Normalization
Lec 5
Database Systems: A Practical Approach
to Design, Implementation and
Management
Carolyn Begg, Thomas Connolly
1
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
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).
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
Data Redundancy
10
Insertion Anomalies
New member of staff joins branch B005
Insert new row into StaffBranch table
Type wrong address: 163 Main St, Glasgow.
Database is now inconsistent!
Establish new branch with no members of staff
B008, 57 Princes St, Edinburgh
No staff members, so staffNo must be NULL
But staffNo is the primary key of the StaffBranch
table, so cannot be NULL!
11
Deletion Anomaly
Mary Howe, staffNo SA9, leaves the company
Delete the appropriate row of StaffBranch
This also deletes details of branch B007 where Mary
Howe works
But no-one else works at branch B007, so we no
longer know the address of this branch!
12
Modification Anomaly
Branch B003 has transferred to a new location
New address is 145 Main St, Glasgow
Must change three rows of the StaffBranch relation
13
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.
14
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.
15
Example - Functional Dependency
16
Identifying Candidate Keys
A candidate key is an attribute, or set of attributes,
that uniquely identifies a row
Must be irreducible
No part of a candidate can ever be NULL
An attribute A that functionally determines every
other attribute of the relation is a candidate key
For each value of A there is exactly one value of
each of the other attributes
So each value of A must identify a single row
17
Identifying Primary Keys
A primary key is a candidate key chosen to identify
rows uniquely within a table
Other candidate keys called alternate keys
Some guidelines on choosing the primary key
Pick the candidate key with fewest attributes
Pick the candidate key with shortest length
Pick the candidate key that makes most sense for
the business!
18
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.
19
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.
20
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.
21
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
22
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.
23
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.
24
First Normal Form (1NF)
A relation in which intersection of each row and
column contains one and only one value.
25
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).
26
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.
27
ClientRental UNF To 1NF By
Flattening
clientNo cName propertyNo pAddress rentStart rentFinish rent ownerNo oName
CR76 John PG4 6 Lawrence St, 1-Jul-00 31-Aug-01 350 CO40 Tina Murphy
Kay Glasgow
PG16 5 Novar Dr, 1-Sep-01 1-Sep-02 450 CO93 Tony shaw
Glasgow
CR56 Aline PG4 6 Lawrence St, 1-Sep-99 10-June-00 350 CO40 Tina Murphy
Stewart Glasgow
PG36 2 Manor Rd, 10-Oct-00 1-Dec-01 375 CO93 Tony shaw
Glasgow
PG16 5 Novar Dr, 1-Nov-02 10-Aug-03 450 CO93 Tony shaw
Glasgow
clientNo cName propertyNo pAddress rentStart rentFinish rent ownerNo oName
CR76 John Kay PG4 6 Lawrence St, 1-Jul-00 31-Aug-01 350 CO40 Tina Murphy
Glasgow
CR76 John Kay PG16 5 Novar Dr, 1-Sep-01 1-Sep-02 450 CO93 Tony shaw
Glasgow
CR56 Aline PG4 6 Lawrence St, 1-Sep-99 10-June-00 350 CO40 Tina Murphy
Stewart Glasgow
CR56 Aline PG36 2 Manor Rd, 10-Oct-00 1-Dec-01 375 CO93 Tony shaw
Stewart Glasgow
CR56 Aline PG16 5 Novar Dr, 1-Nov-02 10-Aug-03 450 CO93 Tony shaw
28 Stewart Glasgow
ClientRental Functional
Dependencies
On the ClientRental relation:
clientNo cName
propertyNo pAddress, rent, ownerNo, oName
ownerNo oName
clientNo, propertyNo cName, pAddress, rentStart,
rentFinish, rent, ownerNo, oName
clientNo, rentStart cName, propertyNo, pAddress,
rentFinish, rent, ownerNo, oName
propertyNo, rentStart clientNo, cName, pAddress,
rentFinish, rent, ownerNo, oName
29
ClientRental Primary Key
Candidate keys are
(clientNo, propertyNo)
(clientNo, rentStart)
(propertyNo, rentStart)
Choose (clientNo, propertyNo) as Primary key
clientNo propertyNo cName pAddress rentStart rentFinish rent ownerNo oName
CR76 PG4 John Kay 6 Lawrence St, 1-Jul-00 31-Aug-01 350 CO40 Tina Murphy
Glasgow
CR76 PG16 John Kay 5 Novar Dr, 1-Sep-01 1-Sep-02 450 CO93 Tony shaw
Glasgow
CR56 PG4 Aline 6 Lawrence St, 1-Sep-99 10-June-00 350 CO40 Tina Murphy
Stewart Glasgow
CR56 PG36 Aline 2 Manor Rd, 10-Oct-00 1-Dec-01 375 CO93 Tony shaw
Stewart Glasgow
CR56 PG16 Aline 5 Novar Dr, 1-Nov-02 10-Aug-03 450 CO93 Tony shaw
Stewart Glasgow
30
Client rental 1NF relation
Write down the ClientRental relation using
standard notation
ClientRental (clientNo, propertyNo, cName, pAddress,
rentStart, rentFinish, rent, ownerNo, oName)
31
Second Normal Form (2NF)
Based on concept of full functional
dependency:
A1, … , An and B are attributes of a relation,
B is fully dependent on A1, … , An if B is functionally
dependent on A1, … , An but not on any proper subset
of A1, … , An.
