unit 6 rdb design

7/25/2019 Unit 6 RDB Design

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Unit VI:Unit VI:

Relational Database DesignRelational Database Design

Pitfalls of Relational Model:

Redundancy and Anomalies Functional Dependency

Normalization its need andob!ecti"es Form

#NF $NF %NF &'NF and (NF


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First Normal Form

R is in frst normal ormi the domainso all attributes o R are atomic

In object relational/object orienteddatabases, attributes can be compositeor multi-valued

But in relational databases, composite

attributes will need to be atten outand multi-valued attributes need to berepresented b another relation


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First Normal FormFirst Normal Form

Domain is atomicif its elements are consideredto be indi"isible units

)*amples of non+atomic domains: ,et of names composite attributes

Identi-cation numbers li.e ',#/# t0at can be

bro.en up into parts

A relational sc0ema R is in -rst normal formift0e domains of all attributes of R are atomic

Non+atomic "alues complicate storage and

encourage redundant 1repeated2 storage of data )*ample: ,et of accounts stored 3it0 eac0

customer and set of o3ners stored 3it0 eac0account

4e assume all relations are in -rst normal


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First Normal Form !"ont#d$

Atomicity is actually a property of 0o3

t0e elements of t0e domain are used5 )*ample: ,trings 3ould normally be

considered indi"isible

,uppose t0at students are gi"en rollnumbers 30ic0 are strings of t0e formCS0012 or EE1127

If t0e -rst t3o c0aracters are e*tracted to

-nd t0e department t0e domain of rollnumbers is not atomic5

Doing so is a bad idea: leads to encodingof information in application program

rat0er t0an in t0e database5


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%italls in Relational &atabase&esi'n

(e can create tables to represent an )Rdesi'n in man di*erent was

"ombine attributes di*erentl to create tables (h do we choose some was over the

others+

Redundanc

Inabilit to represent certain inormation

)' relationships amon' attributes


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)R or Banin' )nterprise


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.chema &ia'ram or the Banin')nterprise


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)ample

"onsider the relation schema0Lending-schema 1 !branch-name, branch-city,assets, customer-name, loan-number, amount)

Redundanc, wh+ Inabilit to represent certain inormation, wh+

"annot store inormation about a branch i no loans eist

"an use null values, but the are di2cult to handle


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(h Redundanc Is Bad+

(astes space

"omplicates updatin', introducin'possibilit o inconsistenc o

assets

value

(e now wh inabilit to representcertain inormation is bad


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&ecomposition

&ecompose the relation schema

Lending-schema into0

Branch-schema = (branch-name, branch-

city,assets)Loan-info-schema = (customer-name,

loan-number, branch-name, amount)


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3ossless-join decomposition

4ll attributes o an ori'inal schema!R) must appear in thedecomposition !R5, R6):

R = R5R6

For all possible relations ron schema

Rr = R5 !r$ R6 !r$


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Non 3ossless-7oin &ecomposition

&ecomposition o R = (A, B) R1= (A) R6= (B)

A B

121

A

B

12

r

A(r) B(r)

A

(r) B

(r) A B

1212

We do not loss any tuple but we lose therelationship between A and B


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60e &an.ing ,c0ema

branch7 1branch_name branch_city assets2

customer7 1customer_id customer_name customer_streetcustomer_city2

loan7 1loan_number amount2

account7 1account_number balance2

employee7 1employee_id5 employee_name telephone_number

start_date2 dependent_name7 1employee_id dname2

account_branch7 1account_number branch_name2

loan_branch7 1loan_number branch_name2

borrower7 1customer_id loan_number2

depositor7 1customer_id account_number2

cust_banker7 1customer_id employee_id type2

works_for7 1worker_employee_id manager_employee_id2

payment7 1loan_numberpayment_numberpayment_datepayment_amount2

savings_account7 1account_number interest_rate2

checking_account7 1account_number overdraft_amount2


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4 "ombined .chema (ithoutRepetition

"onsider combinin' loanbranchand loan

loanamtbr1 !loannumber, amount,branchname$

No repetition !as su''ested b eamplebelow$


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40at About ,maller,c0emas8

,uppose 3e 0ad started 3it0 bor_loan 9o3 3ould 3e .no3 tosplit up 1decompose2 it into borrower and loan8

4rite a rule if t0ere 3ere a sc0ema 1loan_number! amount2 t0enloan_number 3ould be a candidate .ey;

Denote as a functional dependency:

loan_numberamount In bor_loan because loan_numberis not a candidate .ey t0e

amount of a loan may 0a"e to be repeated5 60is indicates t0eneed to decompose bor_loan5

