Normalisation 3NF

8/21/2019 Normalisation 3NF

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Normalisation to 3NF

Database Systems Lecture 11

Natasha Alechina


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In This Lecture

• Normalisation to 3NF

• Data redundancy

• Functional dependencies• Normal forms

• First, Second, and Third Normal Forms

• For more information

• onnolly and !e"" chapter 13

• #llman and $idom ch%3%&%& '(nd edition),3%* '3rd edition)


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+edundancy and Normalisation

• +edundant data

• an be determinedfrom other data in the

database• Leads to arious

problems

• INS-+T anomalies

• #.DAT- anomalies

• D-L-T- anomalies

• Normalisation

• Aims to reduce dataredundancy

• +edundancy ise/pressed in terms ofdependencies

• Normal forms aredefined that do not

hae certain types ofdependency


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First Normal Form

• In most definitions ofthe relational model

• All data alues should

be atomic

• This means that tableentries should besin"le alues, not setsor composite ob0ects

• A relation is said tobe in first normalform '1NF) if all data

alues are atomic


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Normalisation to 1NF

Unnormalised

Module Dept Lecturer Texts

M1 D1 L1 T1, T2

M2 D1 L1 T1, T3

M3 D1 L2 T4 M4 D2 L3 T1, T5

M5 D2 L4 T6

1NF

Module Dept Lecturer Text

M1 D1 L1 T1

M1 D1 L1 T2

M2 D1 L1 T1

M2 D1 L1 T3 M3 D1 L2 T4

M4 D2 L3 T1

M4 D2 L3 T5

M5 D2 L4 T6

To convert to a 1NF relation, split up an

non!atomic values


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.roblems in 1NF


• ant add a module2ith no te/ts

• #.DAT- anomalies

• To chan"e lecturer for1, 2e hae tochan"e t2o ro2s

• D-L-T- anomalies• If 2e remoe 3, 2e

remoe L( as 2ell

1NF


M1 D1 L1 T1

M1 D1 L1 T2

M2 D1 L1 T1

M2 D1 L1 T3

M3 D1 L2 T4

M4 D2 L3 T1 M4 D2 L3 T5

M5 D2 L4 T6


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Functional Dependencies

• +edundancy is oftencaused by a functionaldependency

• A functional dependency'FD) is a lin4 bet2eent2o sets of attributes ina relation

• $e can normalise a

relation by remoin"undesirable FDs

• A set of attributes, A,functionally determines another set, !, or5 there

e/ists a functionaldependency bet2een Aand ! 'A → !), if2heneer t2o ro2s ofthe relation hae thesame alues for all theattributes in A, then theyalso hae the samealues for all theattributes in !%


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-/ample

• 6ID, modode7 → 6First, Last, modName7

• 6modode7 → 6modName7

• 6ID7 → 6First, Last7

ID modode modNameFirst Last

111 8*1.+8 .ro"rammin"9oe !lo""s

((( 8*1D!S DatabasesAnne Smith


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FDs and Normalisation

• $e define a set ofnormal forms

• -ach normal form has

fe2er FDs than thelast

• Since FDs representredundancy, eachnormal form has less

redundancy than thelast

• Not all FDs cause aproblem

• $e identify arious

sorts of FD that do

• -ach normal formremoes a type of FDthat is a problem

• $e 2ill also need a2ay to remoe FDs


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.roperties of FDs

• In any relation• The primary 4ey FDs

any set of attributes

in that relationK → X

• K is the primary 4ey, X is a set ofattributes

• Same for candidate

4eys• Any set of attributes

is FD on itself

X → X

• +ules for FDs• +efle/iity5 If B is a

subset of A then

A → B• Au"mentation5 If A → B then

A # C → B # C

• Transitiity5

If A → B and B → C then A → C


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FD -/ample

• The primary 4ey is6odule, Te/t7 so

6odule, Te/t7 →

6Dept, Lecturer7

• Triial FDs, e"5

6Te/t, Dept7 → 6Te/t7

6odule7 → 6odule7

6Dept, Lecturer7 → 6 7

1NF


M1 D1 L1 T1

M1 D1 L1 T2

M2 D1 L1 T1

M2 D1 L1 T3

M3 D1 L2 T4

M4 D2 L3 T1 M4 D2 L3 T5

M5 D2 L4 T6


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FD -/ample

• :ther FDs are

• 6odule7 → 6Lecturer7

• 6odule7 → 6Dept7

• 6Lecturer7 → 6Dept7

• These are non;triialand determinants 'lefthand side of thedependency) are not4eys%

1NF


M1 D1 L1 T1

M1 D1 L1 T2

M2 D1 L1 T1

M2 D1 L1 T3

M3 D1 L2 T4

M4 D2 L3 T1 M4 D2 L3 T5

M5 D2 L4 T6


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.artial FDs and (NF

• .artial FDs5

• A FD, A → B is a partialFD, if some attribute of A can be remoed andthe FD still holds

• Formally, there is someproper subset of A,

C ⊂ A, such that C → B

• Let us call attributes2hich are part of somecandidate 4ey, 4eyattributes, and the restnon;4ey attributes%

