8.1. Normalization

7/31/2019 8.1. Normalization

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Prof. Margita Kon-Popovska 2006

DATABASE SYSTEMS

Fall 2006

Normalization


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Prof. Margita Kon-Popovska 2006 2

Relation

Definition: A relation is a named, two-dimensional table of data

Table is made up of rows (records), and columns (attribute or field)

Not all tables qualify as relations. Requirements:

Every relation has a unique name.

Every attribute value isatomic(not multivalued, not composite)

Every row is unique (cant have two rows with exactly the same values forall their fields)

Attributes (columns) in tables have unique names

The order of the columns is irrelevant

The order of the rows is irrelevant

NOTE: all relations are in 1st

Normal form


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Example

QuestionIs this a relation? AnswerNo due to repeating groups

QuestionWhats the primary key? AnswerEmp_ID


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Question: Is this a relation-Is this in 1st NF?

Answer : Yes, unique rows and nomultivalued attributes

Question: Whats the primary key? Answer: Composite primary keyEmp_ID, Course_Title


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Data Normalization

Primarily a tool to validate and improve a logical designso that it satisfies certain constraints that avoidunnecessary duplication of data,

i.e. reduce redundancy

Achieve a design that is highly flexible

Ensure that the design is free of certain update,insertion and deletion anomalies

The process of decomposing relations with anomalies toproduce smaller, well-structuredrelations


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Normalization

The process of decomposing complex datastructures into simple relations according to aset of dependency rules.

McFadden and Hoffer


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Well-Structured Relations

A relation that contains minimal data redundancy andallows users to insert, delete, and update rows withoutcausing data inconsistencies

Goal is to avoid anomalies

Insertion Anomaly adding new rows forces user to createduplicate data

Deletion Anomaly deleting rows may cause a loss of data thatwould be needed for other future rows

Modification Anomaly changing data in a row forces changes

to other rows because of duplication

General rule of thumb: a table should not pertain to

more than one entity type


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Possible inconsistencies on updating

null key

insertion anomaly

update

anomaly

potential deletionanomaly

duplication



BCNF

3NF

2NF

Normalization

1NF

Progressively puttingthe relation into a

higher normal form

to get well structuredrelations4NF

5NF

*Domain.Key NF DK/NF



Steps innormalization



First Normal Form (1NF)

No multivalued attributes-Every attribute value is atomic

isin 1NF

is notin 1NF(multivalued attributes)

it is not a relation


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Example: Invoice

How to get Relations (tables) in 1NF


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Stereos To GoInvoice

Order No.

Date / /

Account No.

Item

Number Product Description/Manufacturer Qty Price

Product

Code

1

2

3

4

5

Date Delivered / /

Customer:

Address:

City State Zip Code

10001

5 8 03

0000-000-0000-0

John Smith

2036-26 StreetSacramento CA 95819

SAGX730 Pioneer Remote A/V Receiver

AT10 Cervwin Vega Loudspeakers

CDPC725 Sony Disc-Jockey CD Changer

6 8 03

Subtotal

Shipping & Handling

Sales Tax

Total

132985

10000

10306

153291

1

1

1

56995

35995

39995

Go, Hogs

1/05

Stereos To Go

0000 000 0000 0

John Smith


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Unnormalized table

How would we get 1NF of invoice?

(Invoice-no, Invoice-date, Date-delivered, Cust-account, Cust-name,Cust-addr, Cust-city, Cust-state, Zip-code,Item1, Item_descrip1, Item_qty1, Item_price1,Item2, Item_descrip2, Item_qty2, Item_price2, . . . ,

Item7, Item_descrip7, Item_qty7, Item_price7)

repeatinggroup

A relation is in first normal form if and only ifevery attribute is single-valued for each tuple.

Remove all repeating groups

Create a flat file


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Unnormalized to 1NF

Nominated group of attributesto serve as the key

(form a unique combination)

Repeating groups

eliminated.

Each row retains data forone item.

