DB - ER - 180301b · 2018. 3. 3. · 82453 Green Sally 391-1689 AL TRE141 14987 10/05/10 3 $100...

367

L14:Normalization

CS3200 Databasedesign(sp18 s2)https://course.ccs.neu.edu/cs3200sp18s2/3/1/2018

368

Announcements!

• KeepbringingyournameplatesJ• Outlinetoday- MoreNormalization- Project1discussion&TransactionsafterSpringBreak

369

Closures, Superkeys,and (Candidate) Keys

370

Whatwewillseenext

• ClosuresPart2

• Superkeys &Keys

• Practice:Thekeyorakey?

371

WhyDoWeNeedtheClosure?

• WithclosurewecanfindallFD’seasily

• TocheckifX® A

- ComputeX+

- CheckifAÎ X+

NoteherethatX isaset ofattributes,butA isasingleattribute.WhydoesconsideringFDsofthisformsuffice?

RecalltheSplit/combine rule:Xà A1,…,Xà AnimpliesXà {A1,…,An}

372

UsingClosuretoInferALLFDs

{A,B} à C{A,D} à B{B} à D

Example:GivenF=Step1:ComputeX+,foreverysetofattributesX:

{A}+ = {A}{B}+ = {B,D}{C}+ = {C}{D}+ = {D}{A,B}+ = {A,B,C,D}{A,C}+ = {A,C}{A,D}+ = {A,B,C,D}{A,B,C}+ = {A,B,D}+ = {A,C,D}+ = {A,B,C,D} {B,C,D}+ = {B,C,D}{A,B,C,D}+ = {A,B,C,D}

Noneedtocomputeallofthese- why?

373



Example:GivenF=Step1:ComputeX+,foreverysetofattributesX:

{A}+ = {A}, {B}+ = {B,D}, {C}+ = {C}, {D}+ = {D}, {A,B}+ = {A,B,C,D}, {A,C}+ = {A,C}, {A,D}+ = {A,B,C,D}, {A,B,C}+ = {A,B,D}+ = {A,C,D}+ = {A,B,C,D}, {B,C,D}+ = {B,C,D}, {A,B,C,D}+ = {A,B,C,D}

Step2:EnumerateallFDsXà Y,s.t. YÍ X+ andXÇ Y=Æ:

{A,B} à {C,D}, {A,D} à {B,C},{A,B,C} à {D}, {A,B,D} à {C},{A,C,D} à {B}

374



Example:GivenF=




“YisintheclosureofX”

Step1:ComputeX+,foreverysetofattributesX:

375



Example:GivenF=




TheFDXà Yisnon-trivial

Step1:ComputeX+,foreverysetofattributesX:

376

KeysandSuperkeys

Asuperkey isasetofattributesA1,…,An s.t.foranyother attributeB inR,wehave {A1,…,An}à B

Akey isaminimal superkey(alsocalled"candidatekey")

I.e.allattributesarefunctionallydeterminedbyasuperkey

Thismeansthatnosubsetofakeyisalsoasuperkey (i.e.,droppinganyattributefromthekeymakesitnolongerasuperkey)

377

FindingKeysandSuperkeys

• ForeachsetofattributesX

- ComputeX+

- IfX+ =setofallattributesthenXisasuperkey

- IfXisminimal,thenitisakey

378

ExampleofFindingKeys

Product(name, price, category, color)

{name, category} à price{category} à color

Whatisakey?

379

ExampleofFindingKeys

Product(name, price, category, color)

{name, category} à price{category} à color

{name, category}+ = {name, price, category, color}= thesetofallattributes⟹ thisisasuperkey⟹ thisisakey,sinceneithername norcategoryaloneisasuperkey

380

Practice

• Activity-21.ipynb

381

CompleteNormalization Practice!