Not all decompositions are good5 ,uppose 3e decomposeemployeeinto

employee17 1employee_id employee_name2employee27 1employee_name telephone_number start_date2

60e ne*t slide s0o3s 0o3 3e lose information ++ 3e cannotreconstruct t0e original employeerelation ++ and so t0is is alossy decomposition5


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4 3oss &ecomposition


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"#! "$! ! "n? suc0 t0at

eac0 relation is in good form

t0e decomposition is a lossless+!oindecomposition

@ur t0eory is based on:

functional dependencies

multi"alued dependencies


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Functional Dependencies

Functional dependencies (FDs) are used tospecifyformal measures of the "goodness"of relational designs

FDs and keys are used to define normalformsfor relations

FDs are constraintsthat are derived fromthe meaning and interrelationships of thedata attributes


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Functional Dependencies (2)

A set of attributes Xfunctionally determines a set of

attributes Y if the value of X determines a uniue value for

Y

XY holds if !henever t!o tuples have the same value for

X they must have the same value for Y

If t#$X%&t'$X% then t#$Y%&t'$Y% in any relation instance r()

XY in specifies a constrainton all relation instancesr()

FDs are derived from the real!orld constraints on the

attributes


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*+amples of FD constraints

,ocial ,ecurity -umber determines employee name

,,-*-A.*

/ro0ect -umber determines pro0ect name andlocation

/-1.B* 2/-A.* /345A674-8

*mployee ,,- and pro0ect number determines thehours per !eek that the employee !orks on the

pro0ect

2,,- /-1.B*8 941,


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Functional Dependencies (3)

An FD is a property of the attributes in the

schema

6he constraint must hold on every relation

instance r()

7f : is a key of then : functionallydetermines all attributes in (since !e never

have t!o distinct tuples !ith t#$:%&t'$:%)


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Inference Rules for FDs

;iven a set of FDs F !e can inferadditional FDsthat hold !henever the FDs in F hold

Armstrong


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Additional 1seful 7nference

ules Decomposition

7f X Y> then X Y and X >

1nion 7f X Y and X > then X Y>

/suedotransitivity

7f X Y and Y> then X >

Closureof a set F of FDs is the set F of all FDs

that can be inferred from F


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Introduction to

Normalization Normalization? /rocess of decomposing

unsatisfactory "bad" relations by breaking up their

attributes into smaller relations Normal form? 5ondition using keys and FDs of a

relation to certify !hether a relation schema is in aparticular normal form '-F @-F B5-F based on keys and FDs of a relation

schema C-F based on keys multivalued dependencies


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First Normal Form

Disallo!s composite attributes multivalued

attributes and nested relations attributes

!hose valuesfor an individual tuple are

nonatomic

5onsidered to be part of the definition of

relation


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Second Normal Form

1ses the concepts of FDs primary key

Definitions? Prime attribute attribute that is member of the

primary key :

Full functional dependency a FD Y>!here removal of any attribute from Y means the

FD does not hold any more


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!amples

Second Normal Form 2,,- /-1.B*8 941, is a full FD since neither

,,-941, nor /-1.B* 941, hold

2,,- /-1.B*8 *-A.* is not a full FD (it iscalled apartial dependency) since ,,- *-A.* alsoholds

A relation schema is in second normal form (2NF) ifevery nonprime attribute A in is fully functionallydependent on the primary key

can be decomposed into '-F relations via the processof '-F normaliEation


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"#ird Normal Form

Definition "ransiti$e functional dependency if there a set of

atribute > that are neither a primary or candidate key andboth X > and Y:holds=

*+amples? ,,- D.;,,- is a transitive FD since

,,- D-1.B* and D-1.B* D.;,,- hold ,,- *-A.* is non-transitive since there is no set of

attributes X !here ,,- X and X *-A.*


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@rd-ormal Form

A relation schema is in t#ird normal form(3NF) if it is in '-F and no nonprime

attribute A in is transitively dependent on

the primary key


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%CNF (%oyce&Codd Normal

Form) A relation schema is in %oyce&Codd Normal

Form (%CNF) if !henever an FD X A holds in

then X is a superkey of *ach normal form is strictly stronger than the previous

one? *very '-F relation is in #-F *very @-F relation is in '-F *very B5-F relation is in @-F

6here e+ist relations that are in @-F but not in B5-F 6he goal is to have each relation in B5-F (or @-F)


