Chapter 14: Normalization and Transitive dependency

CHAPTER 14
Basics of Functional Dependencies
and Normalization for Relational
Databases
Slide 14- 2

Chapter Outline
 1 Informal Design Guidelines for Relational Databases
 1.1 Semantics of the Relation Attributes
 1.2 Redundant Information in Tuples and Update Anomalies
 1.3 Null Values in Tuples
 1.4 Spurious Tuples
 2 Functional Dependencies (FDs)
 2.1 Definition of Functional Dependency
Slide 14- 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?
Slide 14- 4

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 Noferferferfewrmal Form)
 - BCNF (Boyce-Codd Normal Form)
 Additional types of dependencies, further normal forms,
relational design algorithms by synthesis are discussed in
Chapter 15
Slide 14- 5

1.1 Semantics of the Relational
Attributes must be clear
 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.
Slide 14- 6

Figure 14.1 A simplified COMPANY
relational database schema
Slide 14- 7
Figure 14.1 A simplified
COMPANY relational
database schema.

1.2 Redundant Information in Tuples and
Update Anomalies
 Information is stored redundantly
 Wastes storage
 Causes problems with update anomalies

Insertion anomalies

Deletion anomalies

Modification anomalies
Slide 14- 8

EXAMPLE OF AN UPDATE ANOMALY
 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.
Slide 14- 9

EXAMPLE OF AN INSERT ANOMALY
No_hours)
 Insert Anomaly:
 Cannot insert a project unless an employee is
assigned to it.
 Conversely
 Cannot insert an employee unless an he/she is
assigned to a project.
Slide 14- 10

EXAMPLE OF A DELETE ANOMALY
No_hours)
 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.
Slide 14- 11

Figure 14.3 Two relation schemas
suffering from update anomalies
Slide 14- 12
Figure 14.3
Two relation schemas
suffering from update
anomalies. (a)
EMP_DEPT and (b)
EMP_PROJ.

Figure 14.4 Sample states for
EMP_DEPT and EMP_PROJ
Slide 14- 13
Figure 14.4
Sample states for EMP_DEPT
and EMP_PROJ resulting from
applying NATURAL JOIN to the
relations in Figure 14.2. These
may be stored as base relations
for performance reasons.

Guideline for 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 anomalies present, then note them
so that applications can be made to take them into
account.
Slide 14- 14

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
Slide 14- 15

1.4 Generation of Spurious Tuples – avoid
at any cost
 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.
Slide 14- 16

3 Normal Forms Based on Primary Keys
 3.1 Normalization of Relations
 3.2 Practical Use of Normal Forms
 3.3 Definitions of Keys and Attributes
Participating in Keys
 3.4 First Normal Form
 3.5 Second Normal Form
 3.6 Third Normal Form
Slide 14- 17

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
Slide 14- 18

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
 Additional properties may be needed to ensure a
good relational design (lossless join, dependency
preservation; see Chapter 15)
Slide 14- 19

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 and BCNF. 4NF rarely used in practice.)
 Denormalization:

The process of storing the join of higher normal form
relations as a base relation—which is in a lower normal form
Slide 14- 20

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.
Slide 14- 21

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.
Slide 14- 22

3.4 First Normal Form
 Disallows
 composite attributes
 multivalued attributes
 nested relations; attributes whose values for an
individual tuple are non-atomic
 Considered to be part of the definition of a
relation
 Most RDBMSs allow only those relations to be
defined that are in First Normal Form
Slide 14- 23

Figure 14.9 Normalization into 1NF
Slide 14- 24
Figure 14.9
Normalization into 1NF. (a) A
relation schema that is not in
1NF. (b) Sample state of
relation DEPARTMENT. (c)
1NF version of the same
relation with redundancy.

3.5 Second Normal Form (1)
 Uses the concepts of FDs, primary key
 Definitions
 Prime attribute: An 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
Slide 14- 25

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 or “second
normalization”
Slide 14- 26

Figure 14.11 Normalizing into 2NF and
3NF
Slide 14- 27
Figure 14.11
Normalizing into 2NF and 3NF. (a)
Normalizing EMP_PROJ into 2NF
relations. (b) Normalizing EMP_DEPT
into 3NF relations.

