NormalizationNormalizationNormalizationNormalization

Chapter 4

Purpose of NormalizationPurpose of Normalization

Normalization A technique for producing a set of relations with desirable

properties, given the data requirements of an enterprise.

The process of normalization is a formal method that identifies relations based on their primary or candidate keys and on the functional dependencies among their attributes.

Normalization supports a number of tests , which can be applied to relations so that a relational schema can be normalized to a specific form to prevent the possible occurrence of update anomalies.

First Normal Form Relation First Normal Form Relation

We saw before that a relation should have the following properties:

A relation in a database has a unique name. Each cell of the relation contains exactly one atomic value. Each attribute has a distinct name within a relation. The values of an attribute are all from the same domain. The order of the attributes has no significance. Each tuple is distinct; there are no duplicate tuples. The order of tuples has no significance, theoretically.

In that case we say that the relation is in

FIRST NORMAL FORM (1NF).

Normalization Process: 1NFNormalization Process: 1NF

Un-normalized form

A table that contains

repeating Groups

S# P Q

P# QTY

S1 P1 300

P2 200

P3 400

P4 200

P5 100

P6 100

S2 P1 300

P2 400

S3 P2 200

S4 P2 200

P4 300

P5 400

First Normal Form A relation in which the inter-

section of each row and column contains one and only one value

S# P# QTY

S1 P1 300 S1 P2 200 S1 P3 400 S1 P4 200 S1 P5 100 S1 P6 100 S2 P1 300 S2 P2 400 S3 P2 200 S4 P2 200 S4 P4 300 S4 P5 400

Sample Database : 1NFSample Database : 1NF

S# Status City P# QTY S1 20 London P1 300

S1 20 London P2 200

S1 20 London P3 400

S1 20 London P4 200

S1 20 London P5 100

S1 20 London P6 100

S2 10 Paris P1 300

S2 10 Paris P2 400

S3 10 Paris P2 200

S4 20 London P2 200

S4 20 London P4 300

S4 20 London P5 400

Constraints

Primary Key : S# , P#

A city has a specific statusA Supplier Is located in one City

First

Update AnomaliesUpdate Anomalies

Insertion Anomalies each time we insert a new part for a supplier we have to

repeat status and city we cannot insert a new supplier before he supplies a part

Deletion Anomaly If we delete the fact that S3 supplies P2 we delete the row and

we do not know anymore that he is located in Paris

Modification Anomalies If S1 moves from London to Berlin we have to modify 6 rows If the status of London changes we have to modify 9 rows in

order to avoid inconsistency

Functional DependenciesFunctional Dependencies

Functional Dependency Describes the relationship between attributes in a relation If A and B are attributes of relation R, B is functionally dependent on

A , if each value of A in R is associated with exactly one value of B in R notation A B Functional dependency diagram

Determinant The determinant of a functional dependency refers to the attribute or

group of attributes on the starting point of the arrow

A BB is functionally

dependent on A

Functional Dependencies in FIRSTFunctional Dependencies in FIRST

QTY

S#

P#

Status

City

Sample Database : 1NFSample Database : 1NF

S# Status City P# QTY S1 20 London P1 300

S1 20 London P2 200

S1 20 London P3 400

S1 20 London P4 200

S1 20 London P5 100

S1 20 London P6 100

S2 10 Paris P1 300

S2 10 Paris P2 400

S3 10 Paris P2 200

S4 20 London P2 200

S4 20 London P4 300

S4 20 London P5 400

Constraints

Primary Key : S# , P#

A city has a specific statusA Supplier Is located in one City

First

Lossless-join and Dependency Preservation Lossless-join and Dependency Preservation PropertiesProperties

Two important properties of decomposition

Lossless-join property enables us to find any instance of the original relation from corresponding instances in the smaller relations.

Dependency preservation property enables us to enforce a constraint on the original relation by enforcing some constraint on each of the smaller relations.

Full Functional DependencyFull Functional Dependency

Full Functional Dependency indicates that 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 a proper subset of A.

e.g. First.(S# , Status ) First.City

First. S# First.City

In fact full functional dependence is a more important concept than functional dependence

Normalization Process: 2NFNormalization Process: 2NF

A relation is in second normal form if it is in first normal form and every non-primary-key attribute is fully functional dependent on the primary key.

S# P# QTY S1 P1 300

S1 P2 200

S1 P3 400

S1 P4 200

S1 P5 100

S1 P6 100

S2 P1 300

S2 P2 400

S3 P2 200

S4 P2 200

S4 P4 300

S4 P5 400

S# Status City S1 20 London

S2 10 Paris

S3 10 Paris

S4 20 London

S5 30 Athens

The reduction consists of a suitable projection

Supplier 5 is inserted

If in a 1NF relation the primary has only oneattribute, the relation is also in 2NF

SPSecond

Functional Dependencies in SP and SecondFunctional Dependencies in SP and Second

QTY

S#

P#

Status

City

S#

Elimination of non-fully functionaldependencies

Normalization Process: 3NFNormalization Process: 3NF

A relation in third normal form is a relation that is in first and second normal form , and in which no non-primary-key attribute is transitively dependent on the primary key.

S# City S1 London

S2 Paris

S3 Paris

S4 London

S5 Athens

SC City Status Athens 30

London 20

Paris 10

CS

Functional Dependencies in SP , SC and CSFunctional Dependencies in SP , SC and CS

QTY

S#

P#

City

City

S#

Status

Elimination oftransitive dependencies

Inter-relational DependencyInter-relational Dependency

QTY

S#

P#

City

S#

S#

Status

The three relations are also in 3NF but there is an inter-relational dependency

Bad decomposition

Normalization Process: BCNFNormalization Process: BCNF

A relation is in Boyce-Codd normal form if and only if every determinant is a candidate key.

This definition doesn’t refers to other normal forms. BCNF is stronger than 3NF

If a relation is in third normal form , violation of the BCNF is quite rare. It may only happen under the specific conditions that the relation :

contains two or more composite candidate keys which overlap and share at least one attribute in common this attribute is fully dependent on the primary key

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

Violation of BCNF may occur in a relation that contains two (or more) composite keys which overlap and share at least one attribute in common.

Multivalued DependencyMultivalued Dependency

In R(A,B,C) the multivalued dependency R.A R.B

holds in R , if and only if the set of B-values matching a given pair (A,C) is independent of the C-value.

Multivalued dependencies always go together in pairs notation R.A R.B R.C functional dependency is a special case of multivalued

dependency example Course Teacher Text

Physics Prof.Green Basic Mechanics

Prof.Brown Optics

Prof. Black

Math Prof.White Modern Algebra

Geometry

CTX

Normalization Process: 4NFNormalization Process: 4NF

Course Teacher Text

Physics Prof.Green Basic Mechanics

Physics Prof.Green Optics

Physics Prof.Brown Basic Mechanics

Physics Prof.Brown Optics

Physics Prof. Black Basic Mechanics

Physics Prof. Black Optics

Math Prof.White Modern Algebra

Math Prof.White Geometry

CTX

Normalized

4NFCourse Teacher

Physics Prof.Green

Physics Prof.Brown

Physics Prof. Black

Math Prof.White

Course Text

Physics Basic Mechanics

Physics Optics

Math Modern Algebra

Math Geometry

CTX.Course CTX.TeacherCTX.Course CTX.Text

Omit multivalued dependencies