basic concepts of Entity relationship diagram

Copyright © 2007 Ramez Elmasri and Shamkant B. Navathe
Chapter 4
Functional Dependencies and
Normalization for Relational
Databases

Chapter Outline
 Informal Design Guidelines for Relational Databases
 Semantics of the Relation Attributes
 Redundant Information in Tuples and Update Anomalies
 Null Values in Tuples
 Spurious Tuples
 Functional Dependencies (FDs)
 Definition of FD
 Inference Rules for FDs
 Equivalence of Sets of FDs
 Minimal Sets of FDs

Chapter Outline
 Normal Forms Based on Primary Keys
 Normalization of Relations
 Practical Use of Normal Forms
 Definitions of Keys and Attributes Participating in Keys
 First Normal Form
 Second Normal Form
 Third Normal Form
 General Normal Form Definitions (For Multiple Keys)

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)

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.

A simplified COMPANY relational
database schema

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

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.

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.

EXAMPLE OF AN 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.

Two relation schemas suffering from
update anomalies

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 anomalies present, then note them
so that applications can be made to take them into
account.

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

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.

Functional Dependencies (1)
 Functional dependencies (FDs)
 Are used to specify formal measures of the
"goodness" of relational designs
 And keys are used to define normal forms for
relations
 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

Copyright © 2007 Ramez Elmasri and Shamkant B. Navathe
Key terms
Here are some key terms for Functional Dependency in
Database:
Key Terms Description
Axiom
Axioms is a set of inference rules used to infer all the functional
dependencies on a relational database.
Decomposition
It is a rule that suggests if you have a table that appears to contain two
entities which are determined by the same primary key then you
should consider breaking them up into two different tables.
Dependent It is displayed on the right side of the functional dependency diagram.
Determinant It is displayed on the left side of the functional dependency Diagram.
Union
It suggests that if two tables are separate, and the PK is the same, you
should consider putting them together
Slide 10- 21

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)
 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])

Inference Rules for FDs (1)
 Given a set of FDs F, we can infer additional FDs that
hold whenever the FDs in F hold
 Armstrong's inference rules:
 IR1. (Reflexive) If Y subset-of X, then X -> Y
 IR2. (Augmentation) If X -> Y, then XZ -> YZ

(Notation: XZ stands for X U Z)
 IR3. (Transitive) If X -> Y and Y -> Z, then X -> Z
 IR1, IR2, IR3 form a sound and complete set of
inference rules
 These are rules hold and all other rules that hold can be
deduced from these

Inference Rules for FDs (2)
 Some additional inference rules that are useful:
 Decomposition: If X -> YZ, then X -> Y and X ->
Z
 Union: If X -> Y and X -> Z, then X -> YZ
 Psuedotransitivity: If X -> Y and WY -> Z, then
WX -> Z
 The last three inference rules, as well as any
other inference rules, can be deduced from IR1,
IR2, and IR3 (completeness property)

Normal Forms Based on Primary Keys
 Normalization of Relations
 Practical Use of Normal Forms
 Definitions of Keys and Attributes
Participating in Keys
 First Normal Form
 Second Normal Form
 Third Normal Form

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
 Additional properties may be needed to ensure a
good relational design (lossless join, dependency
preservation)

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

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.

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 relation

Normalization into 1NF

Normalization nested relations into 1NF

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

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

Normalizing into 2NF and 3NF

Figure 10.11 Normalization into 2NF and
3NF

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.

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

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
 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

General Normal Form Definitions (2)
 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

Chapter Outline
 Informal Design Guidelines for Relational
Databases
 Functional Dependencies (FDs)
 Definition, Inference Rules, Equivalence of Sets of
FDs, Minimal Sets of FDs
 Normal Forms Based on Primary Keys
 General Normal Form Definitions (For Multiple
Keys)

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