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B5-F

2,tudentcourse8 7nstructor

7nstructor

5ourse

Decomposing into ' schemas 2,tudent7nstructor8 2,tudent5ourse8

25ourse7nstructor8 2,tudent5ourse8 25ourse7nstructor8 27nstructor,tudent8

FunctionalFunctional


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FunctionalFunctional

DependenciesDependencies

'onstraints on t0e set of legalrelations5

Reuire t0at t0e "alue for a certainset of attributes determinesuniuely t0e "alue for anot0er set ofattributes5

A functional dependency is ageneralization of t0e notation of akey

i l d i


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Functional &ependencies!"ont$

Bet "be a relation sc0ema " and "

60e functional dependency

0olds on"if and only if for any legal relations r1R2

30ene"er any t3o tuples t#and t$of ragree on t0eattributes t0ey also agree on t0e attributes 60at is

t#C 7 t$ C t#C 7 t$ C

)*ample: 'onsider r1A!# 2 3it0 t0e follo3ing instance of r

@n t0is instance$#does N@6 0old but #$does0old5

1 41 53 7

F i l & d i


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%is a super.ey for relation sc0ema "if andonly if % "

%is a candidate .ey for "if and only if %

" and for no

%! "

Functional dependencies allo3 us to e*pressconstraints t0at cannot be e*pressed usingsuper.eys5 'onsider t0e sc0ema:bor_loan 7 1customer_id! loan_number!amount 2

4e e*pect t0is functional dependency to 0old:loan_numberamountbut 3ould not e*pect t0e follo3ing to 0old:amount customer_name

9 F i l


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9se o Functional&ependencies

4e use functional dependencies to: test relations to see if t0ey are legal under a

gi"en set of functional dependencies5 If a relation ris legal under a set &of functional

dependencies 3e say t0at rsatis-es &

specify constraints on t0e set of legal relations 4e say t0at &0olds on"if all legal relations on "

satisfy t0e set of functional dependencies &

Note: A speci-c instance of a relationsc0ema may satisfy a functional dependencye"en if t0e functional dependency does not0old on all legal instances5 For e*ample a speci-c instance of loanmay by

c0ance satisfyamount customer_name

F ti l & d i


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$ functional dependency istri"ialif it is satis-ed by allinstances of a relation

)*ample' customer_name! loan_number customer_name

customer_name customer_nameIn general is tri"ial if

'losure of a ,et of Functional'losure of a ,et of Functional


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'losure of a ,et of Functional'losure of a ,et of Functional

DependenciesDependencies


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&oyce+'odd Normal Form&oyce+'odd Normal Form

is tri"ial 1i5e5 2

is a super.ey for "

A relation schemaRis in BCNF with respect to a setFof

functional dependencies if for all functional dependenciesinF+of the form

where Rand R,at least one of the following holds:

Example schemanotin BCNF:

bor_loan= (customer_id, loan_number, amount)

becauseloan_number

amount

holds onbor_loan

butloan_number

isnot a superkey

& i . h i t


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&ecomposin' a .chema intoB"NF ,uppose 3e 0a"e a sc0ema " and a

non+tri"ial dependency causes a"iolation of &'NF5

4e decompose "into:

1 U 21 "+ 1 ) 2 2

In our e*ample 7 loan_number

7amountand bor_loanis replaced by

1 U 2 7 1 loan_number! amount2 1 "+ 1 ) 2 2 7 1 customer_id! loan_number2

d d&'NF d D d


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&'NF and Dependency&'NF and Dependency

Preser"ationPreser"ation 'onstraints including functional

dependencies are costly to c0ec. in practiceunless t0ey pertain to only one relation

If it is sucient to test only t0ose

dependencies on eac0 indi"idual relation of adecomposition in order to ensure t0at allfunctional dependencies 0old t0en t0atdecomposition is dependency preserving

&ecause it is not al3ays possible to ac0ie"ebot0 &'NF and dependency preser"ation 3econsider a 3ea.er normal form .no3n asthird normal form


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;hird Normal Form A relation sc0ema "is in t0ird normal form

1%NF2 if for all:

in &E

at least one of t0e follo3ing 0olds:

is tri"ial 1i5e5 2

is a super.ey for "

)ac0 attribute$in G is contained in a candidate.ey for "

1N@6)' eac0 attribute may be in a diHerent candidate.ey2

If a relation is in &'NF it is in %NF 1since in &'NFone of t0e -rst t3o conditions abo"e must 0old25

60ird condition is a minimal rela*ation of &'NFto ensure dependency preser"ation 5


