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... continent of the country.Likewise, the hemisphereinwhichacountryislocatedcanbedeterminedfrom the continentonwhich the countryislocatedand the hemisphere of thatcontinent.TEAMallows the DBEtospecifyvirtualrelationsthatconveysuchadditionalinformation.2 The TEAMSystemArchitecture The design of TEAMreflectsseveralconstraintsimposedby the demandfortransportability;ourdiscussionwillemphasizethoseaspects of the design. The needtodecouple the representation of whatausermeansbyaqueryfrom the procedureforobtainingthatinformationfrom the databaseobviouslyaffected the choice of systemcomponents.Inaddition, the needtoseparate the domain-dependentknowledgetobeacquiredforeachnewdatabasefrom the domain-independentparts of the systeminfluenced the design of the particulardatastructures(or“knowledgesources”)selectedforencoding the informationusedbythesecomponents.Figure2illustrates the majorprocesses of TEAM, the varioussources of knowledgetheyuse,and the flow of language-processingtasksfrom the analysis of anEnglishsentenceto the generation of adatabasequery. The rectangularboxesrepresent the processes,and the ovalstotheirright, the variousknowledgesources. The acquisitionboxon the rightpointstothoseknowledgesourcesthatareaugmentedthroughinteractionwith the DBE.AllothermodulesandknowledgesourcesarebuiltintoTEAMandremainunchangedduringacquisition.Inthissectionwewilllookat the TEAMsystemfromseveralangles.Tobegin,wewillsketch the overallflow of processingduringquestion-answering,describing the variousprocessesinvolvedintransforminganEnglishqueryintoaformaldatabasequery.Because the particularlogicalform(LF)TEAMusestoencode the meaning of aqueryplaysacrucialroleinmediatingbetween the wayqueriesareposedand the wayinformationisobtainedfrom the database,itaffects the design of severalcomponents of the system.Wethenlookinsomewhatmoredetailat the datastructuresthatencodedomain-specificinformation.Finally,wediscuss the overallstrategyusedforacquiringinformationaboutspecificdomainsanddatabases.2.1Flow of Control The flow of controlduringTEAM’stranslation of anatural-languagequeryintoaformalqueryto the databaseisillustratedas the pathon the leftside of Figure2,fromtoptobottom. The transformationtakesplaceintwomajorsteps:first,arepresentation of the literalmeaning of the query,orlogicalform,isconstructed;second,thislogicalformistransformedintoadatabasequery. The translationintologicalformisperformedby the DIALOGICsystem,whichcomprises the following-components,shownsurrounded-by the~ dotted~boxinFigure2: the DIAMONDparser, the DIAGRAMgrammar, the lexicon,semantic-interpretationfunctions,basicpragmaticfunctions,andproceduresfordetermining the scope of quantifiers.Sinceadescription of DIALOGICisprovidedelsewhereGrosS2],letusdiscusshereonlythoseaspects of the systemthatwereinfluencedby the development of TEAM.TwocentraldatastructuresinDIALOGICthatareaffectedbyTEAM’sacquisitionprocessaredescribed: the lexiconand—13—2.3.3AssocIatedProcessesSeveralgeneralpredicateshavesemanticandpragmaticspecialistsassociatedwiththem. The semanticspecialistsareIs-semanticsandDegree-semantics; the pragmaticspecialistsare the Cenitive,Noun-noun,Have, Of, General-preposition,Time,Location,Do-specialist,andComparative. The Is-semanticsspecialistisassociatedwith the predicateISandpropagatessortrestrictionsacrossall the variablesthatarebeingequatedby the ISassertion.Thisspecialistisinvokedpriortopragmaticprocessing(hence the “semantics”label);itattemptstoreconcileanyconflictsitdetectsandmayrevisesomesortpredicationsonvariablesin the process.Forexample,itisusedinprocessing the query,“Whatis