG4PG16

S1S2S2

Description SupplierNo

PROPERTY_ITEM_SUPPLIER

PropertyNo

PG4PG4PG4PG16

BedBedChairBed

S1S2S2S2

Original PROPERTY_ITEM_SUPPLIER