Figure 14.12 Normalization into 2NF and
3NF
Slide 14- 28
Figure 14.12 Normalization into 2NF and 3NF. (a) The
LOTS relation with its functional dependencies FD1
through FD4.
(b) Decomposing into the 2NF relations LOTS1 and
LOTS2. (c) Decomposing LOTS1 into the 3NF relations
LOTS1A and LOTS1B. (d) Progressive normalization of
LOTS into a 3NF design.

3.6 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
Slide 14- 29

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.
Slide 14- 30

Normal Forms Defined Informally
 1st
normal form
 All attributes depend on the key
 2nd
normal form
 All attributes depend on the whole key
 3rd
normal form
 All attributes depend on nothing but the key
Slide 14- 31

4. General Normal Form Definitions (For
Multiple Keys) (1)
 The above definitions consider the primary key
only
 The following more general definitions take into
account relations with multiple candidate keys
 Any attribute involved in a candidate key is a
prime attribute
 All other attributes are called non-prime
attributes.
Slide 14- 32

4.1 General Definition of 2NF (For
Multiple Candidate Keys)
 A relation schema R is in second normal form
(2NF) if every non-prime attribute A in R is fully
functionally dependent on every key of R
 In Figure 14.12 the FD
County_name → Tax_rate violates 2NF.
So second normalization converts LOTS into
LOTS1 (Property_id#, County_name, Lot#, Area, Price)
LOTS2 ( County_name, Tax_rate)
Slide 14- 33

4.2 General Definition of Third Normal
Form
 Definition:
 Superkey of relation schema R - a set of attributes
S of R that contains a key of R

A relation schema R is in third normal form (3NF)
if whenever a FD X → A holds in R, then either:

(a) X is a superkey of R, or

(b) A is a prime attribute of R
 LOTS1 relation violates 3NF because
Area → Price ; and Area is not a superkey in
LOTS1. (see Figure 14.12).
Slide 14- 34

4.3 Interpreting the General Definition of
Third Normal Form
 Consider the 2 conditions in the Definition of 3NF:
A relation schema R is in third normal form (3NF) if
whenever a FD X → A holds in R, then either:

(a) X is a superkey of R, or

(b) A is a prime attribute of R
 Condition (a) catches two types of violations :
- one where a prime attribute functionally determines a non-
prime attribute. This catches 2NF violations due to non-full
functional dependencies.
-second, where a non-prime attribute functionally determines a
non-prime attribute. This catches 3NF violations due to a
transitive dependency.
Slide 14- 35

4.3 Interpreting the General Definition of
Third Normal Form (2)
 ALTERNATIVE DEFINITION of 3NF: We can restate the definition
as:
A relation schema R is in third normal form (3NF) if
every non-prime attribute in R meets both of these
conditions:
It is fully functionally dependent on every key of R
It is non-transitively dependent on every key of R
Note that stated this way, a relation in 3NF also meets the
requirements for 2NF.
 The condition (b) from the last slide takes care of the
dependencies that “slip through” (are allowable to) 3NF but
are “caught by” BCNF which we discuss next.
Slide 14- 36

5. BCNF (Boyce-Codd Normal Form)
 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
 Every 2NF relation is in 1NF
 Every 3NF relation is in 2NF
 Every BCNF relation is in 3NF
 There exist relations that are in 3NF but not in BCNF
 Hence BCNF is considered a stronger form of 3NF
 The goal is to have each relation in BCNF (or 3NF)
Slide 14- 37

Copyright © 2016 Ramez Elmasri and Shamkant B. Navathe Slide 14- 38
Figure 14.13 Boyce-Codd normal form
Figure 14.13
Boyce-Codd normal form. (a) BCNF normalization of LOTS1A with the
functional dependency FD2 being lost in the decomposition. (b) A schematic
relation with FDs; it is in 3NF, but not in BCNF due to the f.d. C B.
→

Chapter 14: Normalization and Transitive dependency

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