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NormalizationNormalization

Bet "be a relation sc0eme 3it0 a set&offunctional dependencies5

Decide 30et0er a relation sc0eme "is ingood; form5

In t0e case t0at a relation sc0eme "is notin good; form decompose it into a set ofrelation sc0eme >"#! "$! ! "n? suc0 t0at

eac0 relation sc0eme is in good form

t0e decomposition is a lossless+!oindecomposition

Preferably t0e decomposition s0ould bedependency preser"ing5


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Functional-&ependenc;heor

4e no3 consider t0e formal t0eoryt0at tells us 30ic0 functionaldependencies are implied logically by a

gi"en set of functional dependencies5 4e t0en de"elop algorit0ms to

generate lossless decompositions into&'NF and %NF

4e t0en de"elop algorit0ms to test if adecomposition is dependency+preser"ing

"losure o a .et o Functional


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"losure o a .et o Functional&ependencies

=iven a set !set o unctional dependencies, there arecertain other unctional dependencies that are lo'icallimplied b ! For eample0 I ABand B", then we can iner thatA"

;he set o allunctional dependencies lo'icall implied b!is the closureo !

(e denote the closure o !b !#$ (e can fnd all oF#b applin' 4rmstron'#s 4ioms0

i , then 1reJe*i"ity2

i , then 1augmentation2 i , and , then 1transiti"ity2

;hese rules are sound!'enerate onl unctional dependencies that actuall

hold$ and

complete!'enerate all unctional dependencies that hold$


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)ample R = (A, B, ", %, &, ')

! = > A B A ""% &"% ' B &?

some members o !@A &

b transitivit romA B and B &

A% ' b au'mentin'A " with =, to 'etA% "%

and then transitivit with "% '

"% &' b au'mentin' "% ' to iner "% "=',

and au'mentin' o "% & to iner"%' &',

and then transitivit


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%rocedure or "omputin' F@

6o compute t0e closure of a set of functionaldependencies F:

& E7 &repeat

for eac0 functional dependency fin &E apply reJe*i"ity and augmentation rules on f add t0e resulting functional dependencies to& Efor eac0 pair of functional dependencies f#and f$in & E

if f#and f$can be combined using transiti"ityt0en add t0e resulting functional dependency to& Euntil & Edoes not c0ange any furt0er

"losure o Functional


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"losure o Functional&ependencies !"ont$

4e can furt0er simplify manualcomputation of &Eby using t0efollo3ing additional rules5 If 0oldsand 0olds t0en

0olds 1union2

If

0olds t0en

0olds and

0olds 1decomposition2

If 0oldsand 0olds t0en

0olds 1pseudotransiti"ity2

60e abo"e rules can be inferred fromArmstrongs a*ioms5

'los re of Attrib te ,ets'losure of Attribute ,ets


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'losure of Attribute ,ets'losure of Attribute ,ets =iven a set o attributes ,defne the closureo

under!!denoted b @$ as the set oattributes that are unctionall determined b under !

4l'orithm to compute @, the closure o under!

result 01 A

30ile!chan'es to result$ dofor eac0 in!dobeginif resultt0en result 01 result

end

)ample o 4ttribute .et


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)ample o 4ttribute .et"losure

" * +$! #! C! ,! -! ./ & * >$ #$ C

C, -C, .# -?

1$,/E

#5result * $,$5result * $#C, +$ C and$ #/%5result * $#C,- +C, -and C,

$,#C/(5result * $#C,-. +C, .and C,

$,#C-/

Is$,a candidate .ey8#5Is A< a super .ey8

#5Does$, " ** Is 1A


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9ses o 4ttribute "losure

60ere are se"eral uses of t0e attribute closurealgorit0m:

6esting for super.ey: 6o test if is a super.ey 3e compute Eand

c0ec. if Econtains all attributes of "5

6esting functional dependencies 6o c0ec. if a functional dependency 0olds

1or in ot0er 3ords is in &E2 !ust c0ec. if E5

60at is 3e compute Eby using attribute closureand t0en c0ec. if it contains 5

Is a simple and c0eap test and "ery useful

'omputing closure of F For eac0 "! 3e -nd t0e closure E and for eac0

SE 3e output a functional dependency S


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"anonical "over

,ets of functional dependencies may 0a"eredundant dependencies t0at can be inferred fromt0e ot0ers For e*ample: $ Cis redundant in: >$# #C?

Parts of a functional dependency may be redundant

)5g5: on R9,: >$# #C $C? can be simpli-ed to>$

# #

C $

?

)5g5: on B9,: >A

# #

C $C

? can be simpli-ed to>A

# #

C $

?

