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1/22/2009 1
Study the methods of first, second, third, Boyce-Codd, fourth and fifth normal form for relational database design, in order to eliminate data redundancy and update abnormality.
Lecture 3 on Data Normalization
1/22/2009 2
Normalization Theory
Refine database design to eliminate abnormalities (irregularities) of manipulating database
1/22/2009 3
1NF, 2NF and 3NF
• Built around the concept of normal forms– Normal form: Contains atomic values only– All normalized relations are in 1NF– 2NF is the subset of 1NF, 3NF is the subset of
2NF and so on…– 3NF is more desirable than 2NF, 2NF is more
desirable than 1NF
1/22/2009 4
BCNF, 4NF and 5NF(PJNF)
• Boyce-Codd Normal Form– A stronger form of 3NF– Every BCNF is also 3NF, but some 3NF are n
ot BCNF
• 4NF and 5NF– Defined recently– Deal with multi-valued dependency (MVD) an
d join dependency (JD)
1/22/2009 5
Relationship between Normal Forms
Universe of relations
1NF relations
2NF relations
3NF relations
BCNF relations
4NF relations5NF/PJNF relations
1/22/2009 6
First Normal Form
• A relation is in 1NF if each attribute contains only one value (not a set of values)
• The primary key (PK) can not be null
1/22/2009 7
First Normal Form
S# S-name Enrollments
S1 Brown C1 Math
C2 Chem
C3 Phys
S2 Smith C2 Chem
C3 Phys
C4 Math
S3 Brown C2 Chem
C3 Phys
Is this relation in 1NF?
Relation STUDENT-A
1/22/2009 8
First Normal Form
S# S-name Enrollments
S1 Brown C1 Math
C2 Chem
C3 Phys
S2 Smith C2 Chem
C3 Phys
C4 Math
S3 Brown C2 Chem
C3 Phys
• NO!!!• Elements in the
domain Enrollments are not atomic
• Could be split into two domains: C# and C-Name
Relation STUDENT-B
1/22/2009 9
First Normal Form
• Enrollments is split into C# and C-Name
• Use S# and C# as a compound PK
• A student may attend several courses and a course may have several students
• So S# and C# has a m:n mapping
S# S-Name C# C-Name
S1 Brown C1 Math
S1 Brown C2 Chem
S1 Brown C3 Phys
S2 Smith C2 Chem
S2 Smith C3 Phys
S2 Smith C4 Math
S3 Brown C2 Chem
S3 Brown C3 Phys
Relation STUDENT-B
1/22/2009 10
Functional Dependency (FD)
• Attribute Y of relation R is functionally dependent on attribute X of R each value of X is associated with exactly one value of Y
• Denoted by X Y• In the relation STUDENT-B:
– S# S-Name– C# C-Name– S#, C# 0
1/22/2009 11
Anomalies using 1NF
• 1NF relations require less complicated application to operate as opposed to unnormalized relations
• Anomalies in insert:– Since PK is composed of C# and S#, both det
ails of student and course must be known before inserting a entry
– Eg: to add a course, at least one student is enrolled
1/22/2009 12
Anomalies using 1NF
• Anomalies in delete:– If all students attending a particular course are
deleted, the course will not be found in the database
• Anomalies in update:– Redundancy of S-Name and C-Name– Increase storage space and effort to modify data item– If a course is modified, all tuples containing that
course must be updated
1/22/2009 13
Second Normal Form
• A relation is in 2NF if it is in 1NF and every non-PK attribute is fully functionally dependant on the PK
• In the relation STUDENT-B– PK: C#, S#– Non-PK attribute: C-Name, S-Name– C#, S# S-Name– S# S-Name– Since S-Name is only partially dependent on the PK,
relation Student-B is not in 2NF
1/22/2009 14
Second Normal Form
• All of them are in 2NF as none of them has partial dependency
• Original information can be reconstructed by natural join operation
S# S-Name
S1 Brown
S2 Smith
S3 Brown
C# C-Name
C1 Math
C2 Chem
C3 Phys
C4 Math
S# C#
S1 C1
S1 C2
S1 C3
S2 C2
S2 C3
S2 C4
S3 C2
S3 C3
Relation STUDENT
Relation COURSE
Relation SC
1/22/2009 15
Anomalies in 2NF
• Suppose we have the relations PRODUCT, MACHINE and EMPLOYEE
• P# M#• P# E#• M# E#• The tuple (P1, M1, E1) means product P1
is manufactured on machine M1 which is operated by employee E1
1/22/2009 16
Anomalies in 2NF