If a person bought 5 items,

we would have five tuples

(Invoice-no, Invoice-date, Date-delivered, Cust-account, Cust-name, Cust-addr, Cust-city, Cust-state, Zip-code,Item, Item_descrip, Item_qty, Item_price)


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1NF

10001 123456 John Smith SAGX730 Pioneer Remote A/V Rec 1 569.95

10001 123456 John Smith AT10 Cerwin Vega Loudspeakers 1 359.95

10001 123456 John Smith CDPC725 Sony Disc Jockey CD 1 399.95

10001 123456 John Smith S/H Shipping 1 100.00

10001 123456 John Smith Tax Sales Tax 1 103.06

Flat File

DescriptionItem

QuantityItemPriceItem


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Functional Dependencies

Functional Dependency: The value of oneattribute (set of attributes) (the determinant)determines the value of another attribute (setof attributes)

Functional dependency B is functionally dependent on A if each value of A

is associated with exactly one value of B

While a primary key is always a determinant,a determinant is not necessarily a primary key

Attribute A Attribute B

Determinant


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Full Functional Dependencies

Full Functional dependency B is full functionally dependent on A if it is functionally

dependant on entire A and not on part of A

Determinant

Attribute BAttribute A1,A2..An


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Functional dependences and Keys

Candidate Key: A unique identifier. One of the candidate keys will

become the primary key

E.g. perhaps there is both credit card number and SS# in atablein this case both are candidate keys

Non-Key attribute, attribute not part of any candidatekey

Each non-key attribute is functionally dependent onevery candidate key (1NF)

Each non-key attribute is fully functionally dependenton every candidate key (2NF)


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Second Normal Form (2NF)

1NF + every non-key attribute is fully functionallydependent on the ENTIRE key

Every non-key attribute must be defined by the entirekey, not by only part of the key

No partial functional dependencies

So Table EMPLOEE2 is NOT in 2NF

(see next slide)


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Functional Dependencies Example

Dependency on entire primary key

Dependency on onlypartof the key

EmpID, CourseTitle DateCompleted

EmpID Name, DeptName, Salary

Therefore, NOT in 2nd Normal Form!!


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Getting it into 2nd Normal Form

Decomposed into two separate relations

Both are fullfunctional

dependencies


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Example: Invoice



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Some of the attributes are dependentupon invoice_number for

their values, some are dependant upon invoice_number anditem, and others are dependentupon item only.

In either case, they are notfunctionally dependenton the entire

key.

Using Invoice number and Item as the key...

(Invoice_number, Invoice_date, Date_delivered, Cust_account,Cust_name, Cust_addr, Cust_city, Cust_state, Zip_code,Item, Item_descrip, Item_qty, Item_price)


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(Invoice_number, Invoice_date, Date_delivered,Cust_account, Cust_name, Cust_addr, Cust_city,Cust_state, Zip_code)

Composite key

Partial dependency

(Invoice_number, Invoice_date, Date_delivered, Cust_account,

Cust_name, Cust_addr, Cust_city, Cust_state, Zip_code)

(Invoice_number, Item, Item_descrip, Item_qty, Item_price)

(Item, Item_descrip)

(Invoice_number, Item, Item_descrip, Item_qty, Item_price)


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Third Normal Form (3NF)

Transitive dependenciesone attribute functionally determines a second, whichfunctionally determines a third)

2NF + no transitive dependenciesA relation is in third normal form if it is in second normalform and no nonkey attribute is transitively dependent onthe key. Remove transitive dependencies

Each nonkey attribute must depend upon the key, the wholekey, and nothing but key.

Kent, 1978


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Example: Relation with transitive dependency

(a) SALES relation with simple data


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Removing a transitive dependency

(a) Decomposing the SALES relation


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Relations in 3NF

Now, there are no transitive dependencies

Both relations are in 3rd NF

CustID Name

CustID Salesperson

Salesperson Region


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Example: Invoice



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From 2NF to 3NF

Which attributes are dependent on others?

Is there a problem?

(Invoice_number, Invoice_date, Date_delivered, Cust_account,Cust_name, Cust_addr, Cust_city, Cust_state, Zip_code)

(Invoice_number, Item, Item_qty, Item_price)

(Item, Item_descrip)


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Transitive Dependencies and Anomalies

Insertion anomalies

To add a new row, all customer (name, address, city,state, zip code, phone) and products (description)must be consistent with previous entries

Deletion anomalies

By deleting a row, a customer or product may ceaseto exist

Modification anomalies To modify a customers or products data in one row,

all modifications must be carried out to all others


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Deletion Anomaly

4377182 John Smith Sacramento CA 95831

4398711 Al Gore Davis CA 95691

4578461 Gray Davis Sacramento CA 95831

4873179 Lisa Carr Reno NV 89557

By deleting customer Al Gore, we would also be deleting

Town Davis, and State California.