Intuiti"ely a canonical co"er of F is a minimal; setof functional dependencies eui"alent to F 0a"ing

no redundant dependencies or redundant parts ofdependencies

)traneous 4ttributes


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)traneous 4ttributes

'onsider a set &of functional dependencies andt0e functional dependency in &5 Attribute A is e*traneous in if$

and &logically implies 1&G > ?2 >1 G$2 ?5 Attribute$is e*traneousin if$

and t0e set of functional dependencies1& G > ?2 > + G$2? logically implies &

ote' implication in t0e opposite direction is tri"ialin eac0 of t0e cases abo"e since a stronger;functional dependency al3ays implies a 3ea.erone

)*ample: $C$#C3 Cis e*traneous in$#Csince $& Ccan be

inferred e"en after deleting C

)


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)traneous 'onsider a set &of functional dependencies

and t0e functional dependency in &5 6o test if attribute A

is e*traneousin

#5compute 1>? G A2Eusing t0e dependencies in &

$5 c0ec. t0at 1>

? G A2Econtains K if it does$is

e*traneous in

6o test if attribute$ is e*traneous in

#5compute E using only t0e dependencies inF 7 1& G > ?2 > + G$2?

$5 c0ec. t0at E contains$4 if it does! $ ise*traneous in

"anonical "over


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"anonical "over

A canonical coverfor &is a set of dependencies &c suc0t0at &logically implies all dependencies in &c!and &clogically implies all dependencies in &!and No functional dependency in &ccontains an e*traneous

attribute and )ac0 left side of functional dependency in &cis uniue5

6o compute a canonical co"er for &:repeat

Use t0e union rule to replace any dependencies in & # #and # $3it0 # # $Find a functional dependency 3it0 ane*traneous attribute eit0er in or inIf an e*traneous attribute is found delete it from

until &does not c0ange Note: Union rule may become applicable after some

e*traneous attributes 0a"e been deleted so it 0as tobe re+applied

"omputin' a "anonical "over


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"omputin' a "anonical "over " 7 1$! #! C/

& * 5$ #C # C $ #$#C?

'ombine$ #C and$ # into$ #C

,et is no3 5$ #C! # C! $#C?

$is e*traneous in$#C

'0ec. if t0e result of deleting A from $#C is implied byt0e ot0er dependencies

Les: in fact #C is already present

,et is no3 5$ #C! # C?

Cis e*traneous in$#C

'0ec. if$ Cis logically implied by$ # and t0e ot0erdependencies

Les' using transiti"ity on$ # and # '5

'an use attribute closure of$in more comple* cases

60e canonical co"er is: $ #

# C

3ossless join &ecomposition


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3ossless-join &ecomposition

For t0e case of"7 1"#! "$2!3e

reuire t0at for all possiblerelations ron sc0ema "

r * "11r 2 "21r 2 A decomposition of "into "#and "$

is lossless !oin if and only if at least

one of t0e follo3ing dependenciesis in &E:

"#"$"#

"#"$"$


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)ample R = (A, B, ")

! = A B, B ") "an be decomposed in two di*erent was

R5= (A, B), R6= (B, ") 3ossless-join decomposition0

R5R

6= >B?and B B"

&ependenc preservin'

R1 = (A, B), R6= (A, ") 3ossless-join decomposition0

R5 R6=>A?andA 4B Not dependenc preservin'

!cannot chec B " without computin' R1R6$

&ependenc %reservation


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p

3et !ibe the set o dependencies

! #that include onl attributes inRi$

4 decomposition is dependenc

preservin', i !!5!6!n $@1 ! #

I it is not, then checin' updates orviolation o unctional dependencies

ma reuire computin' joins, which isepensive

% ti


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%reservation

;o chec i a dependenc is preserved in a

decomposition o Rinto R5, R6, C, Rnwe appl theollowin' test !with attribute closure done withrespect to !$ result 1

30ile!chan'es to result$ dofor eac0Riin the decomposition

t1 !result Ri$@Riresult = result t

I resultcontains all attributes in , then the unctionaldependencis preserved

(e appl the test on all dependencies in ! tochec i a decomposition is dependenc preservin'

;his procedure taes polnomial time, instead othe eponential time reuired to compute !#and!!5!6 !n$@


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)ample R = !A, B, " $

! = >ABB "?

De 1 >A?

Ris not in B"NF &ecomposition R51 !A, B), R61 (B, ")

R5and R6in B"NF

3ossless-join decomposition

&ependenc preservin'


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;estin' or B"NF ;o chec i a non-trivial dependenc causes a

violation o B"NF5 compute @!the attribute closure o $, and6 veri that it includes all attributes o R, that is, it is a

supere o R .implifed test0 ;o chec i a relation schema Ris in

B"NF, it su2ces to chec onl the dependencies in

the 'iven set !or violation o B"NF, rather thanchecin' all dependencies in !@ I none o the dependencies in !causes a violation o

B"NF, then none o the dependencies in !@will cause aviolation o B"NF either

A B, B" *?