2NF - A relation that is in 1NF and every non-
primary-key attribute is fully functionally
dependent on the primary key.
32
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.
33
ClientRental Example: 1NF to 2NF
clientNo propertyNo cName pAddress rentStart rentFinish rent ownerNo oName
CR76 PG4 John Kay 6 Lawrence St, 1-Jul-00 31-Aug-01 350 CO40 Tina Murphy
Glasgow
CR76 PG16 John Kay 5 Novar Dr, 1-Sep-01 1-Sep-02 450 CO93 Tony shaw
Glasgow
CR56 PG4 Aline 6 Lawrence St, 1-Sep-99 10-June-00 350 CO40 Tina Murphy
Stewart Glasgow
CR56 PG36 Aline 2 Manor Rd, 10-Oct-00 1-Dec-01 375 CO93 Tony shaw
Stewart Glasgow
CR56 PG16 Aline 5 Novar Dr, 1-Nov-02 10-Aug-03 450 CO93 Tony shaw
Stewart Glasgow
Partial dependencies are:
clientNo cName
propertyNo pAddress, rent, ownerNo, oName
34
ClientRental Example: clientNo cName
Create new relation Client, with primary key
clientNo
clientNo cName
CR76 John Kay
CR56 Aline
Stewart
Remove cName from the ClientRental relation
clientNo propertyNo pAddress rentStart rentFinish rent ownerNo oName
CR76 PG4 6 Lawrence 1-Jul-00 31-Aug-01 350 CO40 Tina Murphy
St, Glasgow
CR76 PG16 5 Novar Dr, 1-Sep-01 1-Sep-02 450 CO93 Tony shaw
Glasgow
CR56 PG4 6 Lawrence 1-Sep-99 10-June- 350 CO40 Tina Murphy
St, Glasgow 00
CR56 PG36 2 Manor Rd, 10-Oct-00 1-Dec-01 375 CO93 Tony shaw
Glasgow
CR56 PG16 5 Novar Dr, 1-Nov-02 10-Aug-03 450 CO93 Tony shaw
35
Glasgow
ClientRental Example:
propertyNo -> pAddress, rent, ownerNo,
oName
Create new relation PropertyOwner, with primary
key propertyNo
propertyNo pAddress rent ownerNo oName
PG4 6 Lawrence St, Glasgow 350 CO40 Tina Murphy
PG16 5 Novar Dr, Glasgow 450 CO93 Tony shaw
PG36 2 Manor Rd, Glasgow 375 CO93 Tony shaw
Remove attributes pAddress, rent, ownerNo,
oName from the ClientRental relation
clientNo propertyNo rentStart rentFinish
CR76 PG4 1-Jul-00 31-Aug-01
CR76 PG16 1-Sep-01 1-Sep-02
CR56 PG4 1-Sep-99 10-June-00
CR56 PG36 10-Oct-00 1-Dec-01
36 CR56 PG16 1-Nov-02 10-Aug-03
ClientRental Example: 2NF relations
Tidy up, and re-name the ClientRental
relation “Rental”
clientNo propertyNo rentStart rentFinish
CR76 PG4 1-Jul-00 31-Aug-01
CR76 PG16 1-Sep-01 1-Sep-02
CR56 PG4 1-Sep-99 10-June-00
CR56 PG36 10-Oct-00 1-Dec-01
CR56 PG16 1-Nov-02 10-Aug-03
Write down the 2NF relations:
Client ( clientNo, cName)
PropertyOwner ( propertyNo, pAddress, rent, ownerNo, oName)
Rental ( clientNo, propertyNo, rentStart, rentFinish)
37
Third Normal Form (3NF)
Based on concept of transitive dependency:
A, B and C are attributes of a relation such that 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.