• Anomalies in insert:– It is not possible to store the fact that which
machine is operated by which employee without knowing at least one product produced by this machine
• Anomalies in delete:– If an employee is fired the fact that which
machine he operated and what product that machine produced are also lost
1/22/2009 17
Anomalies in 2NF
• Anomalies in update:– If one employee is assigned to operate
another machine then several tuples have to be updated as well
1/22/2009 18
Third Normal Form
• A relation is in 3NF if it is in 2NF and no non-PK attributes is transitively dependent on the PK
• In the manufacture relations:– P# M# and M# E# implies P# E#– So P# E# is a transitive dependency
1/22/2009 19
Third Normal Form
P# M# E#
P1 M1 E1
P2 M2 E3
P3 M1 E1
P4 M1 E1
P5 M3 E2
P6 M4 E1
P# M#
P1 M1
P2 M2
P3 M1
P4 M1
P5 M3
P6 M4
M# E#
M1 E1
M2 E3
M3 E2
M4 E1
MANUFACTURE
R1
R2
• No loss of information
• Insert, delete and update anomalies are eliminated
1/22/2009 20
Boyce/Codd Normal Form
• A relation is BCNF every determinant is a candidate key
• A determinant is an attribute, possibly composite, on which some other attribute is fully functionally dependent
1/22/2009 21
Boyce/Codd Normal Form
• There exists a relation SJT with attributes S (student), J (subject) and T (teacher). The meaning of SJT tuple is that the specified student is taught the specified subject by the specified teacher.
S J T
Smith Math Prof. White
Smith Physics Prof. Green
Jones Math Prof. White
Jones Physics Prof. Brown
Relation SJT
1. For each subject (J), each student (S) of that subject taught by only one teacher (T): FD: S, J T
2. Each teacher (T) teaches only one subject (J): FD: T J
3. Each subject (J) is taught by several teacher: MVD: J TT
1/22/2009 22
Boyce/Codd Normal Form
• There are two determinants: (S, J) and T in functional dependency
• Anomalies in update:– If the fact that Jones studies physics is
deleted, the fact that Professor Brown teaches physics is also lost. It is because T is a determinant but not a candidate key
1/22/2009 23
Boyce/Codd Normal Form
S J
Smith Math
Smith Physics
Jones Math
Jones Physics
T J
Prof. White Math
Prof. Green Physics
Prof. Brown Physics
Relation ST
Relation TJ
Relations (S, J) and (T, J) are in BCNF because all determinants are candidate keys.
1/22/2009 24
Multi-valued Dependency
• Given a relation R with attributes A, B and C. The multi-valued dependence R.A R.B holds the set of B-values matching a given (A-value, C-value) pair in R depends only on the A-value and is independent of the C-value
1/22/2009 25
Fourth Normal Form
• A relation is in 4NF whenever there exists an multi-valued dependence (MVD), say A B, then all attributes are also functionally dependent on A, i.e. A X for all attribute X of the relation
1/22/2009 26
Fourth Normal Form
Course Teacher Text
Physics Prof. Green Basic Mechanics
Physics Prof. Green Principles of Optics
Physics Prof. Brown Basic Mechanics
Physics Prof. Brown Principles of Optics
Physics Prof. Black Basic Mechanics
Physics Prof. Black Principles of Optics
Math Prof. White Modern Algebra
Math Prof. White Projective GeometryRelation CTX (not in 4NF)
1/22/2009 27
Fourth Normal Form
• A tuple (C, T, X) appears in CTX course C can be taught by teacher T and uses X as a reference. For a given course, all possible combinations of teacher and text appear – that is, CTX satisfies the constraint: if tuples (C, T1, X1), (C, T2, X2) both appears, then tuples (C, T1, X2), (C, T2, X1) both appears also
1/22/2009 28
Fourth Normal Form
• CTX contains redundancy
• CTX is in BCNF as there are no other functional determinants
• But CTX is not in 4NF as it involves an MVD that is not an FD at all, let alone an FD in which the determinant is a candidate key
1/22/2009 29
Anomalies in insert
• For example, to add the information that the physics course uses a new text called Advanced Mechanism, it is necessary to create three new tuples, one for each of the three teachers.