&ecompose Rinto R5 1!A,B$ and R6 1!A,",*, +$ Neither o the dependencies in !contain onl attributes rom

!A,",*,+$ so we mi'ht be mislead into thinin' R6satisfesB"NF

In act, dependencA"*in !@shows R6is not in B"NF

;estin' &ecomposition or


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;estin' &ecomposition orB"NF

6o c0ec. if a relation "iin adecomposition of "is in &'NF )it0er test Ri for &'NF 3it0 respect to t0e

restrictionof F to Ri 1t0at is all FDs in FEt0at contain only attributes from Ri2

or use t0e original set of dependencies &t0at 0old on " but 3it0 t0e follo3ing test:

for e"ery set of attributes "i c0ec. t0at E1t0eattribute closure of 2 eit0er includes no attribute of"i+ or includes all attributes of "i5

If t0e condition is "iolated by some in &t0e dependency 1E + 2 "ican be s0o3n to 0old on "i and "i"iolates &'NF5

4e use abo"e dependency to decompose "i

B"NF &ecomposition


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B"NF &ecomposition4l'orithm

result 01 >R ?Adone 01 alseAcompute ! @A30ile 1not done) doif !there is a schema Riin result that is not in B"NF$

t0en beginlet be a nontrivial unctional dependenc thatholds on Ri such that Riis not in ! @,

and = A

result 01 !result Ri) !Ri $ !, ) endelsedone 01 trueK

Note0 each Riis in B"NF, and decomposition is lossless-

join

)ample o B"NF


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)ample o B"NF&ecomposition

" * 1$! #! C 2& * >$#

# C?

ey 7 >$? "is not in &'NF 1# C but

# is not super.ey2

Decomposition "#7 1#! C/

"$7 +$!#/

)ample o B"NF


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)ample o B"NF&ecomposition

@riginal relation" andfunctional dependency& " 71branch_name! branch_city! assets!

customer_name! loan_number! amount 2 & 7>branch_name assets branch_city

loan_number amount branch_name ?ey 75loan_number! customer_name?

Decomposition "#7 1branch_name! branch_city! assets 2 "$7 1branch_name! customer_name! loan_number!

amount 2 "%7 1branch_name! loan_number! amount 2 "(7 1customer_name! loan_number 2

Final decomposition"#! "%! "(

%reservation


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%reservation

R = !., /, L $! = >./ L

L / ?

;wo candidate es 1./ and.L R is not in B"NF 4n decomposition o Rwill ail

to preserve

./ L ;his implies that testin' or./L reuires a join

It is not always possible to get a BCNF decomposition that is

dependency preserving

;hird Normal Form0


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;hird Normal Form0Eotivation

;here are some situations where B"NF is not dependenc preservin', and e2cient checin' or F& violation on updates

is important

.olution0 defne a weaer normal orm,called ;hird Normal Form !NF$ 4llows some redundanc !with resultant

problemsA we will see eamples later$

But unctional dependencies can be checedon individual relations without computin' ajoin

;here is alwas a lossless-join, dependenc-preservin' decomposition into NF

l


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NF )ample

Relation R:

" * 16! %! 2& * >6% ! % ?

63o candidate .eys: 6% and6

"is in %NF

6% 6% is a super.ey

% % is contained in acandidate .ey

Redundanc in NF


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;here is some redundanc in thisschema

)ample o problems due toredundanc in NF

R = !., /, L)! = >./ L, L / ?

J

j1

j2

j3

null

Ll1

l1

l1

l2

Kk1

k1

k1

k2

repetition of information (e.g., the relationshipl1,k1)

need to use null values (e.g., to represent the relationship l2,k2where there is no corresponding value forJ).