the area of Nepal?”toascertainthat the variablecorrespondingto the “what”isaWORLDC-AREA,notaCONT-AREA. The Degree-semanticsspecialistreplaces the generalpredicateDEGREE -OF withamorespecificone.Forexample,bydeterminingthatpredication(DEGREE -OF peakix)refersto the predicatePEAK-HEIGHT—i.e.,thatitisequivalentto the predication(PEAK-HEIGHT-OPpeakiz) the specialistallowsTEAMtofurtherconstrain the sort of xtobealinear-measure,thusallowing the comparativespecialistinvokedduringpragmaticprocessingtomake the rightchoicebetween the alternatives of comparing the heights of twoobjectsandcomparinganobject’sheightwithaheightvalue. The (Jenitive,Noun-noun,Have,and Of specialistsreplace the vaguepredicatesGENITWE,NN(fornoun-nouncombinations),HAVE,and OF withmorespecificones. The individualspecialistsdifferonlyslightly, the differencesreflecting the specialrestrictionsassociatedwitheachconstruction. The General-prepositionspecialistisassociatedwithON,FROM,WITH,andIN,convertingthesepredicatesintotheirappropriatedomain-specificcounterparts.Forexample, the Do-specialistdeterminesthat the phrase“countriesinAsia”meansthosecountriescforwhich the predication(WORLDC-CONTINENT -OF cASIA)holds. The Time-specialistandLocation-specialistservetomapTIME -OF andLOCATION -OF intopredicatesthatareappropriatefor the databaseathand.Theycanbeinvokedobliquelyby the interrogativeconstructions“when” ... and“where.” The Do-specialistreplaces the predicateDO(from the verb“do”)withamorespecificverbchosenfromthoseacquiredforadomain.Although“do”doesnotappearas the mainverbveryoftenin the databasequerytask, the translatorsdeduceitsimpliedpresenceinsomequeries—forinstanceinsuchcomparativequestionsas“WhatcountriescovermoreareathanPeruLdoes~?”. The comparativespecialistexamines the twoarguments of acomparisontodeterminewhether the comparisontobemadeisbetweentwoattributevalues(e.g.,Jack’sheightandsevenfeet)orbetweenanentityandsomevalue(e.g.,Jackandsevenfeet).In the lattercase,TEAMtriestoidentify the appropriateattribute of the entity(e.g.,Jack’sheight).2.3.4DatabaseSchema The translationfromlogicalformtoSODAqueryrequiresknowing the exactstructure of the targetdatabaseand the mannerinwhich the predicatesappearingin the logicalformareassociatedwith the relationsin the database.Thisinformationisprovidedby the databaseschema,whichincludes the followinginformation8:•Definition of sortsinterms of databaserelations(subject)orfields(andfieldvalueforsortsderivedfromfeaturefields). 8The schematranslatoralsousescertaininformationin the conceptualschema,includingtaxonomicinformationin the sorthierarchyanddelineationinformationassociatedwithnonsortpredicates.—18—Figure5:Acquiring the VirtualRelationsPKCONTandHEMICwindowforquestionsandanswers.When the DBEuses the mousetoselectone of the itemsfrom the threemenus,aset of questionsappearsin the question-answeringareaat the bottom of the display,towhichhecanthenrespond.One of the generalprinciples of acquisitionisevidentfromthisdisplay,namely,that the acquisitioniscenteredupon the relationsandfieldsin the database,becausethisis the informationmostfamiliarto the DBE. The answerstoeachquestioncanaffect the lexicon, the conceptualschema,and the databaseschema. The DBEneednotbeaware of exactlywhyTEAMposes the questionsitdoes—allhehastodoisanswerthemcorrectly.Even the entriesdisplayedin the wordmenuowetheirpresencetoquestionsabout the database. The DBEvolunteersentriestothismenuonlyin the case of verbacquisition,tosupplyanadjectivecorrespondingtosomenounalreadyinTEAM’slexicon,ortoenterasynonymforsomelexicon-residentword. The DBEisassumednottohaveanyknowledge of formallinguisticsor of