1/22/2009 30
Fourth Normal Form
Course Teacher
Physics Prof. Green
Physics Prof. Brown
Physics Prof. Black
Math Prof. White
Course Text
Physics Basic Mechanics
Physics Principles of Optics
Math Modern Algebra
Math Projective Geometry
Relation CT Relation CX
• 4NF is an improvement over BCNF, in that it eliminates another form of undesirable structure
1/22/2009 31
Fifth Normal Form
• Join dependency: relation R satisfies the JD (X, Y,…Z) it is the join of its projections on X, Y,…Z where X, Y,…Z are subsets of the set of attributes of R
• A relation is in 5NF/PJNF (Projection-join normal form) every join dependency in R is implied by the candidate keys of R
• 5NF is the ultimate normal form with respect to projection and join
1/22/2009 32
Fifth Normal Form
S# P# J#
S1 P1 J2
S1 P2 J1
S2 P1 J1
S1 P1 J1
S# P#
S1 P1
S1 P2
S2 P1
J# S#
J2 S1
J1 S1
J1 S2
P# J#
P1 J2
P2 J1
P1 J1
S# P# J#
S1 P1 J2
S1 P1 J1
S1 P2 J1
S2 P1 J2
S2 P1 J1
Join over P#
Spurious
Join over (J#, S#)
•SPJ is the join of all of its three projections,not of any two!
Relation SPJJS PJ
SP
1/22/2009 33
Join Dependence constraint
Condition: JD(join dependence) in relation R(S#, P#, J#)
Constraint: if R1(S#, P#), R2(P#, J#) and R3(J#, S#) exists
then R(S#, P#, J#) exists
1/22/2009 34
Connection Trap
Condition: Without JD(join dependence) in relation (S#, P#, J#)
Connect trap: if R1(S#, P#), R2(P#, J#) and R3(J#, S#) exists
then R(S#, P#, J#) may not exist and R1, R2 and R3 may not be able to be connected
1/22/2009 35
Abnomalies in insert with JD
If insert (S1, P1, J2), (S1, P2, J1), and
(S2, P1, J1)
Then (S1, P1, J1) must also be inserted
On the other hand, if one of (S1, P1, J2), (S1, P2, J1) and (S2, P1, J1) is deleted, then (S1, P1, J1) must also be deleted.
1/22/2009 36
Fifth Normal Form (5NF)
S# P#
S1 P1
S1 P2
S2 P1
J# S#
J2 S1
J1 S1
J1 S2
P# J#
P1 J2
P2 J1
P1 J1
JS PJ SP
1/22/2009 37
Steps in normalization
1. Decompose all data structures that are not 2D into 2D relations of segments
2. Eliminate any partial dependency
3. Eliminate any transitive dependency
4. Eliminate any remaining FD in which determinant is not a candidate key
5. Eliminate any MVD6. Eliminate any JD that are
implied by candidate keys
Unnormalized form
1NF
2NF
3NF
BCNF
4NF
5NF/PJNF
1/22/2009 38
Lecture Summary
The 1NF, 2NF, 3NF, BCNF, 4NF and 5NF are to split the unnormalized table into normalized table(s), and which can eliminate data redundancy and update abnormality. The higher norm form implies the lower norm form.
1/22/2009 39
Review Question
Explain the differences between Third Normal Form and Boyce Codd Normal Form with respect to functional dependencies.
Why Boyce Codd is called “Strong” third normal form?
How can one normalize relations of Third Normal Form into Boyce Codd Normal Form?
1/22/2009 40
Tutorial Question Describe and derive the unnormal, first, second and third normal form
for the following unnormal form including 12 data fields with 4 of them are in repeating groups in a table. Identify the functional dependencies of each normal form.
Class number: ___________________ Class name: ___________________
Location: ___________________Begin date ___________________
End date ___________________ Instructor name ___________________
Instructor address ___________________ Instructor phone no ___________________
Student Number Student name Student address Grade
……………….. ……………. ……………….. ………….
……………….. ……………. ……………….. ………….
Where “…….” are repeating group of data in the record
1/27/2009 41
Reading Assignment
Chapter 10 Functional Dependencies and Normalization for Relational Databases and Chapter 11 Relational Database Design Algorithms and Further Dependencies of “Fundamentals of Database Systems” fifth edition, by Elmasri & Navathe, Pearson, 2007.