Second normal form5

• A relation is in secondnormal form '(NF) if it is

in 1NF and no non;4eyattribute is partiallydependent on acandidate 4ey

• In other 2ords, no C → B

2here is a strict subsetof a candidate 4ey and !is a non;4ey attribute%


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Second Normal Form

• 1NF is not in (NF

• $e hae the FD

6odule, Te/t7 →

6Lecturer, Dept7• !ut also

6odule7 → 6Lecturer, Dept7

• And so Lecturer andDept are partially

dependent on theprimary 4ey

1NF


M1 D1 L1 T1

M1 D1 L1 T2

M2 D1 L1 T1

M2 D1 L1 T3

M3 D1 L2 T4

M4 D2 L3 T1

M4 D2 L3 T5

M5 D2 L4 T6


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+emoin" FDs

• Suppose 2e hae arelation + 2ith scheme Sand the FD A → ! 2here

A ! < 6 7∩• Let < S = 'A # !)

• In other 2ords5

• A = attributes on the lefthand side of the FD

• ! = attributes on theri"ht hand side of the FD

• = all other attributes

• It turns out that 2e cansplit + into t2o parts5

• +1, 2ith scheme # A

• +(, 2ith scheme A # !• The ori"inal relation can

be recoered as thenatural 0oin of +1 and+(5

• + < +1 NAT#+AL 9:IN +(


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1NF to (NF = -/ample1NF


M1 D1 L1 T1

M1 D1 L1 T2

M2 D1 L1 T1 M2 D1 L1 T3

M3 D1 L2 T4

M4 D2 L3 T1

M4 D2 L3 T5

M5 D2 L4 T6

2NFa

Module Dept Lecturer

M1 D1 L1

M2 D1 L1

M3 D1 L2 M4 D2 L3

M5 D2 L4

2NF"

Module Text

M1 T1

M1 T2

M2 T1 M2 T3

M3 T4

M4 T1

M4 T5

M1 T6


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.roblems +esoled in (NF

• .roblems in 1NF

• INS-+T = ant add amodule 2ith no te/ts

• #.DAT- = To chan"electurer for 1, 2ehae to chan"e t2oro2s

• D-L-T- = If 2e

remoe 3, 2eremoe L( as 2ell

• In (NF the first t2oare resoled, but notthe third one

2NFa


M1 D1 L1

M2 D1 L1

M3 D1 L2 M4 D2 L3

M5 D2 L4


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.roblems +emainin" in (NF


• ant add lecturers2ho teach no modules

• #.DAT- anomalies• To chan"e the

department for L1 2emust alter t2o ro2s

• D-L-T- anomalies• If 2e delete 3 2e

delete L( as 2ell

2NFa


M1 D1 L1

M2 D1 L1 M3 D1 L2

M4 D2 L3

M5 D2 L4


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Transitie FDs and 3NF

• Transitie FDs5

• A FD, A → C is atransitie FD, if there

is some set B suchthat A → B and B → C are non;triial FDs

• A → B non;triialmeans5 B is not a

subset of A• $e hae

A → B → C

• Third normal form

• A relation is in thirdnormal form '3NF) if

it is in (NF and nonon;4ey attribute istransitiely dependenton a candidate 4ey


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Third Normal Form

• (NFa is not in 3NF

• $e hae the FDs

6odule7 → 6Lecturer7

6Lecturer7 → 6Dept7

• So there is atransitie FD from theprimary 4ey 6odule7to 6Dept7

2NFa


M1 D1 L1

M2 D1 L1 M3 D1 L2

M4 D2 L3

M5 D2 L4


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(NF to 3NF = -/ample

2NFa


M1 D1 L1 M2 D1 L1

M3 D1 L2

M4 D2 L3

M5 D2 L4

3NFa

Lecturer Dept

L1 D1 L2 D1

L3 D2

L4 D2

3NF"

Module Lecturer

M1 L1 M2 L1

M3 L2

M4 L3

M5 L4


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.roblems +esoled in 3NF

• .roblems in (NF

• INS-+T = ant addlecturers 2ho teach

no modules• #.DAT- = To chan"e

the department for L12e must alter t2oro2s

• D-L-T- = If 2e delete3 2e delete L( as2ell

• In 3NF all of these areresoled 'for this relation =but 3NF can still haeanomalies>)

3NFa

Lecturer Dept

L1 D1

L2 D1 L3 D2

L4 D2

3NF"Module Lecturer

M1 L1

M2 L1

M3 L2

M4 L3 M5 L4


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Normalisation and Desi"n

• Normalisation isrelated to D! desi"n

• A database should

normally be in 3NF atleast

• If your desi"n leads toa non;3NF D!, thenyou mi"ht 2ant to

reise it

• $hen you find youhae a non;3NF D!

• Identify the FDs that

are causin" a problem

• Thin4 if they 2ill leadto any insert, update,or delete anomalies

• Try to remoe them


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Ne/t Lecture

• ore normalisation

• Lossless decomposition? 2hy our reduction

to (NF and 3NF is lossless• !oyce;odd normal form '!NF)

• @i"her normal forms

• Denormalisation

• For more information• onnolly and !e"" chapter 1

• #llman and $idom chapter 3%&

Documents

Normalisation 3NF