natural-languageprocessingmethods.Heisassumed,however,toknowsomegeneralfactsaboutEnglish—forexample,whatpropernouns,verbs,plurals,andtenseare,butnothingmoredetailedthanthat.Ifmoresophisticatedlinguisticinformationisrequired,asin the case of verbacquisition,TEAMproceedsbyaskingquestionsaboutsamplesentences,allowing the DBEtorelyonhisintuitionasanativespeaker,andextracting the informationitneedsfromhisresponses.Virtualrelationsarespecifiediconically. The leftside of Figure5shows the acquisition of avirtualrelationthatidentifies the continent(PKCONT-CONTINENT,derivedfromWORLDC-CONTINENT) of apeak(PKCONT-NAME,fromPEAK-NAME)byperformingadatabasejoinon the PEAK-COUNTRYandWORLDC-CONTINENTfields.Similarly, the rightside of Figure5shows the acquisition of the virtualrelationthatencodes the hemisphere(HEMIC-HEMI) of acountry(HEMIC.NAME)byjoiningon the WORLDC-CONTINENTandCONT-NAMEfields.Ifhewishes, the DBEcanchangepreviousanswers.Incrementalupdatesarepossiblebecausemost of the methodsforupdating the variousTEAMstructures(lexicon,schemata)weredevisedtoundo the effects of previousanswersbefore the effects of newanswerscouldbeasserted.Helpinformationisalwaysavailabletoassist the DBEwhenheisunsurehowtoansweraquestion.Selecting the questiontextwith the mouseproducesamoreelaboratedescription of the informationTEAMistryingtoelicit,usuallyaccompaniedbypertinentexamples.Finally, the acquisitioncomponentkeepstrack of whatinformationremainstobesuppliedbeforeTEAMhas the minimumitneedstohandlequeries. The DBEdoesnothavetodeterminehimselfhowmuchinformationissufficient;allhehastodoistoperceivethatnoacquisitionwindowindicatesremainingunansweredquestions. Of course, the DBEcanalwaysprovideinformationbeyond the minimum—forexample,bysupplyingadditionalverbs,derivedadjectives,orsynonyms.—20—

... abasefor the optimizerbuildsaveryclearandconciseframeworkformodularization of the DBI’soptimizercode,andfacilitatesincrementaldevelopmentandtesting. The rulesaretranslatedby the optimizergeneratorintoexecutablesourcecode,whichiscompiledandlinkedwith the supportfunctionsandotherdatabasesoftware.Interpretativetechniqueswereruledoutbyourresearchbecause the resultingoptimizers,includingoneprototypeimplementationundertakeninProlog,arelimitedto the interpreter’ssearchstrategy,andboundtobeslow.Oneinterestingdesignissuethatremainsistoprovidegeneralsupportforpredicatesassomeform of predicateislikelytoappearinalldatamodels.Writing the DBIcodeforpredicates,andoperatorargumentsingeneral,was the hardestpart of developingouroptimizerprototypes.In the currentdesign, the DBImustdesignhisorherowndatastructuresandprovideall the operationsonthemforbothruleconditionsandargumenttransferfunctions.Itmaybedifficulttoinventagenerallysatisfyingdefinitionandsupportforpredicates,butitwouldbeasignificantimprovement of the optimizergenerator. The factthatpredicatesareaspecialcase of argumentsposesanadditionalchallenge,since the overalldesign of the argumentdatastructuremuststillremainwith the DBI.Moregenerally,werealizethat the optimizergeneratorworkslargelyon the syntacticlevel of the algebra. The semantics of the datamodelareleftto the DBI’scode.Thishas the advantage of allowing the DBImaximalfreedomwith the type of datamodelimplemented,butithas the disadvantage of leavingasignificantamount of codingto the DBI.Wethereforewouldliketoincorporatesomesemanticknowledge of the datamodelinto the descriptionfile.This,however,isalong-termgoaltowhichwehavenotyetgivenmuchattention.6.Acknowledgements The authorappreciates the generoussupportandadvicebyDavidDeWitt,MikeCarey,and the studentmembers of the EXODUSproject.ReferencesBarrl98l.A.BarrandE.A.Feigenbaum, The Handbook of ArtificialIntelligence,WilliamKaufman,Inc.,LosAltos,CA.