; i NF


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;estin' or NF

GptimiHation0 Need to chec onl F&s in !,need not chec all F&s in !#

9se attribute closure to chec or eachdependenc , i is a supere

I is not a supere, we have to veri ieach attribute in is contained in acandidate e o R this test is rather more epensive, since it involve

fndin' candidate es

testin' or NF has been shown to be N%-hard Interestin'l, decomposition into third normal

orm !described shortl$ can be done inpolnomial time

%NF Decomposition%NF Decomposition


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ppAlgorit0mAlgorit0m

3et !cbe a canonical cover or !i 01 8Afor eac0 unctional dependenc in !cdoif none o the schemas R0, 5 0 i contains t0en begini 01 i # 5ARi 01 endifnone o the schemas R0, 5 0 i contains a candidatee or Rt0en begini 01i @ 5ARi01 an candidate e or Rendreturn (R5, R6, , Ri)

!"ont $


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!"ont$

4bove al'orithm ensures0

each relation schema Riis in NF

decomposition is dependencpreservin' and lossless-join

%roo o correctness is at end o thispresentation !clic here$

NF &ecomposition0 4n


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NF &ecomposition0 4n)ample

Relation schema0

custbanerbranch = !customerid, em2loyeeid,branchname, ty2e $

;he unctional dependencies or this relationschema are01$ customerid, em2loyeeid branchname, ty2e

3$ em2loyeeid branchname4$ customerid, branchname em2loyeeid

(e frst compute a canonical cover branchname is etraneous in the rhs o the 5st

dependenc

No other attribute is etraneous, so we 'et F" 1 customerid, em2loyeeid ty2e

em2loyeeid branchname customerid, branchname em2loyeeid


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;he forloop 'enerates ollowin' NF schema0

!customerid, em2loyeeid, ty2e $ !em2loyeeid, branchname$ !customerid, branchname, em2loyeeid)

Gbserve that !customerid, em2loyeeid, ty2e $ contains a candidatee o the ori'inal schema, so no urther relation schema needs beadded

I the F&s were considered in a di*erent order, with the 6ndoneconsidered ater the rd,

!em2loyeeid, branchname$would not be included in the decomposition because it is a subset o

!customerid, branchname, em2loyeeid)

Einor etension o the NF decomposition al'orithm0 at end o or loop,detect and delete schemas, such as !em2loyeeid, branchname$, which

are subsets o other schemas result will not depend on the order in which F&s are considered

;he resultant simplifed NF schema is0

!customerid, em2loyeeid, ty2e$ !customerid, branchname, em2loyeeid)

"omparison o B"NF and


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"omparison o B"NF andNF

It is alwas possible to decompose a relationinto a set o relations that are in NF suchthat0

the decomposition is lossless

the dependencies are preserved

It is alwas possible to decompose a relationinto a set o relations that are in B"NF such

that0 the decomposition is lossless

it ma not be possible to preserve dependencies

&esi'n =oals


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&esi'n =oals


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Eultivalued &ependencies!E&s$

3et Rbe a relation schema and let RandR$ ;he multi5alued de2endency

holds on Ri in an le'al relation r(R),or allpairs or tuples t5 and t3in rsuch that t5JK 1t3 JK, there eist tuples t4and tLin r suchthat0t5JK 1 t3 JK 1 tJK 1 tLJK

tJK 1 t5 JKtJR K 1 t6JR KtL JK 1 t6JKtLJR K 1 t5JR K

E& !" t $


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E& !"ont$ ;abular representation o

) l


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)ample

3et Rbe a relation schema with a set oattributes that are partitioned into nonemptsubsets

6, 7, 8

(e sa that 6 7 !6multidetermines7 $i and onl i or all possible relations r !R $My5,95, w5 rand My5,96, w6 r

thenMy5,95, w6 rand My5,96, w5 r

Note that since the behavior o7and 8areidentical it ollows that6 7 i 68

) ample !"ont $


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)ample !"ont$ In our eample0

course teachercourse boo

;he above ormal defnition is supposed toormaliHe the notion that 'iven a

particular value o 6 !course$ it hasassociated with it a set o values o7(teacher) and a set o values o 8 (boo),and these two sets are in some senseindependent o each other

Note0 I 6 7 then 6 7 Indeed we have !in above notation$75= 76;he claim ollows

9se o Eultivalued


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&ependencies (e use multivalued dependencies in two was0

5 ;o test relations to determinewhether the are le'alunder a 'iven set o unctional and multivalueddependencies

6 ;o speci constraintson the set o le'al relations (eshall thus concern ourselves onlywith relations thatsatis a 'iven set o unctional and multivalueddependencies

I a relationrails to satis a 'iven multivalued

dependenc, we can construct a relations r thatdoes satis the multivalued dependenc baddin' tuples to r$

;heor o E&s


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;heor o E&s

From the defnition o multivalued dependenc, wecan derive the ollowin' rule0 I , then

;hat is, ever unctional dependenc is also amultivalued dependenc

;he closure&@o *is the set o all unctional andmultivalued dependencies lo'icall implied b * (e can compute &@rom *, usin' the ormal defnitions

o unctional dependencies and multivalueddependencies

(e can mana'e with such reasonin' or ver simple

multivalued dependencies, which seem to be mostcommon in practice

For comple dependencies, it is better to reason aboutsets o dependencies usin' a sstem o inerence rules

