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Department of computer science and engineering chines university of Hong kong Department of computer science and engineering chines university of Hong kong

Department of computer science and engineering chines university of Hong kong - PDF document

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Department of computer science and engineering chines university of Hong kong - PPT Presentation

FunctionalDependenciesPart2 InpracticeitisoftenthecasethatsomeFDsareeasiertoseewhileothersaremoresubtleandhardertoobserveSomeofthosesubtleFDsfortunatelycanbederivedfromtheeasyonesInotherwordst ID: 336855

FunctionalDependencies:Part2 Inpractice itisoftenthecasethatsomeFDsareeasiertosee whileothersaremoresubtleandhardertoobserve.SomeofthosesubtleFDs fortunately canbederivedfromtheeasyones.Inotherwords

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Indesigningadatabase,forthepurposeofminimizingredundancy,weneedtocollectasetFoffunctionaldependencies(FD)thatre ecttheconstraintsoftheunderlyingapplication.Ideally,wedonotwanttomissanyFD,i.e.,wewanttoobtainanFthatisaslargeaspossible.However,inpractice,FDcollectionisadicultprocess.NoonecanguaranteealwaysdiscoveringallFDs. FunctionalDependencies:Part2 Inpractice,itisoftenthecasethatsomeFDsareeasiertosee,whileothersaremoresubtleandhardertoobserve.SomeofthosesubtleFDs,fortunately,canbederivedfromtheeasyones.Inotherwords,thederivationpermitsusto\rescue"someFDsthathaveskippedourattention.HowaboutthesubtleFDsthatcannotbederivedfromtheeasyones?Thereisnothingwecandoaboutthem,unfortunately,andwillhavetocontinuethedesignwithoutthem.Thisiswhyevenanexperienceddatabaseprofessionalmaynotalwaysbeabletocomeupwithaperfectdesign! FunctionalDependencies:Part2 LetusidentifyanimportantspecialtypeofFDs: De nition AfunctionaldependencyX!YisregularifYcontainsonlyasingleattribute. Forexample,AB!Cisregular,butAB!CDisnot,whereA;B;C,andDareattributes. FunctionalDependencies:Part2 ThereisanequivalencethatexplainswhywecancaptureallirregularFDsbyconsideringonlyregularones: AnirregularFDX!A1A2:::At(whereXisanattributeset,andeachAi(1it)isanattribute)isequivalentto:X!A1X!A2:::X!AtExample:AB!CDifandonlyifAB!CandAB!D. FunctionalDependencies:Part2 Again,letFbethesetofFDswehavecollected.Then: De nition TheclosureofF,denotedasF+,isthesetofallregularFDsthatcanbederivedfromF. DonotconfusetheclosureofFwiththeclosureofanattributeset. FunctionalDependencies:Part2 Example.Assumethatthereare4attributesA;B;C;D,andthatF=fA!B;B!Cg.Then,F+includesallthefollowingFDs:A!A,A!B,A!C,B!B,B!C,C!C,D!D,AB!A,AB!B,AB!C,AC!A,AC!B,AC!C,AD!A,AD!B,AD!C,AD!D,BC!B,BC!C,BD!B,BD!C,BD!D,CD!C,CD!D,ABC!A,ABC!B,ABC!C,ABD!A,ABD!B,ABD!C,ABD!D,BCD!B,BCD!C,BCD!D,ABCD!A,ABCD!B,ABCD!C,ABCD!D. FunctionalDependencies:Part2 FindingtheClosureofaSetofFDs algorithm(F)/*FisasetofFDs*/1.F+=;2.foreachpossibleattributesetX3.computetheclosureX+ofXonF4.foreachattributeA2X+5.addtoF+theFD:X!A5.returnF+ FunctionalDependencies:Part2 Example.Assumethatthereare4attributesA;B;C;D,andthatF=fA!B;B!Cg.TocomputeF+,we rstget: A+=AB+=AC+=ABC+=fA;B;Cg B+=BC+=fB;Cg C+=fCg D+=fDg AD+=fA;Dg BC+=fB;Cg BD+=BCD+=fB;C;Dg ABD+=ABCD+=fA;B;C;Dg ACD+=fA;C;DgItiseasytogeneratetheFDsinF+fromtheclosuresoftheaboveattributesets. FunctionalDependencies:Part2 CandidateKeyRevisited Increatingatable,itmayseemthatsofarwehavebeenspecifyingcandidatekeysbasedonourpreferences.ThisillusioniscreatedbecausewedidnotunderstandFDs.Infact,candidatekeysarenotuptousatall.Instead,theyareuniquelydeterminedbythesetFoffunctionaldependenciesfromtheunderlyingapplication.Seethenextslide. FunctionalDependencies:Part2 CandidateKeyRevisited LetFbeasetofFDs,andRarelation. De nition AcandidatekeyisasetXofattributesinRsuchthat X+includesalltheattributesinR. ThereisnopropersubsetYofXsuchthatY+includesalltheattributesinR. Note:ApropersubsetYisasubsetofXsuchthatY6=X(i.e.,XhasatleastoneelementnotinY). FunctionalDependencies:Part2 Example.ConsideratableR(A;B;C;D),andthatF=fA!B;B!Cg. Aisnotacandidatekey,becauseA+=fA;B;CgwhichdoesnotincludeD. ABDisnotacandidatekeyeventhoughABD+=fA;B;C;Dg.ThisisbecauseAD+=fA;B;C;Dg,namely,thereisapropersubsetADofABDsuchthatAD+includesalltheattributes. ADisacandidatekey. FunctionalDependencies:Part2