(1981).Blasgenl977.M.BlasgenandK.Eswaran,“StorageandAccessinRelationalDatabases,”IBMSystemsJournal16(4)(1977).Carey1986.MJ.Carey,DJ.DeWitt,D.Frank,G.Graefe,J.E.Richardson,EJ.Shekita,andM.Muralikrishna, The Architecture of the EXODUSExtensibleDBMS:APreliminaryReport,”Proceedings of the Int’lWorkshoponObject-OrientedDatabaseSystems,pp.52-65(September1986).Careyl986a.MJ.Carey,DJ.DeWitt,J.E.Richardson,andE.J.Shekita,“ObjectandFileManagementin the EXODUSExtensibleDatabaseSystem,”Proceedings of the ConferenceonVeryLargeDataBases,pp.91-100(August1986).DeWittl984.DJ.DeWitt,R.Katz,F.Olken,L.Shapiro,M.Stonebraker,andD.Wood,“ImplementationTechniquesforMainMemoryDatabaseSystems,”Proceedings of the ACMSIGMODConference,pp.1-8(June1984).Graefel987.G.GraefeandDJ.DeWitt, The EXODUSOptimizerGenerator,”Proceedings of the ACMSIGMODConference,pp.160-171(May1987).42operations.Aswewillsee,thisiscriticaltoaplug-compatiblesoftwaretechnology.Second,thereareotheralgorithmsbesides the threelistedabove.Toaddanewinvertedfileretrievalalgorithm,onesimplyaddsanothercase. The sameappliesforotherabstractoperations(e.g.,abstractrecordinsertion,deletion,etc.).Theytooareimplementedascasestatements,andnewalgorithmsareincludedasadditionalcases.Introducinganotheralgorithmtoprocessanabstractfileorabstractlinkoperationiscalledalgorithmextensibility.Third,anelement of queryoptimizationcanbeseeninthisexample.WhenaRET(AF,Q)istobeprocessed, the cheapestavailablealgorithmisselected.Thisisaccomplishedbyevaluatingcostfunctionsforeachalgorithmandchoosing the cheapestalgorithm. The codetemplateformakingthisoptimizationdecisionhas the followingorganization:$RET(AF,Q)/*takenfromINDEXmodule*/retum(minimum _of ($RET(F,Q),/*Mgicostfunction~/$USE_1_INDEX(AF,Q,$RET(I~,Q~)~$ACC(F,p)),1*A1g2costfunction*1$USE_n_IND1CES(AF,Q,$RET(I~,Q~).$ACC(F,p))1*A1g3costfunction*1)Twopoints.First, the costfunctions$USE_1_INDEXand$USE_n_INDICEShavealgorithmstodeterminewhichindicestousetoprocess~inordertoachieve the optimalperformance.(Astherearemanysuchalgorithms, the algorithmthatisactuallyusedcouldbeaparameterto the $RET(AF,Q)costfunction.Doingsowouldprovideasimplemeansbywhichoptimizingalgorithmscouldbechanged). The informationaboutwhatindicestouseisretainedaspart of the optimizationprocess,andislaterusedwhen the selectedalgorithmsareexecuted.Second,notethatactualexpressionsfor the costfunctionsforindexfileretrieval$RET(I~,Q~)anddatafileaccessing$ACC(F,p)arenotspecified;onlywhen the implementation of thesefilesisgiveninamoduleexpressioncanactualcostexpressionsbeassignedtothesefunctions.Insummary, the buildingblocks of DBMSsareparameterizedandnonparameterizedfiletypes. The softwarebuildingblocksare the algorithmsthatmapoperationsonabstractfilestooperationsonconcretefiles. The costmodelbuildingblocksarecostfunctionsthatareassociatedwiththeseoperationmappings.Composition of buildingblocksisconsideredin the nextsection.4.SyntheticDBMSsandSyntheticPerformanceModelsAsmentionedin the previoussection,asimpleinvertedDBMS,similartoINGRES,isdescribedby the moduleexpressionNDEXHEAP,BPLUS].Inthisparticularexample,datafileoperationsreferencedin the INDEXalgorithmsaremappedtoheapfileoperations,andindexfileoperationsaremappedtoB+treeoperations.LetCbeaconceptualfile,Dbeitscorrespondingdatafile,I~beanindexfile,andQbeaselectionpredicate. The algorithmstoretrieveconceptualrecordsareacomposition of INDEX,BPLUS,andHEAPretrievalandaccessalgorithms:RET(C,Q)(case(use_$RET(C,Oj_to_choose_cheapest) of Mgi:RET_HEAP(D,Q);Alg2:USE_1_INDEX(C,Q,RET_BPLUS(IJ,Q~).ACC_IiEAP(D,p));A1g3:USE_n_INDICES(C,Q,RET_BPLUS(I~,Q~).ACC_HEAP(D,p)); The