Database Theory & Practice (4) : Data Normalization

Information Systems Development 3 (SHAPE HK)
Lecture 6 : Data Normalisation
Normalisation (1)
• What is Normalisation?
Informally, normalisation can be thought of as a process defined
within the theory of relational database to break up larger
relations into many small ones using a set of rules. Normalisation
resolve problems with data anomalies and redundancy. It is
essentially a two-step process to:
1. put the data into tabular form (by removing repeating groups);
2. to remove duplicated records to separate tables.
As we work through the normalisation process, we will make use
of data that relates to the Bus Depots’ Database – a description
and E-R model of which was handed out in last weeks session and
is also available from the resource area.
Normalisation (2)
• Un-normalised data (1)
Well-normalised databases have a design that reflects the true dependencies
between entities, allowing the data to be updated quickly with little risk of
introducing inconsistencies. Before discussing how to design a wellnormalised database using Codd's normalisation techniques, we first consider
a poor database design.
Consider for example a relation 'bus' which includes bus registration number,
model, type number, type description, depot name (note that names have
changed slightly from the study for the purposes of this example):
registration no
type number
type description
Al 23ABC
Volvo 8700
Daf SB220
Mercedes 709D
Mercedes Citaro
Daf SB220
Normalisation (3)
• Un-normalised data (2)
There are several problems with the previous relation:
– Redundancy - the 'type description' is repeated for each 'type number' in
the relation. The 'model' is also repeated for a particular 'type
description', for example a Routemaster is always a doubledecker bus
– Update anomalies - as a consequence of the redundancy, we could
update the 'type description' in one tuple, while leaving it fixed in
– Deletion anomalies - if we should delete all the buses of a particular
type, we might lose all the information about that type
– Insertion anomalies - the inverse to deletion anomalies is we cannot
record a new type in our table unless there exists a bus of that type - for
example if there is the type 'open top' we cannot store this in our
database. To get around this we might put null values in the type number
and description components of a tuple for that bus, but when we enter
an item for that supplier, will we remember to delete the tuple with
Normalisation (4)
• Functional dependencies (1)
A formal definition for the term functional dependence is:
Given a relation which has attributes (x, y, ...), we say that an attribute y is
functionally dependent on another attribute x, if (and only if) each x value
has associated with it precisely one y value (at any one time).
For example, examine the following relation:
Cleaner no.
Cleaner name
Cleaner salary
Depot no.
Normalisation (5)
In the previous diagram, attributes cname, csalary and dno are
each functionally dependent on attribute cno - given a particular
cno value, there exists precisely one corresponding value for each of
the cname, csalary and dno.
In general then, the same x-values may appear in many different
tuples of the relation; if y is functionally dependent on x, then every
one of these tuples must contain the same value.
Going back to the cleaner example, we can represent these functional
dependencies diagrammatically as:
Normalisation (6)
The previous figure is an example of a determinacy diagram. The arrow
line can be read as 'depends on' (reading from left to right). So we say, for
example, 'cno depends on cname'. We can also 'read' the diagram from
right to left. This time the arrowed line is read as 'functionally dependent
on'. So we say, for example 'cname is functionally dependent on cno'.
The attribute or group of attributes on the left-hand side are called the
determinant. The determinant of a value is not necessarily the primary
key. In the example, cno is a determinant of cname because knowing the
cleaner's number we can determine the cleaner's name.
Recognizing the functional dependencies is an essential part of
understanding the meaning or semantics of the data. The fact that
cname, csalary and dno are functionally dependent on cno means
that each cleaner has one name, has one salary and works at precisely one
Normalisation (7)
• Functional dependencies (2)
Composite attributes
The notion of functional dependence can be extended to cover the case where the
determinant (particularly the primary key) is composite, i.e. it consists of more that one
Full functional dependence
An attribute y is defined to be fully functionally dependent on attribute x if it is
functionally dependent on x and not functionally dependent on any subset of the
attributes of x where it is a composite attribute.
Partial dependencies
The opposite of full functional dependence is partial dependence. Where we have data
values that depend on only a part of the primary key, then we have a partial
Transitive dependencies
This occurs when the value of an attribute is not determined directly from the primary
key, but through the value of another attribute and this attribute in turn is determined
by the primary key.
Normalisation (8)
• The normal forms
A number of normal forms have been proposed, but the first five normal
forms have been widely accepted.
The normal forms progress from first normal form, to second, and so on.
Data in second normal form implies that it is also in first normal form - i.e.
each level of normalisation implies that the previous level has been met.
Other normal forms such as Boyce-Codd (BCNF) which is an extension of
Normalisation (9)
Correspondence between the normal forms:
Normalisation (10)
• Normal form example
Consider the following example forms that record information about
cleaners at the Middlesex Depot and the buses they look after. Note
that three extra attributes, roster number, roster date and job
complete have been added to the original model. The cleaner ticks
against the appropriate job after he/she has completed the cleaning
of a particular bus.
