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Normalisation

Connolly, Ch. 13

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Overview

• Normalisation– Steps

• 1NF– Removing repeating groups

• 2NF– Partial dependencies

– Removing partial dependencies

• 3NF– Transitive dependencies

– Removing transitive dependencies

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Normalisation

• “A formal technique for analysing relationsbased on their primary key and functionaldependencies.” [Codd].

• Process– Analyse each relation using a set of rules

– If a relation does meet a rule• Decompose the relation into two or more relations

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Normalisation Steps

Each step in the process reduces the update anomalies that can occur.

0NF

1NF

2NF

3NF

BCNF

4NF

5NF

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Unnormalised Form (0NF)

• A 0NF relation may have:– Multivalued attributes

• Some attributes have more than one value

– Composite attributes• Some attributes consist of multiple parts

– Nested relations• Some attributes contain another relation

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0NF Example

Proj-id, Proj-Start-Date, Location and Weeks-on-Projectcontain multiple values

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First Normal Form (1NF)

• Definition– “A relation in which the intersection of each row

and column contains one and only one value.”• “No repeating groups”

• A 1NF relation does not contain– Multivalued attributes

– Composite attributes

– Nested relations

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Converting 0NF to 1NF

• “Remove repeating groups”– Start with a 0NF relation which contains...

• a key that identifies a set of attributes

• and a set of attributes that repeat

– Remove the repeating attributes and place them in aseparate relation

– Include a copy of the original key in the newrelation

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1NF - Identify the Repeating Group

Key Repeating Group

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1NF - Remove the Repeating GroupEmp1

EmpProj1

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1NF Relations

Emp1(emp-no, emp-name, dept, manager)

EmpProj1(emp-no, proj-id, proj-start-date, location, weeks-on-project)

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Second Normal Form (2NF)

• Definition– “A relation that is in 1NF and every non-primary-

key attribute is fully dependent on the primary key.”• “Remove partial dependencies”

• A 2NF relation is one that– Is in 1NF

– and contains no partial dependencies

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Partial Dependency on the Key

• An attribute that is dependent on part of the key

(A, B, C, D)

AB → CA → D

D is partially dependent on the key (AB)

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Converting 1NF to 2NF

• Identify all partial dependencies

• Ignore all relations with a single attributeprimary key

– This relation is in 2NF

• Create a new relation– Remove the partially determined attribute

– Copy part of the primary key

Emp1

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2NF - Identify Partial Dependencies

EmpProj1

Proj-Start-Date is dependent on part of the key.

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2NF - Remove Partial Dependency

Proj2

EmpProj2

Create a relation with the proj-start-date attribute and a copy of the proj-id attribute.

Remove the proj-start-dateattribute.

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2NF Relations

Emp2(emp-no, emp-name, dept, manager)

EmpProj2(emp-no, proj-id, location, weeks-on-project)

Proj2(proj-id, proj-start-date)

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Third Normal Form (3NF)

• Definition– “A relation that is in 2NF and every non-primary-

key attribute is dependent on the primary key only.”• “Remove transitive dependencies.”

• A 3NF relation is one that– Is in 3NF

– and contains no transitive dependencies

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Transitive Dependency on the Key

• An attribute that is dependent on an attributeother than the key

(A, B, C, D)

AB → CC → D

D is transitively dependent on the key (AB)through C

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Converting 2NF to 3NF

• Identify all transitive dependencies

• Ignore all relations with two attributes

• For each transitive dependency– Create a new relation

– Remove the transitively determined attribute

– Copy the determining attribute

Proj2

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3NF - Identify Transitive Dependencies

Manager is dependent on a non-key attribute.

Emp2

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3NF - Remove Transitive Dependency

Dept3

Emp3Remove the managerattribute.

Create a relation withthe manager attribute anda copy of the dept attribute.

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3NF Relations

Emp3(emp-no, emp-name, dept)

Dept3(dept, manager)

EmpProj2(emp-no, proj-id, location, weeks-on-project)

Proj2(proj-id, proj-start-date)

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Third Normal Form

Process1NF - Remove repeating groups

2NF - Remove partial dependencies

3NF - Remove transitive dependencies

Emp3

Dept3

Proj3

EmpProj3