abovealgorithmswerederivedbyreplacingRET(D,Q)withRET_HEAP(D,Q),RET(I~,Q~)withRET_BPLUS(IJ,Q~).andACC(D,p)withACC_HEAP(D,p).34MESH,MESHisacomplexnetwork of pointers.Ateachstepin the search, the transformationperformedis the onewhichcarries the mostpromisethatitwilleventually,viasubsequenttransformations,leadto the optimalqueryevaluationplan. The crucialelementinthissearchstrategyis the promisecalculation,called the promiseevaluationfunction.Itmustinclude the currentqueryandplan,otherqueriesandplanswhichhavewerefoundearlierin the searchprocess,andinformationabout the transformationruleinvolved. The mostnaturalmeasureforpromiseis the costimprovement of the accessplans.3.Modularization of DBICodeInanextensibledatabasesystem,therearealwayssomepartsin the optimizer(andinothercomponentsaswell)thatcannotbeexpressedinarestricted,e.g.rule-basedlanguage.Thesepartsarebestwrittenin the DBI’simplementationlanguage.Asoftwaretoolisusedtocombine the rulesand the DBI’ssourcecode.Foreasyextensibility,itisveryimportanttoassist the DBIindividing the codeintomeaningful,independentmodules.Notonlyisamodularoptimizereasiertoimplement,weenvisionthisasanaidformaintainingadatabasemanagementsystemthatevolvesovertime.Someoptimizercomponentscanonlybedefinedafter the datamodelhasbeendefined(data-model-dependentcomponents),andhencemustbeprovidedby the DBI.Inthissection,wewillbrieflyreviewthesecomponents,andhowtheyarebrokenintomodules.Wegenerallyassociatetheseprocedureswithone of the conceptsthatwehaveintroducedearlier,namelyoperators,methods,andrules.3.1.Data-Model-DependentDataStructuresTherearetwotypes of data-model-dependentdatastructuresthatareimportantin the optimizationprocess.First,thereareargumentsforoperatorsandmethods.Second,inalmostallcasesitisdesirabletomaintainsomedictionaryinformationforintermediateresultsinaquerytree.Wetermsuchdictionaryinformationproperties of the intermediateresults.Sincedefiningthesedatastructuresispart of customizinganextensibledatabasesystem, the optimizationcomponent of suchasystemmusttreatthesestructuresas“blackboxes”.InEXODUS,wedefineanduseaproceduralinterfacetomaintainandqueryproperties.Furthermore,wedistinguishbetweenoperatorandmethodarguments,andbetweenoperator-dependentandmethod-dependentproperties.Asanexamplefromarelationalsystem,cardinalityandtuplewidthareoperator-dependentproperties,whereassortorderisamethod-dependentproperty.3.2.RulesandConditionsIn the EXODUSoptimizationconcept, the set of operators, the set of methods,transformationrules,andimplementationrulesare the centralcomponentsthat the DBIspecifiestoimplementanoptimizer. The rulesarenon-procedural;theyaregivenasequivalencelawsthat the generatortranslatesintocodetoperformtreetransfonnations.Each of theserulesshouldbeself-contained.Onlythenisitpossibletoexpand the rulesetsafelyas the datamodelevolves. The rulesexpressequivalence of querytrees.Treeexpressions,i.e.algebraicexpressions,embody the shape of atreeand the operatorsinit.Forsomerules,however,applicabilitydoesnotdependon the tree’sshapeand the operatorsalone.Forexample,sometransformationsmightonlybepossibleifanoperatorargumentsatisfiesacertaincondition.Sinceoperatorargumentsshouldbedefinedby the DBI,suchconditionscannotbeexpressedinadatamodelindependentform.Weallow the DBItoaugmentruleswithsourcecodetoinspect the operatorarguments, the datadictionary,etc.3.3.CostFunctionsAsmentionedearlier,processingcostoccursbyexecutingaparticularalgorithm. The costcalculationiscloselyrelatedto the processingmethodbeingexecuted.Hence,weassociatecostfunctionswith the methods,andcalculate the cost of aqueryexecutionplanas the sum of the costs of the methodsinvolved. The