38
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.
39
ClientRental Example: 2NF to 3NF
Consider the relation:
PropertyOwner ( propertyNo, pAddress, rent, ownerNo, oName)
We have functional dependencies
propertyNo ownerNo
ownerNo oName
So oName is transitively dependent on propertyNo,
the primary key
40
ClientRental Example: Remove
Transitive Dependency On Primary Key
Create new relation Owner, with primary key
ownerNo and attribute oName
ownerNo oName
CO40 Tina Murphy
CO93 Tony shaw
Remove oName from PropertyOwner relation
propertyNopAddress rent ownerNo
PG4 6 Lawrence 350 CO40
St, Glasgow
PG16 5 Novar Dr, 450 CO93
Glasgow
PG36 2 Manor Rd, 375 CO93
Glasgow
41
ClientRental Example: 3NF Relations
Tidy up, and re-name PropertyOwner
relation “PropertyForRent”
propertyNo pAddress rent ownerNo
PG4 6 Lawrence St, Glasgow 350 CO40
PG16 5 Novar Dr, Glasgow 450 CO93
PG36 2 Manor Rd, Glasgow 375 CO93
Write down the 3NF relations:
Client ( clientNo, cName)
Rental ( clientNo, propertyNo, rentStart, rentFinish)
PropertyOwner ( propertyNo, pAddress, rent, ownerNo)
Owner (ownerNo, oName)
42
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.
43
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.
44
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.
45
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).
46
BCNF Example
Consider the relation:
ClientInterview (clientNo, interviewdate, interviewTime,
staffNo, roomNo)
clientNo interviewDate interviewTime staffNo roomNo
CR76 13-May-02 10:30 SG5 G101
CR56 13-May-02 12:00 SG5 G101
CR74 13-May-02 12:00 SG37 G102
CR56 1-Jul-02 10:30 SG5 G102
47
BCNF Example: Functional
dependencies
Functional dependencies are
fd1: clientNo, interviewdate interviewTime, staffNo,
roomNo
fd2: staffNo, interviewdate, interviewTime clientNo
fd3: roomNo, interviewdate, interviewTime staffNo,
clientNo
fd4: staffNo, interviewdate roomNo
48
BCNF Example
ClientInterview relation is in 3NF
Is ClientInterview relation in BCNF?
fd1: the determinant, (clientNo, interviewdate), is the
primary key
fd2 and fd3: both determinants are candidate keys
fd4: its determinant is NOT a candidate key
49
BCNF Example
Create new relation StaffRoom with the attributes
from fd4:
Determinant attributes form the primary key of the
new relation
Include dependent attributes in the relation
staffNo interviewDate roomNo
SG5 13-May-02 G101
SG5 13-May-02 G101
SG37 13-May-02 G102
SG5 1-Jul-02 G102
50
BCNF Example
Remove the dependent attributes of fd4 from the
ClientInterview relation and rename it Interview.
clientNo interviewDate interviewTime staffNo
CR76 13-May-02 10:30 SG5
CR56 13-May-02 12:00 SG5
CR74 13-May-02 12:00 SG37
CR56 1-Jul-02 10:30 SG5
Write down the BCNF relations:
StaffRoom (staffNo, interviewdate, roomNo)
Interview (clientNo, interviewdate, interviewTime,
staffNo)
51
Review of Normalization (UNF to BCNF)
52
Review of Normalization (UNF to BCNF)
53
Review of Normalization (UNF to BCNF)
54
Review of Normalization (UNF to BCNF)
55