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- Chapter 13

Normalization

Transparencies - Chapter 13 Objectives

Purpose of normalization.

Problems associated with redundant data.

Identification of various types of update anomalies

such as insertion, deletion, and modification

anomalies.

How to recognize appropriateness or quality of the

design of relations.

2 - Chapter 13 Objectives

How functional dependencies can be used to group

attributes into relations that are in a known normal form.

How to undertake process of normalization.

How to identify most commonly used normal forms,

namely 1NF, 2NF, 3NF, and Boyce–Codd normal form

(BCNF).

How to identify fourth (4NF) and fifth (5NF) normal

forms.

3 - Normalization

Main objective in developing a logical data

model for relational database systems is to

create an accurate representation of the data,

its relationships, and constraints.

To achieve this objective, must identify a

suitable set of relations.

4 - Normalization

Four most commonly used normal forms are first

(1NF), second (2NF) and third (3NF) normal

forms, and Boyce–Codd normal form (BCNF).

Based on functional dependencies among the

attributes of a relation.

A relation can be normalized to a specific form to

prevent possible occurrence of update anomalies.

5 - Data Redundancy

Major aim of relational database design is to

group attributes into relations to minimize data

redundancy and reduce file storage space

required by base relations.

Problems associated with data redundancy are

illustrated by comparing the following Staff

and Branch relations with the StaffBranch

relation.

6 - Data Redundancy

7 - Data Redundancy

StaffBranch relation has redundant data: details

of a branch are repeated for every member of

staff.

In contrast, branch information appears only

once for each branch in Branch relation and only

branchNo is repeated in Staff relation, to

represent where each member of staff works.

8 - Update Anomalies

Relations that contain redundant information

may potentially suffer from update anomalies.

Types of update anomalies include:

Insertion

Deletion

Modification.

9 - Lossless join and Dependency Preservation

Properties

Two important properties of decomposition:

Lossless join property enables us to find any

instance of original relation from

corresponding instances in the smaller

relations.

Dependency preservation property enables us

to enforce a constraint on original relation by

enforcing some constraint on each of the

smaller relations.

10 - Functional Dependency

Main concept associated with normalization.

Functional Dependency

Describes relationship between attributes in

a relation.

If A and B are attributes of relation R, B is

functionally dependent on A (denoted A

B), if each value of A in R is associated with

exactly one value of B in R.

11 - Functional Dependency

Property of the meaning (or semantics)

of the attributes in a relation.

Diagrammatic representation:

Determinant of a functional dependency refers

to attribute or group of attributes on left hand

side of the arrow.

12 - Example - Functional Dependency

13 - Functional Dependency

Main characteristics of functional dependencies

used in normalization:

have a 1:1 relationship between attribute(s)

on left and right hand side of a dependency;

hold for all time;

are nontrivial.

14 - Functional Dependency

Complete set of functional dependencies for a given

relation can be very large.

Important to find an approach that can reduce set to

a manageable size.

Need to identify set of functional dependencies (X)

for a relation that is smaller than complete set of

functional dependencies (Y) for that relation and has

property that every functional dependency in Y is

implied by functional dependencies in X.

15 - Functional Dependency

Set of all functional dependencies implied by a

given set of functional dependencies X called

closure of X (written X+).

Set of inference rules, called Armstrong’s

axioms, specifies how new functional

dependencies can be inferred from given ones.

16 - Functional Dependency

Let A, B, and C be subsets of the attributes of

relation R. Armstrong’s axioms are as follows:

1. Reflexivity

If B is a subset of A, then A → B

2. Augmentation

If A → B, then A,C → B,C

3. Transitivity

If A → B and B → C, then A → C

17 - The Process of Normalization

Formal technique for analyzing a relation based

on its primary key and functional dependencies

between its attributes.

Often executed as a series of steps. Each step

corresponds to a specific normal form, which

has known properties.

As normalization proceeds, relations become

progressively more restricted (stronger) in

format and also less vulnerable to update

anomalies.

18 - Relationship Between Normal Forms

19 - Unnormalized Form (UNF)

A table that contains one or more repeating

groups.

To create an unnormalized table:

transform data from information source

(e.g. form) into table format with columns

and rows.

20 - First Normal Form (1NF)

A relation in which intersection of each row

and column contains one and only one value.

21 - UNF to 1NF

Nominate an attribute or group of attributes to

act as the key for the unnormalized table.