382

ParkingTickets:OriginalList

383


ST ID L Name F Name Phone No St Lic Lic No Ticket # Date Code Fine

38249 Brown Thomas 111-7804 FL BRY 123 15634 10/17/10 2 $25


82453 Green Sally 391-1689 AL TRE 141 14987 10/05/10 3 $100


82453 Green Sally 391-1689 AL TRE-141 17892 12/13/10 2 $25

384


ST ID L Name F Name Phone No St Lic Lic No Ticket # Date Code Fine






385

ParkingTickets:Relationin1NF

STID LName FName PhoneNo StLic LicNo Ticketnr Date Code Fine






ParkingTickets

386

ParkingTickets:Relationin1NF







ParkingTickets

387

ParkingTickets:Dependencydiagram








Assume,eachstudentcanhavemaximalonecar:

ParkingTickets

388










ParkingTickets

389









Nextassume,studentscanhavemorethanonecar:


ParkingTickets

390











ParkingTickets

391

ParkingTickets:Relationsin3NF



392




STID LName FName PhoneNo StLic LicNo

Code Fine

Ticketnr Date Code@ STID@

Student

TicketCode

Ticket

393




394




STID LName FName PhoneNo

Code Fine

Ticketnr Date Code@ StLic@ LicNo@

Student

TicketCode

Ticket

StLic LicNo STID@Car

395

ParkingTickets:AddingViolationAssume,eachstudentcanhavemaximalonecar:


Code Fine


Student

TicketCode

Ticket

396

ParkingTickets:AddingViolationAssume,eachstudentcanhavemaximalonecar:


Code Fine


Student

TicketCode

Ticket

Violation

397

ParkingTickets:ERDiagram


Code Fine


Student

TicketCode

Ticket

Violation

ERdiagramsdonotshowforeignkeys!

398

CompleteNormalization Practice!

399

Example:DreamHomeRental

Source:Connolly,Begg:Databasesystems,4thed,p.423,2005.

MembersofDreamHomeinspectproperties• Whenstaffarerequiredtoundertaketheseinspections,theyareallocateda

companycarforuseonthedayoftheinspections.(Onecarperperson&day)• However,acarmaybeallocatedtoseveralmembersofstaffasrequired

throughouttheworkingday.• Amemberofstaffmayinspectseveralpropertiesonagivendate,buta

propertyisonlyinspectedonceonagivendate.

StaffPropertyInspectionpropertyNo pAddress iDate iTime comments staffNo sName carReg

PG4 6LawrenceSt,Glasgow

18-Oct-03 10:00 needtoreplacecrockery

SG37 AnnBeech M231JGR

22-Apr-04 09:00 ingoodorder SG14 DavidFord M533HDR

1-Oct-04 12:00 damprotinbathroom

SG14 DavidFord N721HFR

PG16 5NovarDr,Glasgow

22-Apr-04 13:00 replacelivingroomcarpet

SG14 DavidFord M533HDR

24-Oct-04 14:00 goodcondition SG37 AnnBeech N721HFR

Canadatabasestorethisinformation?Isitin1NF?

400







StaffPropertyInspectionpropertyNo iDate iTime pAddress comments staffNo sName carReg

PG4 18-Oct-03 10:00 6LawrenceSt,Glasgow

needtoreplacecrockery


PG4 22-Apr-04 09:00 6LawrenceSt,Glasgow

ingoodorder SG14 DavidFord M533HDR


damprotinbathroom


PG16 22-Apr-04 13:00 5NovarDr,Glasgow replacelivingroomcarpet


PG16 24-Oct-04 14:00 5NovarDr,Glasgow goodcondition SG37 AnnBeech N721HFR

No!Onlynowadatabasecanstoretheinformation:1NFButwestillneedaprimarykey

401







StaffPropertyInspectionpropertyNo iDate iTime pAddress comments staffNo sName carReg


needtoreplacecrockery


PG4 22-Apr-04 09:00 6LawrenceSt,Glasgow

ingoodorder SG14 DavidFord M533HDR


damprotinbathroom


PG16 22-Apr-04 13:00 5NovarDr,Glasgow replacelivingroomcarpet


PG16 24-Oct-04 14:00 5NovarDr,Glasgow goodcondition SG37 AnnBeech N721HFR

Now1NF+PK

402



propertyNo iDate iTime pAddress comments staffNo sName carReg





StaffPropertyInspection

DrawallFDs

403




(full,PK)