Fourth Normal Form


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Fourth Normal Form 4 relation schema Ris in LNF with

respect to a set *o unctional andmultivalued dependencies i or allmultivalued dependencies in *@o the

orm , where Rand R, atleast one o the ollowin' hold0

is trivial !ie, or = R)

is a supere or schema R I a relation is in LNF it is in B"NF

Restriction o Eultivalued


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&ependencies

60e restriction of D to Riis t0eset Diconsisting of All functional dependencies in DE

t0at include only attributes of Ri

All multi"alued dependencies of t0e

form + Ri2

30ere Ri and is in DE

LNF &ecomposition


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p4l'orithm result:1 >R?A

done01 alseAcom2ute *@A3et &idenote the restriction o &@to Ri

30ile !not done$if !there is a schema Riin result that is not in LNF$

t0en

beginlet be a nontrivial multivalued dependencthat holds on Risuch that Ri is not in *i, and =A

result 01 !result - Ri$ !Ri- $ !, $Aend

else done01 trueANote0 each Riis in LNF, and decomposition is lossless-

join

)ample


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)ample R1!A, B, ", %, &, '$

! 1>A BB&'"% &?

Ris not in LNF sinceABandAis not a supereor R

&ecompositiona$ R11 !A, B$ !R1is in LNF$

b$ R61 !A, ", %, &, '$ !R3is not in LNF$

c$ RF1 !", %, &$ !RFis in LNF$

d$ R:1 !A, ", %, '$ !R:is not in LNF$ .inceABand B&',A&',A'

e$ R;1 !A, '$ !R;is in LNF$

$R


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Further Normal Forms oin dependencies'eneraliHe multivalued

dependencies lead to pro!ect+!oin normal form 1%7NF$ !alsocalled -ft0 normal form$

4 class o even more 'eneral constraints, leadsto a normal orm called domain+.ey normalform

%roblem with these 'eneraliHed constraints0 arehard to reason with, and no set o sound andcomplete set o inerence rules eists


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'%rocess

(e have assumed schema Ris 'iven Rcould have been 'enerated when convertin'

)-R dia'ram to a set o tables

Rcould have been a sin'le relation containin'allattributes that are o interest !called

uni"ersal relation$ NormaliHation breas Rinto smaller relations

Rcould have been the result o some ad hocdesi'n o relations, which we then test/convertto normal orm

)R Eodel and NormaliHation


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)R Eodel and NormaliHation

(hen an )-R dia'ram is careull desi'ned,identiin' all entities correctl, the tables 'eneratedrom the )-R dia'ram should not need urthernormaliHation


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PerformancePerformance May 3ant to use non+normalized sc0ema for performance

For e*ample displaying customer_namealong 3it0account_numberand balancereuires !oin of account3it0 depositor

Alternati"e #: Use denormalized relation containingattributes of accountas 3ell as depositor3it0 all abo"eattributes

faster loo.up

e*tra space and e*tra e*ecution time for updates

e*tra coding 3or. for programmer and possibility oferror in e*tra code

Alternati"e $: use a materialized "ie3 de-ned as account depositor

&ene-ts and dra3bac.s same as abo"e e*cept noe*tra coding 3or. for programmer and a"oids possibleerrors

Gther &esi'n Issues


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Gther &esi'n Issues

.ome aspects o database desi'n are not cau'ht bnormaliHation

)amples o bad database desi'n, to be avoided0Instead o earnings !com2anyid, year, amount $, use earnings3, earnings3;, earnings3


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Eodelin' ;emporal &ata

>em2oral datahave an association time interval durin' whichthe data are 5alid$ 4 sna2shotis the value o the data at a particular point in

time .everal proposals to etend )R model b addin' valid time to

attributes, e' address o a customer at di*erent points in time entities, e' time duration when an account eists relationships, e' time durin' which a customer owned an

account But no accepted standard 4ddin' a temporal component results in unctional

dependencies liecustomerid customerstreet, customercity

not to hold, because the address varies over time 4 tem2oral functional de2endency P Q holds on schema R

i the unctional dependenc P Q holds on all snapshots orall le'al instances r !R $

Eodelin' ;emporal &ata


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!"ont$ In practice, database desi'ners ma add

start and end time attributes to relations

)' course!courseid, coursetitle$

course!courseid, coursetitle, start, end$

"onstraint0 no two tuples can have overlappin' validtimes

unit 6 rdb design

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