Invoice number


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TransitiveDependencies

Invoice_number

Invoice_date

Date_delivered

Cust_accountCust_name

Cust_addr

Cust_city

Cust_state

Zip_code

Item

Item_descripInvoice_number+Item

Item_qty

Item_price

A condition where A, B, Care attributes of a relationsuch that if A B andB C, then C is

transitively dependent onA via B (provided that A isnot functionally dependent

on B or C).

Why Should City and State Be Separated from


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Why Should City and State Be Separated fromCustomer Relation?

City and state are dependent on zip code for their valuesand not the customers identifier (i.e., key).

Zip_code City, State

Otherwise,

Cust_account Cust_addr, Zip_code City, State

In which case, you have transitive dependency.


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3NF

Invoice Relation(Invoice_number, Invoice_date, Date_delivered, Cust_account)

Customer Relation(Cust_account, Cust_name, Cust_addr, Zip_code)

Zip_code Relation(Zip_code, City, State)

Invoice_items Relation(Invoice_number, Item, Item_qty, Item_price)

Items Relation(Item, Item_descrip)


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Further Anomalies

DVD-A110 PanasonicPV-4210 PanasonicPV-4250 Panasonic

CT-32S35 PAN

Inconsistency

DVD-A110 PanasonicPV-4210 PanaSonicPV-4250 Pana SonicCT-32S35 PAN

In Item-decript manufacturer

name is contained

It will be useful to change all

Panasonic products

manufacturer name to

Panasonic USA

Item Item_descrip

Insert a new Panasonic product


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3NF

Invoice Relation(Invoice_number, Invoice_date, Date_delivered, Cust_account)

Customer Relation(Cust_account, Cust_name, Cust_addr, Zip_code)

Zip_code Relation(Zip_code, City, State)

Invoice_items Relation(Invoice_number, Item, Item_qty, Item_price)

Items Relation(Item, Item_descrip)

Since the Items relation contains the manufacturers name in thedescription, a separate Manufacturers relation can be created

Manufacturers Relation(Manuf_code, Manuf_name)

First to Third Normal Form (1NF 3NF)


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First to Third Normal Form (1NF - 3NF)

1NF: A relation is in first normal form if and only if everyattribute is single-valued for each tuple(remove therepeating or multi-value attributes and create a flat file)

2NF: A relation is in second normal form if and only if it

is in first normal form and the nonkey attributes are fullyfunctionally dependent on the key(remove partialdependencies)

3NF: A relation is in third normal form if it is in second

normal form and no nonkey attribute is transitivelydependent on the key(remove transitive dependencies)


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Example (Employee)


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Example (Employee)

EMPLOYEE (EmpId, Name, Dept, Salary, Course1, DateTook1, Fee1,

Course2, DateTook2, Fee2, )


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If employees can take a course more than once: TOOK_COURSE ( EmpId, Course, DateTook)

2NF


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Example (Hospital)

Patient # Surgeon # Surg. date Patient Name Patient Addr Surgeon Surgery Postop drug g s ide effec

1111

145

311

Jan 1,

1995; June

12, 1995 John White

15 New St.

New York,

NY

Beth Little

Michael

Diamond

Gallstone

s removal;

Kidney

stones

removal

Penicillin,

none-

rash

none

1234

243

467

Apr 5,1994 May

10, 1995 Mary Jones

10 Main St.

Rye, NY

Charles

FieldPatricia

Gold

Eye

Cataract

removalThrombos

is removal

Tetracyclin

e none

Fever

none

2345 189

Jan 8,

1996 Charles Brown

Dogwood

Lane

Harrison,

NY

David

Rosen

Open

Heart

Surgery

Cephalosp

orin none

4876 145Nov 5,1995 Hal Kane

55 Boston

Post Road,

Chester,CN Beth Little

Cholecystectomy Demicillin none

5123 145

May 10,

1995 Paul Kosher

Blind Brook

Mamaronec

k, NY Beth Little

Gallstone

s

Removal none none

6845 243

Apr 5,

1994 Dec15, 1984 Ann Hood

Hilton Road

Larchmont,NY CharlesField

Eye

Cornea

Replacem

ent Eye

cataractremoval Tetracycline Fever

NF


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1NF

Patient # Surgeon # Surgery DatePatient NamePatient AddrSurgeon Name Surgery Drug admin ide Effect