parameters of acostfunctionare the characteristics of the datastreamsservingasinputsinto the method,e.g. the number of dataobjectsineachinputdatastream,and the methodargument,e.g.apredicate.3.4.PropertyFunctions The characteristics of the datastreamwhichareneededasparametersto the costfunctionsaredatamodel-dependent.Thus,theymustbedefinedby the DBI.Weattachcharacteristics,whichwecallproperties,withboth the operatorsand the methods.Operators(andtheirarguments)determine the logicalproperties of anodeinaquerytree,e.g.cardinality.Aparticularalgorithmormethodchosendefinesphysicalproperties of an39Lohmanl985.0.Lohman,C.Mohan,L.Haas,D.Daniels,B.Lindsay,P.Selinger,andP.Wilms,“QueryProcessinginR*,”pp.31-47inQueryProcessinginDatabaseSystems,ed.J.W.Schmidt,Spnnger,Berlin(1985).Mackertl986.L.F.MackertandG.M.Lohman,“R*OptimizerValidationandPerformanceEvaluationforLocalQueries,”Proceedings of the ACMSIGMODConference,pp.84-95(May1986).Mackertl986a.L.F.MackertandG.M.Lohman,“R*OptimizerValidationandPerformanceEvaluationforDistributedQueries,”Proceedings of the ConferenceonVeryLargeDataBases,pp.149-159(August1986).Richardson1987.J.E.RichardsonandMJ.Carey,“ProgrammingConstructsforDatabaseSystemImplementationinEXODUS,”Proceedings of the ACMSIGMODConference,pp.208-219(May1987).Selingerl979.P.GriffithsSelinger,M.M.Astrahan,D.D.Chamberlin,R.A.Lone,andT.G.Price,“AccessPathSelectioninaRelationalDatabaseManagementSystem,”Proceedings of the ACMSIGMODConference,(June1979).4Joinindicescouldbeusedinmanydifferentstoragemodels.However,inordertosimplifyourdiscussionregardingqueryoptimization,wepresent the integration of joinindicesinasimplestoragemodelwithsingleattributeclusteringandselectionindices.Thenweillustrate the impact of the storagemodelwithjoinindiceson the optimization of non—recursivequeries,assumedtobeSPJqueries.Inparticular,efficientaccessplans,where the mostcomplex(andcostly)part of the querycanbeperformedthroughindices,canbegeneratedby the queryoptimizer.Finally,weillustrate the use of joinindicesin the optimization of recursivequeries,wherearecursivequeryismappedintoaprogram of relationalalgebraenrichedwithatransitiveclosureoperator.2.StorageModelwithJoinIndices The storagemodelprescribes the storagestructuresandrelatedalgorithmsthataresupportedby the databasesystemtomap the conceptualschemainto the physicalschema.Inarelationalsystemimplementedonadisk—basedarchitecture,conceptualrelationscanbemappedintobaserelationson the basis of twofunctions,partitioningandreplicating.All the tuples of abaserelationareclusteredbasedon the value of oneattribute.Weassumethateachconceptualtupleisassignedasurrogatefortupleidentity,calledaTID(tupleidentifier).ATIDisavalueuniqueforalltuples of arelation.Itiscreatedby the systemwhenatupleisinstantiated.TID’spermitefficientupdatesandreorganizations of baserelations,sincereferencesdonotinvolvephysicalpointers. The partitioningfunctionmapsarelationintooneormorebaserelations,whereabaserelationcorrespondstoaTIDtogetherwithanattribute,severalattributes,orall the conceptualrelation’sattributes. The rationaleforapartitioningfunctionis the optimization of projection,bystoringtogetherattributeswithhighaffinity,i.e.,frequentlyaccessedtogether. The replicatingfunctionreplicatesoneormoreattributesassociatedwith the TID of the relationintooneormorebaserelations. The primaryuse of replicatedattributesisforoptimizingselectionsbasedonthoseattributes.Anotheruseisforincreasedreliabilityprovidedbythoseadditionaldatacopies.inthispaper,weassumeasimplestoragemodel ... astobe(easonablyefficient.Inlogicqueriesitisexpectedthat the number of relationscaneasilyexceed10—15relations.InKBZ86],wepresentedaquadratictimealgorithmthatcomputes