Normalisation (11)
The un-normalised relation:
Normalisation (12)
• First normal form (1 NF)
The next step in the normalisation process is to remove the repeating groups
from the unnormalised relation. A relation is in 1 NF if - and only if - all
domains contain only atomic or single values, i.e. all repeating groups of data
are removed.
A repeating group is a group of attributes that occurs a number of times for
each record in the relation. So for example, in the Roster relation, each roster
record has a group of buses (roster record 104 has 6 buses).
Selecting a suitable key for the table
In order to convert an un-normalised relation into first normal form, we must
identify the key attribute(s) involved. From the un-normalised relation we can
see that each roster has a roster_no, each cleaner a cno, each depot a
dno, each bus a reg_no and each type a tno. In order to convert an unnormalised relation into normal form, we also have to identify a key for the
whole relation. Bearing this definition in mind, on examination the primary
key of the relation is roster-no, reg_no.
We now draw the determinacy diagram for the roster relation, showing the
attributes which are dependent on the primary key:
Normalisation (13)
Determinacy diagram for the first normal form:
Normalisation (14)
Roster relation in first normal form:
Normalisation (15)
• The problems with 1 NF are:
– Redundancy - e.g. roster date, cleaner name etc. repeated
– Insertion anomaly - a cleaner cannot be inserted into the
database unless he/she has a bus to clean
– Deletion anomaly - deleting a tuple might lose information from
the database. For example, if a cleaner cleaning a particular bus
leaves the company, then we lose information for the buses he
– Update anomaly - e.g. a change to the cleaner name means it
must change in all tuples which include that cleaner name.
Normalisation (16)
• Second normal form (2NF)
We now describe the second step in the normalisation process using the
relation above which is in first normal form.
Firstly we determine the functional dependencies on the identifying
attributes (i.e. the primary key (roster_no, reg_no) and its parts.
If the key is composite, the other attributes must be functionally
dependent on the whole of the key. In other words we are looking for
partial functional dependencies. In the example, roster date is functionally
dependent on the partial key roster_no - there is only one
roster_date for a particular roster_no. Also cno, cname, dno,
dname etc are all functionally dependent on the partial key reg_no.
The attribute 'status', however, is the only attribute fully functionally
dependent on the whole of the primary key.
Normalisation (17)
Determinacy diagram for the second normal form:
Normalisation (18)
Roster in first second normal form:
Normalisation (19)
2NF has less redundancy than 1NF as we have removed repeating
However there are still a number of problems:
– Redundancy - for example, in the Bus relation, cleaner name is
repeated for each cleaner number
– Insertion anomaly - a cleaner cannot be inserted into the database
unless he/she is responsible for at least one bus
– Deletion anomaly - deleting a tuple might lose information from the
database. For example, if we delete a cleaner who is only responsible
for that one bus, then we lose information about the cleaner
– Update anomaly - e.g. a change to the cleaner name means changes
must be made in all tuples which include that cleaner name.
Normalisation (20)
• Third normal form (3NF)
A 3NF relation is in 2NF but also it must satisfy the non-transitive
dependency rule, which states that every non-key attribute must be nontransitively dependent on the primary key. Another way of saying this is
that a relation is in 3NF if all its non-key attributes are directly dependent
on the primary key. Transitive dependencies are resolved by creating new
relations for each entity.
There are three transitive dependencies in the Bus relation above as is
illustrated by vertical lines in the 2NF determinacy diagram. For example:
cno is functionally dependent on reg_no; cname is functionally
dependent on reg_no. Additionally, cname is functionally dependent
We therefore have the transitive dependency:
reg_no determines cno and cno determines cname then
reg_no determines cname
Two other transitive dependencies are identified involving tname and
dname. The determinacy diagrams for third normal form are given on the
next slide:
Normalisation (21)
Determinacy diagram for the third normal form:
Normalisation (22)
Roster in third normal form:
Normalisation (24)
Steps of the Normalisation process (1) :
Normalisation (24)
What is it?
What does
process do?
How is it achieved?
1 NF
Relation in 1 NF if
- it contains scalar (atomic)
values only
- Removes
repeating groups
- Make a separate relation
for each group of related
- Give each new relation a
primary key
2 NF
Relation in 2NF if
- in I NF
- all non-key attributes are
dependent on the whole
of the primary key and
not part of it
- Removes
redundant data
- If an attribute depends on
only part of a multi
value key, remove it to a
separate table
3 NF
Relation in 3NF if
- in 2NF
- non-key attributes are
dependent on primary
key and independent of
each other
- i.e. non-key attribute
must be non-transitively
dependent on the primary
- a non-key attribute is
changed, that change
should not affect the
- Removes
attributes not
dependent on
the key thereby
further reducing
- Make a separate relation
for attributes transitively
dependent on the
primary key
- Give each new relation a
primary key
- Original relation will
include a foreign key to
link to new relation
An Introduction to Database Systems (8th ed.), C J Date, Addison Wesley 2004
Database Management Systems, P Ward & G Defoulas, Thomson 2006
Database Systems Concepts (4th ed.), A Silberschatz, H F Korth & S Sudarshan, McGraw-Hill

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