1111 145 01-Jan-95 John White

15 New St.

New York,

NY Beth Little

Gallstone

s removal Penicillin rash

1111 311 12-Jun-95 John White

15 New St.

New York,

NY

Michael

Diamond

Kidney

stones

removal none none

1234 243 05-Apr-94 Mary Jones

10 Main St.

Rye, NY Charles Field

Eye

Cataract

removal

Tetracyclin

e Fever

1234 467 10-May-95 Mary Jones

10 Main St.

Rye, NY Patricia Gold

Thrombos

is removal none none

2345 189 08-Jan-96

Charles

Brown

Dogwood

Lane

Harrison,

NY David Rosen

Open

Heart

Surgery

Cephalosp

orin none

4876 145 05-Nov-95 Hal Kane

55 Boston

Post Road,

Chester,

CN Beth Little

Cholecyst

ectomy Demicillin none

5123 145 10-May-95 Paul Kosher

Blind Brook

Mamaronec

k, NY Beth Little

Gallstone

s

Removal none none

6845 243 05-Apr-94 Ann Hood

Hilton Road

Larchmont,

NY Charles Field

Eye

Cornea

Replacem

ent

Tetracyclin

e Fever

6845 243 15-Dec-84 Ann Hood

Hilton Road

Larchmont,

NY Charles Field

Eye

cataract

removal none none

2NF


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2NF

Patient # Patient Name Patient Address

1111 John White

15 New St. New

York, NY

1234 Mary Jones

10 Main St. Rye,

NY

2345

Charles

Brown

Dogwood Lane

Harrison, NY

4876 Hal Kane

55 Boston Post

Road, Chester,

5123 Paul Kosher

Blind Brook

Mamaroneck, NY

6845 Ann HoodHilton RoadLarchmont, NY

Surgeon # Surgeon Name

145 Beth Little

189 David Rosen

243 Charles Field

311 Michael Diamond

467 Patricia Gold


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Patient # Surgeon # Surgery Date Surgery Drug Admin Side Effects

1111 145 01-Jan-95

Gallstones

removal Penicillin rash

1111 311 12-Jun-95

stones

removal none none

1234 243 05-Apr-94

Eye Cataract

removal Tetracycline Fever

1234 467 10-May-95

Thrombosis

removal none none

2345 189 08-Jan-96

Open Heart

Surgery

Cephalospori

n none

4876 145 05-Nov-95

Cholecystect

omy Demicillin none

5123 145 10-May-95

Gallstones

Removal none none

6845 243 15-Dec-84

Eye cataract

removal none none

6845 243 05-Apr-94

Eye Cornea

Replacement Tetracycline Fever


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Example

Work on

project

3NF


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3NF

Find candidate keys, primary keys, all functional


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dependences and transform following relations in 3NF

Housing

StId Dorm Fee

100 B1101 1000

101 B1102 1100

102 B2101 1000

StId Dorm, StId Fee

not in 3NF because of DormFee

1.


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EXAM(S#, Name, P#, NameCourse, Mark)

STUDENT(S#, Name,P#, NnameCourse)

STUDENT(S#,P#, Na,e, NameCourse, Gender,

Mark, Data)

4.

E l i d t li


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Explain update anomalies

PRODUCTION(P#, M#, E#)

P1 M1 E1

P2 M2 E3

P3 M1 E1P4 M1 E1

P5 M3 E2

P6 M4 E1

P#M#P# E#

M# E#

P stands for Product

M stands for Machine

E stands for Employee

Willinsertion

produce inconsistence


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Determine Candidate keys and primarykey, functional dependences

and see if this relation could be normalizedAdvisory

St Id Major Advisor

100 Math Smith

100 Language Ringo

101 Language Yung

101 Math Smith

102 Math Peris

Documents

8.1. Normalization