404




(partial)

(full,PK)

(transitive)






405




(partial)

(full,PK)

(transitive)






(other)

406




(partial)

(full,PK)

(transitive)

(CandidateK)

(CandidateK)






(other)

407



propertyNo pAddress

(PK,nowfull,formerpartial)

staffNo sName

propertyNo@

iDate iTime comments staffNo@ carReg

(PK,nowfull,formertransitive)

Property

Staff

Inspection

(other)

(PK)

408



propertyNo pAddressProperty

propertyNo@

iDate@ iTime comments staffNo@Inspection

iDate staffNo@ carRegStaffCar

staffNo sNameStaff

(PK)

Wealsoneedtokeeptrackofthefactthat"staffno@"wasalreadyaforeignkeybeforeweputitintoanothertable

Extraquestion:WenowhaveacompositeFK(idate,staffno)fromINSPECTIONtoSTAFFCAR.Thus(idate,staffno)isacompositePKinSTAFFCAR.Assumeweliketoreplaceitwithasurrogatekey.Howwouldtheresultingcompletelynormalizedtableslooklike?

409

scid iDate staffNo@ carReg



propertyNo pAddressProperty

propertyNo@

scid@ iTime commentsInspection

StaffCar

staffNo sNameStaff

(PK)

Thisisnowfullynormalized.Downside:weneedtojoinINSPECTIONwithSTAFFCAReverytimeweliketofindoutaboutwhenaproperty(by"properyNo")waslastinspected

410

Boyce-Codd Normal Form

411

QuickrecapFDs• FunctionalDependency:Thevalueofonesetofattributes(thedeterminant)

uniquelydeterminesthevalueofanothersetofattributes(thedependents)• Asuperkey isasasetofattributesofarelationschemauponwhichallattributes

oftheschemaarefunctionallydependent.• Acandidatekey(CK) isanattributeornon-redundantcombinationofattributes

thatuniquelyidentifiesarowinarelation• 2NF:noPartialFD:AFDinwhichoneormorenonkeyattributesarefunctionally

dependentonpart(butnotall)ofthePK• 3NF:noTransitivedependency:AnFDbetweentwo(ormore)nonkeyattributes

412

Boyce-CoddNormalForm(BCNF)

• Boyce-Coddnormalform(BCNF)- ArelationisinBCNF,ifandonlyif,everydeterminantisacandidatekey.

• Thedifferencebetween3NFandBCNFisthatforafunctionaldependencyAàB,- 3NFallowsthisdependencyinarelationifBisaprimary-keyattribute andAisnotacandidatekey,

- whereasBCNFinsiststhatforthisdependencytoremaininarelation,Amustbeacandidatekey.

413

3NFtoBCNF

Source:Hoffer,Ramesh,Topi,Moderndatabasemanagement,10th ed,AppendixB,2010.

414

3NFtoBCNF

415

3NFtoBCNF

Source:Hoffer,Ramesh,Topi,Moderndatabasemanagement,10th ed,AppendixB,2010.

416

BCNFvs3NF• BCNF:ForeveryfunctionaldependencyX->YinasetF offunctionaldependenciesoverrelationR,either:- XisasuperkeyofR- (orYisasubsetofX)

• 3NF:ForeveryfunctionaldependencyX->YinasetFoffunctionaldependenciesoverrelationR,either:- XisasuperkeyofR,or- YisasubsetofKforsomekeyKofR

• N.b., nosubsetofakeyisakey- (orYisasubsetofX)

417

BacktoConceptualDesign

• NowthatweknowhowtofindFDs,it’sastraight-forwardprocess:

- Searchfor“bad”FDs

- Ifthereareany,thenkeepdecomposingthetableintosub-tablesuntilnomorebadFDs

- Whendone,thedatabaseschemaisnormalized

Recall:thereareseveralnormalforms…

418


• Mainideaisthatwedefine“good”and“bad”FDsasfollows:

- Xà Aisa“goodFD”ifXisa(super)key• Inotherwords,ifAisthesetofallattributes

- Xà Aisa“badFD”otherwise

• Wewilltrytoeliminatethe“bad”FDs!