Identify repeating group(s) in unnormalized

table which repeats for the key attribute(s).

22 - UNF to 1NF

Remove repeating group by:

entering appropriate data into the empty

columns of rows containing repeating data

(‘flattening’ the table).

Or by

placing repeating data along with copy of

the original key attribute(s) into a separate

relation.

23 - Second Normal Form (2NF)

Based on concept of full functional

dependency:

A and B are attributes of a relation,

B is fully dependent on A if B is functionally

dependent on A but not on any proper subset of A.

2NF - A relation that is in 1NF and every non-

primary-key attribute is fully functionally dependent

on the primary key.

24 - 1NF to 2NF

Identify primary key for the 1NF relation.

Identify functional dependencies in the

relation.

If partial dependencies exist on the

primary key remove them by placing them

in a new relation along with copy of their

determinant.

25 - Third Normal Form (3NF)

Based on concept of transitive dependency:

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

if A → B and B → C,

then C is transitively dependent on A through

B. (Provided that A is not functionally

dependent on B or C).

3NF - A relation that is in 1NF and 2NF and in

which no non-primary-key attribute is transitively

dependent on the primary key.

26 - 2NF to 3NF

Identify the primary key in the 2NF relation.

Identify functional dependencies in the

relation.

If transitive dependencies exist on the

primary key remove them by placing them

in a new relation along with copy of their

determinant.

27 - General Definitions of 2NF and 3NF

Second normal form (2NF)

A relation that is in 1NF and every non

primary key attribute is fully functionally

dependent on any candidate key.

Third normal form (3NF)

A relation that is in 1NF and 2NF and in

which no non primary key attribute is

transitively dependent on any candidate key.

28 - Boyce–Codd Normal Form (BCNF)

Based on functional dependencies that take

into account all candidate keys in a relation,

however BCNF also has additional constraints

compared with general definition of 3NF.

BCNF A relation is in BCNF if and only if

every determinant is a candidate key.

29 - Boyce–Codd normal form (BCNF)

Difference between 3NF and BCNF is that for a

functional dependency A B, 3NF allows this

dependency in a relation if B is a primary key

attribute and A is not a candidate key.

Whereas, BCNF insists that for this dependency to

remain in a relation, A must be a candidate key.

Every relation in BCNF is also in 3NF. However,

relation in 3NF may not be in BCNF.

30 - Boyce–Codd normal form (BCNF)

Violation of BCNF is quite rare.

Potential to violate BCNF may occur in a

relation that:

contains two (or more) composite candidate

keys;

the candidate keys overlap (ie. have at least

one attribute in common).

31 - Review of Normalization (UNF to BCNF)

32 - Review of Normalization (UNF to BCNF)

33 - Review of Normalization (UNF to BCNF)

34 - Review of Normalization (UNF to BCNF)

35 - Fourth Normal Form (4NF)

Although BCNF removes anomalies due to

functional dependencies, another type of

dependency called a multi valued dependency

(MVD) can also cause data redundancy.

Possible existence of MVDs in a relation is due

to 1NF and can result in data redundancy.

36 - Fourth Normal Form (4NF) MVD

Dependency between attributes (for example,

A, B, and C) in a relation, such that for each

value of A there is a set of values for B and a

set of values for C. However, set of values for B

and C are independent of each other.

37 - Fourth Normal Form (4NF)

MVD between attributes A, B, and C in a

relation using the following notation:

A B

A >> C

38 - Fourth Normal Form (4NF)

MVD can be further defined as being trivial or

nontrivial.

MVD A >> B in relation R is defined as being trivial

if (a) B is a subset of A or (b) A B = R.

MVD is defined as being nontrivial if neither (a) nor

(b) are satisfied.

Trivial MVD does not specify a constraint on a

relation, while a nontrivial MVD does specify a

constraint.

39 - Fourth Normal Form (4NF)

Defined as a relation that is in BCNF and

contains no nontrivial MVDs.

40 - 4NF - Example

41 - Fifth Normal Form (5NF)

A relation decomposed into two relations must have

lossless join property, which ensures that no

spurious tuples are generated when relations are

reunited through a natural join.

However, there are requirements to decompose a

relation into more than two relations.

Although rare, these cases are managed by join

dependency and fifth normal form (5NF).

42 - Fifth Normal Form (5NF)

A relation that has no join dependency.

43 - 5NF - Example

44