1. Database Design: Normalization
Reading: C&B, Chaps 14

2. In this lecture you will learn
Mathematical notions behind relational model
Normalization
Dept. of Computer Science, University of Aberdeen

3. Dept. of Computer Science, University of Aberdeen
Introduction
Relations derived from ER model may be ‘faulty’
May cause data redundancy, and insert/delete/update anomalies
We use some mathematical (semantic?) properties of relations to
locate these faults and
fix them
Dept. of Computer Science, University of Aberdeen

4. Mathematical notions behind relational model
Set – a collection of objects characterized by some defining property
E.g. a column in a database table such as last names of all staff
Cross Product of sets – one of the operations (X) on sets
E.g. consider two sets, set of all first names and set of all last names in the staff table
fName = {Mary, David}
lName = {Howe, Ford}
fNameXlName = {(Mary,Howe), (Mary,Ford), (David, Howe), (David, Ford)}
Relation – defined between two sets and is a subset of cross product between those two sets
E.g. FirstNameOf = {(Mary, Howe), (David, Ford)}
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Relational model
The name ‘relational model’ comes from this mathematical notion of relation
Where a relation is a set (collection) of tuples that have related objects such as first name and last name of the same person
E.g. (fName, lName) is a relation
We can have relations over any number of sets
E.g. (staffNo, fName, lName, position)
In general we can denote a relation as (A,B,C,D,….,Z) where A, B, C and Z are all its attribute sets
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Function
A function is a special kind of relation
In a relation (X,Y), if every value of X is associated with exactly one value of Y, then we say Y is a function of X.
E.g. the relation {(1,2),(2,4),(3,6),(4,8)} is a function, Y = 2*X for 0<X<5 X Y
Only one arrow can start from any single value in X 1 2 3 4 2 4 6 8
Dept. of Computer Science, University of Aberdeen

7. Functional Dependency
If Y is a function of X
Y is dependent on X,
there is a relationship of functional dependency between Y and X
In databases, we work with relations in general form (A,B,C,D,……,Z)
Functional Dependency
Describes 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.
We are interested in finding such functional dependencies among database relations
Dept. of Computer Science, University of Aberdeen

8. Functional Dependency
Is a 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.
If the determinant can maintain the functional dependency with a minimum number of attributes, then we call it full functional dependency
Dept. of Computer Science, University of Aberdeen

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Data Redundancy
Major aim of relational database design is
to group attributes into relations to minimize data redundancy and
to reduce file storage space required by base relations.
Data redundancy is undesirable because of the following anomalies
‘Insert’ anomalies
‘Delete’ anomalies
‘Update’ anomalies
We illustrate these anomalies with an example
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Data Redundancy
Dept. of Computer Science, University of Aberdeen

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Anomalies
Insert anomalies
Try to insert details for a new member of staff into StaffBranch
You also need to insert branch details that are consistent with existing details for the same branch
Hard to maintain data consistency with StaffBranch
Delete anomalies
Try to delete details for a member of staff from StaffBranch
You also loose branch details in that tuple (row)
Update anomalies
Try to update the value of one of the attributes of a branch
You also need to update that information in all the tuples about the same branch
Dept. of Computer Science, University of Aberdeen

12. Decomposition of Relations
Staff and Branch relations which are obtained by decomposing StaffBranch do not suffer from these anomalies
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.
Dept. of Computer Science, University of Aberdeen

13. 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.
Given a relation, use the following cycle
Find out what normal form it is in
Transform the relation to the next higher form by decomposing it to form simpler relations
You may need to refine the relation further if decomposition resulted in undesirable properties
Dept. of Computer Science, University of Aberdeen

14. 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.
Example 1 – address and name fields are composite
Name
Address
Phone
Sally Singer
123 Broadway New York, NY, 11234
(111)
Jason Jumper
456 Jolly Jumper St. Trenton NJ, 11547
(222)
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Another example of UNF
Example 2 – repeating columns for each client &
composite name field
Rep ID
Representative
Client 1
Time 1
Client 2
Time 2
Client 3
Time 3
TS-89
Gilroy Gladstone
US Corp.
14 hrs
Taggarts
26 hrs
Kilroy Inc.
9 hrs
RK-56
Mary Mayhem
Italiana
67 hrs
Linkers
2 hrs
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First Normal Form (1NF)
A relation in which intersection of each row and column contains one and only one value.
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).
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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.
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Example 1 ID
First
Last
Street
City
State
Zip
Phone
564
Sally
Singer
123 Broadway
New York NY
11234
(111)
565
Jason
Jumper
456 Jolly Jumper St.
Trenton NJ
11547
(222)
Address field has been expressed in terms of constituent parts,
such as street, city and postcode
Name field has been expressed in terms of last name and first name
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Example 2
Table structure has been changed
Data related to representative repeated
Representative name expressed in terms of last name and first name
Rep ID
Rep First Name
Rep Last Name
Client
Time With Client
TS-89
Gilroy
Gladstone
US Corp
14 hrs
Taggarts
26 hrs
Kilroy Inc.
9 hrs
RK-56
Mary
Mayhem
Italiana
67 hrs
Linkers
2 hrs
Dept. of Computer Science, University of Aberdeen

20. Dept. of Computer Science, University of Aberdeen
Example 2
A new field ClientID introduced
RepId and ClientID combination acts as the primary key
Rep ID*
Rep First Name
Rep Last Name
Client ID*
Client
Time With Client
TS-89
Gilroy
Gladstone
978
US Corp
14 hrs
665
Taggarts
26 hrs
782
Kilroy Inc.
9 hrs
RK-56
Mary
Mayhem
221
Italiana
67 hrs
982
Linkers
2 hrs
Dept. of Computer Science, University of Aberdeen

21. Second Normal Form (2NF)
Based on concept of full functional dependency:
A and B are attributes of a relation R,
B is fully dependent on A (denoted A->B) 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.
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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.
Dept. of Computer Science, University of Aberdeen

23. Dept. of Computer Science, University of Aberdeen
Example 2NF
Rep ID*
Client ID*
Time With Client
TS-89
978
14 hrs
665
26 hrs
782
9 hrs
RK-56
221
67 hrs
982
2 hrs
4 hrs
Rep ID*
First Name
Last Name
TS-89
Gilroy
Gladstone
RK-56
Mary
Mayhem
Client ID*
Client Name
978
US Corp
665
Taggarts
782
Kilroy Inc.
221
Italiana
982
Linkers
Original table decomposed into smaller tables
Each of them are in 2NF
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24. Dept. of Computer Science, University of Aberdeen
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.
Dept. of Computer Science, University of Aberdeen

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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.
Dept. of Computer Science, University of Aberdeen

26. Dept. of Computer Science, University of Aberdeen
Normalization Flow
UNF
Remove repeating groups
1NF
Remove partial dependencies
2NF
Remove transitive dependencies
3NF
More normalized forms
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27. Dept. of Computer Science, University of Aberdeen
Conclusion
Quality of the relations derived from ER models is unknown
Normalization is a systematic process of either assessing or converting these relations into progressively stricter normal forms
Advanced normal forms such as Boyce-Codd normal form (BNCF), 4NF and 5NF exist
Dept. of Computer Science, University of Aberdeen