419


• Whydoesthisdefinitionof“good”and“bad”FDsmakesense?

• IfXisnota(super)key,itfunctionallydeterminessomeoftheattributes;therefore,thoseotherattributescanbeduplicated

- Recall:thismeansthereisredundancy- Andredundancylikethiscanleadtodataanomalies!

EmpID Name Phone Position

E0045 Smith 1234 Clerk

E3542 Mike 9876 Salesrep

E1111 Smith 9876 Salesrep

E9999 Mary 1234 Lawyer

420

Boyce-CoddNormalForm

BCNFisasimpleconditionforremovinganomaliesfromrelations:

Inotherwords:thereareno“bad”FDs

ArelationRisinBCNF if:

if{A1,...,An}à B isanon-trivial FDinR

then{A1,...,An}isasuperkey forR

Equivalently: ∀ setsofattributesX,either(X+ =X)or(X+ =allattributes)

421

Example

Whatisthekey?{SSN,PhoneNumber}

Name SSN PhoneNumber CityFred 123-45-6789 206-555-1234 SeattleFred 123-45-6789 206-555-6543 SeattleJoe 987-65-4321 908-555-2121 WestfieldJoe 987-65-4321 908-555-1234 Westfield

{SSN} à {Name,City}

⟹Not inBCNF

ThisFDisbadbecauseitisnot asuperkey

422

Example

Name SSN CityFred 123-45-6789 SeattleJoe 987-65-4321 Madison

SSN PhoneNumber123-45-6789 206-555-1234123-45-6789 206-555-6543987-65-4321 908-555-2121987-65-4321 908-555-1234

Let’scheckanomalies:• Redundancy?• Update?• Delete?

{SSN} à {Name,City}

NowinBCNF!

ThisFDisnowgoodbecauseitisthekey

423

BCNFDecompositionAlgorithm

BCNFDecomp(R):FindXs.t.:X+ ≠XandX+≠[allattributes]

if (notfound)then Return R

let Y=X+ - X,Z=(X+)Cdecompose R intoR1(XÈ Y)andR2(XÈ Z)

Return BCNFDecomp(R1),BCNFDecomp(R2)

424


BCNFDecomp(R):Findasetofattributes Xs.t.:X+ ≠XandX+≠

[allattributes]




FindasetofattributesXwhichhasnon-trivial“bad”FDs,i.e.isnotasuperkey,usingclosures

425


BCNFDecomp(R):Finda setofattributesXs.t.:X+ ≠XandX+≠

[allattributes]




Ifno“bad”FDsfound,inBCNF!

426


BCNFDecomp(R):FindasetofattributesXs.t.:X+ ≠XandX+≠

[allattributes]




LetYbetheattributesthatXfunctionallydetermines(+thatarenotinX)

AndletZbethecomplement,theotherattributesthatitdoesn’t

427



[allattributes]




X ZY

R1 R2

Splitintoonerelation(table)withXplustheattributesthatXdetermines(Y)…

428



[allattributes]




X ZY

R1 R2

AndonerelationwithXplustheattributesitdoesnotdetermine(Z)

429



[allattributes]




Proceedrecursivelyuntilnomore“bad”FDs!

430

R(A,B,C,D,E)BCNFDecomp(R):FindasetofattributesXs.t.:X+ ≠XandX+≠

[allattributes]




Example

{A} à {B,C}{C} à {D}

431

Example

R(A,B,C,D,E){A}+ ={A,B,C,D}≠{A,B,C,D,E}

R1(A,B,C,D){C}+ ={C,D}≠{A,B,C,D}

R2(A,E)R11(C,D) R12(A,B,C)

R(A,B,C,D,E)

{A} à {B,C}{C} à {D}

432

Practice

• Activity-22.ipynb

DB - ER - 180301b · 2018. 3. 3. · 82453 Green Sally 391-1689 AL TRE141 14987 10/05/10 3 $100...

Documents

Transcript of DB - ER - 180301b · 2018. 3. 3. · 82453 Green Sally 391-1689 AL TRE141 14987 10/05/10 3 $100...