normalization in SQL BEST NOTES PPT AVAILABLE

Chapter 10
Functional Dependencies and
Normalization for Relational
Databases
Copyright © 2004 Pearson Education, Inc.

Copyright © 2004 Ramez Elmasri and Shamkant Navathe
Elmasri/Navathe, Fundamentals of Database Systems, Fourth Edition Chapter 10-3
1 Informal Design Guidelines for
Relational Databases (1)
 What is relational database design?
The grouping of attributes to form "good" relation schemas
 Two levels of relation schemas
– The logical "user view" level
– The storage "base relation" level
 Design is concerned mainly with base relations
 What are the criteria for "good" base relations?

Informal Design Guidelines for
Relational Databases (2)
 We first discuss informal guidelines for good
relational design
 Then we discuss formal concepts of functional
dependencies and normal forms
- 1NF (First Normal Form)
- 2NF (Second Normal Form)
- 3NF (Third Normal Form)
- BCNF (Boyce-Codd Normal Form)

1.1 Semantics of the Relation
Attributes
GUIDELINE 1: Informally, each tuple in a relation
should represent one entity or relationship
instance. (Applies to individual relations and their
attributes).
 Attributes of different entities (EMPLOYEEs, DEPARTMENTs,
PROJECTs) should not be mixed in the same relation
 Only foreign keys should be used to refer to other entities
 Entity and relationship attributes should be kept apart as much as
possible.
Bottom Line: Design a schema that can be explained
easily relation by relation. The semantics of
attributes should be easy to interpret.

Figure 10.1 A simplified COMPANY
relational database schema
Note: The above figure is now called Figure 10.1 in Edition 4

1.2 Redundant Information in
Tuples and Update Anomalies
 Mixing attributes of multiple entities may cause
problems
 Information is stored redundantly wasting storage
 Problems with update anomalies
– Insertion anomalies
– Deletion anomalies
– Modification anomalies

EXAMPLE OF AN UPDATE
ANOMALY (1)
Consider the relation:
EMP_PROJ ( Emp#, Proj#, Ename, Pname, No_hours)
 Update Anomaly: Changing the name of project
number P1 from “Billing” to “Customer-
Accounting” may cause this update to be made for
all 100 employees working on project P1.

EXAMPLE OF AN UPDATE
ANOMALY (2)
 Insert Anomaly: Cannot insert a project unless
an employee is assigned to .
Inversely - Cannot insert an employee unless an
he/she is assigned to a project.
 Delete Anomaly: When a project is deleted, it
will result in deleting all the employees who work
on that project. Alternately, if an employee is the
sole employee on a project, deleting that employee
would result in deleting the corresponding project.

Figure 10.3 Two relation schemas
suffering from update anomalies

Figure 10.4 Example States for EMP_DEPT
and EMP_PROJ

Guideline to Redundant Information
in Tuples and Update Anomalies
 GUIDELINE 2: Design a schema that does not
suffer from the insertion, deletion and update
anomalies. If there are any present, then note them
so that applications can be made to take them into
account

1.3 Null Values in Tuples
GUIDELINE 3: Relations should be designed such
that their tuples will have as few NULL values as
possible
 Attributes that are NULL frequently could be
placed in separate relations (with the primary key)
 Reasons for nulls:
– attribute not applicable or invalid
– attribute value unknown (may exist)
– value known to exist, but unavailable

1.4 Spurious Tuples
 Bad designs for a relational database may result in
erroneous results for certain JOIN operations
 The "lossless join" property is used to guarantee
meaningful results for join operations
GUIDELINE 4: The relations should be designed to
satisfy the lossless join condition. No spurious
tuples should be generated by doing a natural-join
of any relations.

Spurious Tuples (2)
There are two important properties of decompositions:
(a) non-additive or losslessness of the corresponding
join
(b) preservation of the functional dependencies.
Note that property (a) is extremely important and
cannot be sacrificed. Property (b) is less stringent
and may be sacrificed. (See Chapter 11).

2.1 Functional Dependencies (1)
 Functional dependencies (FDs) are used to specify
formal measures of the "goodness" of relational
designs
 FDs and keys are used to define normal forms for
relations
 FDs are constraints that are derived from the
meaning and interrelationships of the data
attributes
 A set of attributes X functionally determines a set
of attributes Y if the value of X determines a
unique value for Y

Functional Dependencies (2)
 X -> Y holds if whenever two tuples have the same value
for X, they must have the same value for Y
 For any two tuples t1 and t2 in any relation instance r(R):
If t1[X]=t2[X], then t1[Y]=t2[Y]
 X -> Y in R specifies a constraint on all relation instances
r(R)
 Written as X -> Y; can be displayed graphically on a
relation schema as in Figures. ( denoted by the arrow: ).
 FDs are derived from the real-world constraints on the
attributes

Examples of FD constraints (1)
 social security number determines employee name
SSN -> ENAME
 project number determines project name and
location
PNUMBER -> {PNAME, PLOCATION}
 employee ssn and project number determines the
hours per week that the employee works on the
project
{SSN, PNUMBER} -> HOURS

Examples of FD constraints (2)
 An FD is a property of the attributes in the schema
R
 The constraint must hold on every relation
instance r(R)
 If K is a key of R, then K functionally determines
all attributes in R (since we never have two
distinct tuples with t1[K]=t2[K])

3.1 Normalization of Relations (1)
 Normalization: The process of decomposing
unsatisfactory "bad" relations by breaking up their
attributes into smaller relations
 Normal form: Condition using keys and FDs of a
relation to certify whether a relation schema is in a
particular normal form