the optimalordering of conjunctivequerieswhen the queryisacyclic.Further,thisalgorithmwasextendedtoincludecyclicqueriesandothercostmodels.Moreover, the algorithmhasprovedtobeheuristicallyveryeffectiveforcyclicqueriesonce the minimumcostspanningtreeisusedas the treequeryforoptimizationV86].Anotherapproachtosearching the largesearchspaceistouseastochasticalgorithm.Intuitively, the minimumcostpermutationcanbefoundbypicking,randomly,a“large”number of permutationsfrom the searchspaceandchoosing the minimumcostpermutation.Obviously, the number of permutationsthatneedtobechosenapproaches the size of the searchspaceforareasonableassurance of obtaining the minimum.Thisnumberisclaimedtobemuchsmallerbyusingatechniquecalledsimulatedannealing1W87]andthistechniquecanbeusedin the optimization of conjunctivequeries.Insummary, the problem of enumerating the searchspaceisconsidered the majorproblemhere.3.2.NonrecursiveQueries:Wefirstpresentasimpleoptimizationalgorithmfor the executionspace{MP,PS,PP,PR}(i.e.,anyflatten/unflattentransformationisdisallowed),usingwhich the issuesarediscussed.Asin the case of conjunctivequeryoptimization,wepushselect/projectdownto the firstoperationonarelationandlimit the enumerationto{MP,PR}.Recallthat the processinggraphforanyexecution of anonrecursivequeryisanAND/ORtree.Firstconsider the casewhenwematerialize the relationforeachpredicatein the rulebase.Aswedonotallow the flatten/unflattentransformation,wecanproceedasfollows:optimizealowestsubtreein the AND/ORtree.Thissubtreeisaconjunctivequery,asallchildreninthissubtreeareleaves(i.e.,baserelations),andwemayuse the exhaustivecasealgorithm of the previoussection.Afteroptimizing the subtree,wereplace the subtreebya“baserelation”andrepeatthisprocessuntil the treeisreducedtoasinglenode.Itiseasytoshowthatthisalgorithmexhausts the searchspace{PR}.Further,suchanalgorithmisreasonablyefficientifnumber of predicatesin the bodydoesnotexceed10—15.Inordertoexploitsidewaysinformationpassingbychoosingpipelinedexecutions,wemake the followingobservation.Becauseall the subtreeswerematerialized, the bindingpattern(i.e.,allargumentsunbound) of the head of anyrulewasuniquelydetermined.Consequently,wecouldoutlineabottom-upalgorithmusingthisuniquebindingforeachsubtree.Ifwedoallowpipelinedexecution,then the subtreemaybeboundindifferentways,dependingon the ordering of the siblings of the root of the subtree.Consequently, the subtreemaybeoptimizeddifferently.Observethat the number of bindingpatternsforapredicateispurelydependenton the number of arguments of thatpredicate.So the extensionto the abovebottom-upalgorithmistooptimizeeachsubtreeforallpossiblebindingsandtouse the costfor the appropriatebindingwhencomputing the cost of joiningthissubtreewithitssiblings. The maximumnumber of bindingsisequalto the cardinality of the powerset of the arguments.Inordertoavoidoptimizingasubtreewithabindingpatternthatmayneverbeused,atop-downalgorithmcanbedevised.Inanycase, the algorithmisexpectedtobereasonablyefficientforsmallnumbers of arguments,k,and of predicatesin the body,n.Whenkand/ornareverylarge,itmaynotbefeasibletousethisalgorithm.Weexpectthatkisunlikelytobelarge,buttheremayberulebasesthathavelargen.Itisthenpossibletouse the polynomialtimealgorithmor the stochasticalgorithmpresentedin the previoussection.Eventhoughwedonotexpectktobeverylarge,itwouldbecomfortingifwecanfindanapproximationforthiscasetoo.Thisremainsatopicforfurtherresearch.Insummary, the technique of pushingselect/projectinagreedywayforagivenordering(i.e.,asidewaysinformationpassing)canbe ... astobe(easonablyefficient.Inlogicqueriesitisexpectedthat the number