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BITSPilaniHyderabad Campus

Dr.R.GururajCS&IS Dept.

Database Design & Applications

(SS ZG 518)

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BITS Pilani, Hyderabad Campus

Lecture Session-7

Functional Dependencies and Normal Forms (Ch.10 & 11)

Content

Introduction to Schema Refinement

Functional Dependencies

Inference RulesNormalization

Normal Forms (1NF and 2NF)

3 NF and BCNF

Decomposition requirements

Lossless join decomposition

Dependency preserving decomposition

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A good database design practice is essential to developgood relational schemas at logical level.

Good database design is needed for:

Clarity in understanding the database and

To formulate good queries

This is achieved by schema refinement.

Introduction to Database Design


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Functional Dependency is a constraint between two sets

of attributes from the database.

Function DependencyDenoted by X Y between two sets of attributes in R,

and specifies a constraint on the possible tuples that can

form a relational instance rof R.

Values of Y component are determined by X component.

(or) Y is functionally dependent on X.

Functional Dependencies


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XY

Thus, X functionally determines Y in a relation schema R if

and only if whenever two tuples of r(R) agree on their X

values they must necessarily agree on their Y values, butYX is not true (need not be)

Ex: ssn ename; {ssn, pnumber} Hours

Note:FDs cannot be inferred. They should be defined by someonewho knows the semantics of the database very well.


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Dname Dnumber Mgrssn Mgrstartdate

Department {DnumberDname, Mgrssn,mgrstartdate}

Essn Pno Hours

Work_on {Essn, pno} Hours

Diagrammatic Notation


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Rule 1(1R1): (Reflexing)If X Y then X Y otherwise non trivial

Rule 2(1R2) (Argumentation)

X Y; then XZ YZ

Rule 3(1R3) (Transitive)

X

Y ; Y

Z; Then X

Z;Rule 4(IR4) (Decomposition or projective rule)

X YZ then X Y; & X Z;

Rule 5(IR5) (union rule)

X A; X B ; then X AB

Rule 6(IR6) (Pseudo transitive)

X Y ; WY Z; then WX Z;

We can find the closure F+of F, by repeated application of rules IR-1 to

IR-3. These rules are called asArmstrongs Inference rules.

Inference Rules for FDs


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Normalizationprocess is first proposed by

Raymond Boyce and Edgar Coddin 1972.

Normalization of data is the process of analyzing relation

schemas based on their FDs and PKs/Keys to achieve thedesirable properties of

(i)Minimal redundancy

(ii)Minimal anomalies

Normalization & Normal forms


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DId Dname Dloc

10 Engg HYD

CHENNAI

20 Mark HYD

MUMBAI

1. First Normal Form (INF)

It states that the domain of any attribute must include only

atomic (single / simple/ individual) values.

In the example given below, under the column Dloceach

row has more than on values.

Ex.: Dept


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2. Second Normal Form (2NF)It is based on full functional dependency.

{X A} is fully functional if we remove any attribute from X then

that FD does not hold anymore.

Condition for 2NF: All non-key attributes are fully functionally dependent onkey (or) no non-key attribute should be dependent on part of key(partial

dependency).

eid pnum Hours ename ploc


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Here, {ename} is a non key attribute anddetermined by {eid}which is part of the key. Hence

we say that enamenot fully functionally dependent

on key.

The relation shown is not in 2NF. Now we candecompose this in to three relations as shown

below.

eid ename pnum ploc eid pnum hours


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3. Third Normal form (3NF)

It is based on transitive dependency.

According to this, a relation should not have a non key attribute

functionally determined by another non key attribute. i.e., there should

be no transitive dependency.

eid addressename dnum dname dloc

Not in 3NF, because Dnameis transitively dependent on eid.


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Now we can decompose the above into 2 relations.

eid addressename dnum Dnum Dname dloc

Condition for 3NF

For each FD, X A in database

i) X must be a superkey or

ii) A is key attribute


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As we have seen, decomposition (of a bigger relation R

into smaller ones), is a major step in the process of

normalization.

But during this activity of decomposition, we need tomake sure that the decomposition is losslessand

dependency preserving

Decomposition and Desirable properties


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1

( )R

r r 2 ( )R r

1

( )R

r

Let C represent a set of constraints on the database. A decomposition{R1, R2, R3,.R4} of a relation schema R is a lossless join

decomposition for R if all relation instances ron R that are legal under

C.

.= r

= projection of ron R1

rrelation instance in R

F = FDs on R

(or) {R} {R1, R2}

*

Loss-less join Decomposition


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Test for Lossless join property


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Given a set of dependencies F on R, the projection of F on Ri

denoted by

(where Riis a subset of R); is the set of FDs X Y in F+such that the

attributes in X Y are contained in Ri.

1 2( ) ( ) ...., ( )

mR R R

F F F F

Then it is dependency preserving decomposition.

- is projection of F on R1.1 ( )R f

Dependency Preserving Decomposition


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Summary

Introduction to Database Design

Functional Dependencies and Inference Rules

Concepts in Normalization

Normal Forms (1NF,2NF,3 NF and BCNF)

Desirable properties of Decomposition

(requirements)

Lossless join decomposition and tests

Dependency preserving decomposition and tests

ss zg518-l7.ppt

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