Normalization of Relations (2)
 2NF, 3NF, BCNF based on keys and FDs of a
relation schema
 4NF based on keys, multi-valued dependencies :
MVDs; 5NF based on keys, join dependencies :
JDs (Chapter 11)
 Additional properties may be needed to ensure a
good relational design (lossless join, dependency
preservation; Chapter 11)

3.2 Practical Use of Normal Forms
 Normalization is carried out in practice so that the
resulting designs are of high quality and meet the desirable
properties
 The practical utility of these normal forms becomes
questionable when the constraints on which they are based
are hard to understand or to detect
 The database designers need not normalize to the highest
possible normal form. (usually up to 3NF, BCNF or 4NF)
 Denormalization: the process of storing the join of higher
normal form relations as a base relation—which is in a
lower normal form

3.3 Definitions of Keys and Attributes
Participating in Keys (1)
 A superkey of a relation schema R = {A1, A2, ....,
An} is a set of attributes S subset-of R with the
property that no two tuples t1 and t2 in any legal
relation state r of R will have t1[S] = t2[S]
 A key K is a superkey with the additional
property that removal of any attribute from K will
cause K not to be a superkey any more.

Definitions of Keys and Attributes
Participating in Keys (2)
 If a relation schema has more than one key, each
is called a candidate key. One of the candidate
keys is arbitrarily designated to be the primary
key, and the others are called secondary keys.
 A Prime attribute must be a member of some
candidate key
 A Nonprime attribute is not a prime attribute—
that is, it is not a member of any candidate key.

3.2 First Normal Form
Disallows composite attributes, multivalued
attributes, and nested relations; attributes
whose values for an individual tuple are
non-atomic
Considered to be part of the definition of
relation

Figure 10.8 Normalization into 1NF

3.3 Second Normal Form (1)
 Uses the concepts of FDs, primary key
Definitions:
 Prime attribute - attribute that is member of the
primary key K
 Full functional dependency - a FD Y -> Z
where removal of any attribute from Y means the
FD does not hold any more
Examples: - {SSN, PNUMBER} -> HOURS is a full FD
since neither SSN -> HOURS nor PNUMBER -> HOURS hold
- {SSN, PNUMBER} -> ENAME is not a full FD (it is called a
partial dependency ) since SSN -> ENAME also holds

Second Normal Form (2)
A relation schema R is in second normal
form (2NF) if every non-prime attribute A
in R is fully functionally dependent on the
primary key
R can be decomposed into 2NF relations via
the process of 2NF normalization

Figure 10.11 Normalization into 2NF

3.4 Third Normal Form (1)
Definition:
 Transitive functional dependency - a FD X -> Z
that can be derived from two FDs X -> Y and Y -> Z
Examples:
- SSN -> DMGRSSN is a transitive FD since
SSN -> DNUMBER and DNUMBER -> DMGRSSN hold
- SSN -> ENAME is non-transitive since there is no set of
attributes X where SSN -> X and X -> ENAME

Third Normal Form (2)
 A relation schema R is in third normal form
(3NF) if it is in 2NF and no non-prime attribute A
in R is transitively dependent on the primary key
 R can be decomposed into 3NF relations via the
process of 3NF normalization
NOTE:
In X -> Y and Y -> Z, with X as the primary key, we consider this a
problem only if Y is not a candidate key. When Y is a candidate key,
there is no problem with the transitive dependency .
E.g., Consider EMP (SSN, Emp#, Salary ).
Here, SSN -> Emp# -> Salary and Emp# is a candidate key.

Elmasri/Navathe, Fundamentals of Database Systems, Fourth Edition
Normalization to 3NF
Chapter 10-32

Summary of Normal Forms
Chapter 10-33

BCNF(Boyce-Codd
Normal Form )
 BCNF deals with relations that have multiple
candidate keys. A relation is in BCNF if every
non-key attribute is dependent on some candidate
key.
 A relation schema R is in Boyce-Codd Normal
Form (BCNF) if whenever an FD X -> A holds in
R, then X is a superkey of R
 Each normal form is strictly stronger than the previous one
Chapter 10-34

BCNF
Consider the relation
BOOK( ISBN,Title, price,page_count)
FDs of this relation are
– ISBN-> price
– ISBN->page_count
– Title-> price
– Title-> page_count
There are two candiadate keys ISBN and title and
all non-key attributes are dependent on them, so
book is in BCNF.
Chapter 10-35

BCNF
But some times candidate keys overlap,
BOOK_RATING(ISBN,Title, R_id,Rating)
The candidate keys are
(ISBN,R_id)
(Title,R_id)
This relation is not in BCNF as, candidate
keys are composite and overlapping.b
however this is in 3NF.
Chapter 10-36

BCNF
This can be resolved by decomposing the
relation into two
Book_title_info(ISBN,title)
Review(R_id, ISBN, rating)
Another solution is
Book_title_info(ISBN,title)
Review(R_id, title, rating)
Chapter 10-37

4th Normal Form
Multivalued Dependencies-
It is a consequence of 1st NF, which
disallows an attribute to have multiple
values.
A relation schema R is in 4NF, with respect
to set of functional dependencies, F, if for
every nontrivial multivalued dependence
X->-> Y in F, X is a super key of R.
Chapter 10-38

5th Normal Form
Lossless join property says that original
relation must be recovered from the small
relations that result from decomposition.
Let R be a relation schema, and R1,
R2…,Rn be decompositions of R, R is said
to satisfy the join dependency
*(R1,R2..,Rn) if and only if
 R1(R)  R2(R)  R3(R)= R
Chapter 10-39

A relation is in 5NF IF
It is in 4NF and
It can not be further non-loss decomposed
Definition:- a relation schema R is in 5th
Normal Form, with respect to functional
dependncies F and join dependencies if, for
every join dependency *(R1,R2,…Rn), in
F, every Ri is super key of R.
Chapter 10-40

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