of relationscaneasilyexceed10—15relations.InKBZ86],wepresentedaquadratictimealgorithmthatcomputes the optimalordering of conjunctivequerieswhen the queryisacyclic.Further,thisalgorithmwasextendedtoincludecyclicqueriesandothercostmodels.Moreover, the algorithmhasprovedtobeheuristicallyveryeffectiveforcyclicqueriesonce the minimumcostspanningtreeisusedas the treequeryforoptimizationV86].Anotherapproachtosearching the largesearchspaceistouseastochasticalgorithm.Intuitively, the minimumcostpermutationcanbefoundbypicking,randomly,a“large”number of permutationsfrom the searchspaceandchoosing the minimumcostpermutation.Obviously, the number of permutationsthatneedtobechosenapproaches the size of the searchspaceforareasonableassurance of obtaining the minimum.Thisnumberisclaimedtobemuchsmallerbyusingatechniquecalledsimulatedannealing1W87]andthistechniquecanbeusedin the optimization of conjunctivequeries.Insummary, the problem of enumerating the searchspaceisconsidered the majorproblemhere.3.2.NonrecursiveQueries:Wefirstpresentasimpleoptimizationalgorithmfor the executionspace{MP,PS,PP,PR}(i.e.,anyflatten/unflattentransformationisdisallowed),usingwhich the issuesarediscussed.Asin the case of conjunctivequeryoptimization,wepushselect/projectdownto the firstoperationonarelationandlimit the enumerationto{MP,PR}.Recallthat the processinggraphforanyexecution of anonrecursivequeryisanAND/ORtree.Firstconsider the casewhenwematerialize the relationforeachpredicatein the rulebase.Aswedonotallow the flatten/unflattentransformation,wecanproceedasfollows:optimizealowestsubtreein the AND/ORtree.Thissubtreeisaconjunctivequery,asallchildreninthissubtreeareleaves(i.e.,baserelations),andwemayuse the exhaustivecasealgorithm of the previoussection.Afteroptimizing the subtree,wereplace the subtreebya“baserelation”andrepeatthisprocessuntil the treeisreducedtoasinglenode.Itiseasytoshowthatthisalgorithmexhausts the searchspace{PR}.Further,suchanalgorithmisreasonablyefficientifnumber of predicatesin the bodydoesnotexceed10—15.Inordertoexploitsidewaysinformationpassingbychoosingpipelinedexecutions,wemake the followingobservation.Becauseall the subtreeswerematerialized, the bindingpattern(i.e.,allargumentsunbound) of the head of anyrulewasuniquelydetermined.Consequently,wecouldoutlineabottom-upalgorithmusingthisuniquebindingforeachsubtree.Ifwedoallowpipelinedexecution,then the subtreemaybeboundindifferentways,dependingon the ordering of the siblings of the root of the subtree.Consequently, the subtreemaybeoptimizeddifferently.Observethat the number of bindingpatternsforapredicateispurelydependenton the number of arguments of thatpredicate.So the extensionto the abovebottom-upalgorithmistooptimizeeachsubtreeforallpossiblebindingsandtouse the costfor the appropriatebindingwhencomputing the cost of joiningthissubtreewithitssiblings. The maximumnumber of bindingsisequalto the cardinality of the powerset of the arguments.Inordertoavoidoptimizingasubtreewithabindingpatternthatmayneverbeused,atop-downalgorithmcanbedevised.Inanycase, the algorithmisexpectedtobereasonablyefficientforsmallnumbers of arguments,k,and of predicatesin the body,n.Whenkand/ornareverylarge,itmaynotbefeasibletousethisalgorithm.Weexpectthatkisunlikelytobelarge,buttheremayberulebasesthathavelargen.Itisthenpossibletouse the polynomialtimealgorithmor the stochasticalgorithmpresentedin the previoussection.Eventhoughwedonotexpectktobeverylarge,itwouldbecomfortingifwecanfindanapproximationforthiscasetoo.Thisremainsatopicforfurtherresearch.Insummary, the technique of pushingselect/projectinagreedywayforagivenordering(i.e.,asidewaysinformationpassing)canbe...