地理信息系统中英文对照外文翻译文献

中英文对照外文翻译(文档含英文原文和中文翻译)ASurveyonSpatio-TemporalDataWarehousingAbstractGeographicInformationSystems(GIS)havebeenextensivelyusedinvariousapplicationdomains,rangingfromeconomical,ecologicalanddemographicanalysis,tocityandrouteplanning.Nowadays,organizationsneedsophisticatedGIS-basedDecisionSupportSystem(DSS)toanalyzetheirdatawithrespecttogeographicinformation,representednotonlyasattributedata,butalsoinmaps.Thus,vendorsareincreasinglyintegratingtheirproducts,leadingtotheconceptofSOLAP(SpatialOLAP).Also,inthelastyears,andmotivatedbytheexplosivegrowthintheuseofPDAdevices,thefieldofmovingobjectdatahasbeenreceivingattentionfromtheGIScommunity.However,notmuchhasbeendoneinprovidingmovingobjectdatabaseswithOLAPfunctionality.InthefirstpartofthispaperwesurveytheSOLAPliterature.WethenmovetoSpatio-TemporalOLAP,inparticularaddressingtheproblemoftrajectoryanalysis.Wefinallyprovideanin-depthcomparativeanalysisbetweentwoproposalsintroducedinthecontextoftheGeoPKDDEUproject:theHermes-MDCsystem,andPiet,aproposalforSOLAPandmovingobjects,developedattheUniversityofBuenosAires,Argentina.Keywords:GIS,OLAP,DataWarehousing,MovingObjects,Trajectories,AggregationINTRODUCTIONGeographicInformationSystems(GIS)havebeenextensivelyusedinvariousapplicationdomains,rangingfromeconomical,ecologicalanddemographicanalysis,tocityandrouteplanning(Rigaux,Scholl,&Voisard,2001;Worboys,1995).SpatialinformationinaGISistypicallystoredindifferentso-calledthematiclayers(alsocalledthemes).Informationinthemescanbestoredindatastructuresaccordingtodifferentdatamodels,themostusualonesbeingtherastermodelandthevectormodel.Inathematiclayer,spatialdataisannotatedwithclassicalrelationalattributeinformation,of(ingeneral)numericorstringtype.Whilespatialdataisstoredindatastructuressuitableforthesekindsofdata,associatedattributesareusuallystoredinconventionalrelationaldatabases.SpatialdatainthedifferentthematiclayersofaGISsystemcanbemappedunivocallytoeachotherusingacommonframeofreference,likeacoordinatesystem.Theselayerscanbeoverlappedoroverlayedtoobtainanintegratedspatialview.Ontheotherhand,OLAP(OnLineAnalyticalProcessing)(Kimball,1996;Kimball&Ross,2002)comprisesasetoftoolsandalgorithmsthatallowefficientlyqueryingmultidimensionaldatabases,containinglargeamountsofdata,usuallycalledDataWarehouses.InOLAP,dataisorganizedasasetofdimensionsandfacttables.Inthemultidimensionalmodel,datacanbeperceivedasadatacube,whereeachcellcontainsameasureorsetof(probablyaggregated)measuresofinterest.Aswediscusslater,OLAPdimensionsarefurtherorganizedinhierarchiesthatfavorthedataaggregationprocess(Cabibbo&Torlone,1997).Severaltechniquesandalgorithmshavebeendevelopedforqueryprocessing,mostoftheminvolvingsomekindofaggregateprecomputation(Harinarayan,Rajaraman,&Ullman,1996).TheneedforOLAPinGISDifferentdatamodelshavebeenproposedforrepresentingobjectsinaGIS.ESRI()firstintroducedtheCoveragedatamodeltobindgeometricobjectstonon-spatialattributesthatdescribethem.Later,theyextendedthismodelwithobject-orientedsupport,inawaythatbehaviorcanbedefinedforgeographicfeatures(Zeiler,1999).TheideaoftheCoveragedatamodelisalsosupportedbytheReferenceModelproposedbytheOpenGeospatialConsortium().Thus,inspiteofthemodelofchoice,thereisalwaystheunderlyingideaofbindinggeometricobjectstoobjectsorattributesstoredin(mostly)object-relationaldatabases(Stonebraker&Moore,1996).Inaddition,querytoolsincommercialGISallowuserstooverlapseveralthematiclayersinordertolocateobjectsofinterestwithinanarea,likeschoolsorfirestations.Forthis,theyuseindexingstructuresbasedonR-trees(Gutman,1984).GISquerysupportsometimesincludesaggregationofgeographicmeasures,forexample,distancesorareas(e.g.,representingdifferentgeologicalzones).However,theseaggregationsarenottheonlyonesthatarerequired,aswediscussbelow.Nowadays,organizationsneedsophisticatedGIS-basedDecisionSupportSystem(DSS)toanalyzetheirdatawithrespecttogeographicinformation,representednotonlyasattributedata,butalsoinmaps,probablyindifferentthematiclayers.Inthissense,OLAPandGISvendorsareincreasinglyintegratingtheirproducts(see,forinstance,MicrostrategyandMapInfointegrationin/,and/).Inthissense,aggregatequeriesarecentraltoDSSs.ClassicalaggregateOLAPqueries(like“totalsalesofcarsinCalifornia”),andaggregationcombinedwithcomplexqueriesinvolvinggeometriccomponents(“totalsalesinallvillagescrossedbytheMississippiriverandwithinaradiusof100kmaroundNewOrleans”)mustbeefficientlysupported.Moreover,navigationoftheresultsusingtypicalOLAPoperationslikeroll-upordrill-downisalsorequired.TheseoperationsarenotsupportedbycommercialGISinastraightforwardway.OneofthereasonsisthattheGISdatamodelsdiscussedaboveweredevelopedwith“transactional”queriesinmind.Thus,thedatabasesstoringnonspatialattributesorobjectsaredesignedtosupportthose(nonaggregate)kindsofqueries.Decisionsupportsystemsneedadifferentdatamodel,wherenon-spatialdata,probablyconsolidatedfromdifferentsectorsinanorganization,isstoredinadatawarehouse.Here,numericaldataarestoredinfacttablesbuiltalongseveraldimensions.Forinstance,ifweareinterestedinthesalesofcertainproductsinstoresinagivenregion,wemayconsiderthesalesamountsinafacttableoverthethreedimensionsStore,TimeandProduct.Inordertoguaranteesummarizability(Lenz&Shoshani,1997),dimensionsareorganizedintoaggregationhierarchies.Forexample,storescanaggregateovercitieswhichinturncanaggregateintoregionsandcountries.Eachoftheseaggregationlevelscanalsoholddescriptiveattributeslikecitypopulation,theareaofaregion,etc.TofulfilltherequirementsofintegratedGIS-DSS,warehousedatamustbelinkedtogeographicdata.Forinstance,apolygonrepresentingaregionmustbeassociatedtotheregionidentifierinthewarehouse.Besides,systemintegrationincommercialGISisnotaneasytask.Inthecurrentcommercialapplications,theGISandOLAPworldsareintegratedinanad-hocfashion,probablyinadifferentway(andusingdifferentdatamodels)eachtimeanimplementationisrequired,evenwhenadatawarehouseisavailablefornon-spatialdata.AnIntroductoryExample.Wepresentnowareal-worldexampleforillustratingsomeissuesinthespatialwarehousingproblematic.WeselectedfourlayerswithgeographicandgeologicalfeaturesobtainedfromtheNationalAtlasWebsite().Theselayerscontainthefollowinginformation:states,cities,andriversinNorthAmerica,andvolcanoesinthenorthernhemisphere(publishedbytheGlobalVolcanismProgram-GVP).Figure1showsadetailofthelayerscontainingcitiesandriversinNorthAmerica,displayedusingthegraphicinterfaceofthePietimplementationwediscusslaterinthepaper.Notethedensityofthepointsrepresentingcities(particularlyintheeasternregion).Riversarerepresentedaspolylines.Figure2showsaportionoftwooverlayedlayerscontainingstates(representedaspolygons)andvolcanoesinthenorthernhemisphere.Thereisalsonon-spatialinformationstoredinaconventionaldatawarehouse.Inthisdatawarehouse,dimensiontablescontaincustomer,storesandproductinformation,andafacttablecontainsstoressalesacrosstime.Also,numericalandtextualinformationonthegeographiccomponentsexist(e.g.,population,area),storedasusualasattributesoftheGISlayers.Inthescenarioabove,conventionalGISandorganizationaldatacanbeintegratedfordecisionsupportanalysis.Salesinformationcouldbeanalyzedinthelightofgeographicalfeatures,convenientlydisplayedinmaps.Thisanalysiscouldbenefitfromtheintegrationofbothworldsinasingleframework.Eventhoughthisintegrationcouldbepossiblewithexistingtechnologies,ad-hocsolutionsareexpensivebecause,besidesrequiringlotsofcomplexcoding,theyarehardlyportable.Tomakethingsmoredifficult,ad-hocsolutionsrequiredataexchangebetweenGISandOLAPapplicationstobeperformed.ThisimpliesthattheoutputofaGISquerymustbeprobablyexportedasmembersindimensionsofadatacube,andmergedforfurtheranalysis.Forexample,supposethatabusinessanalystisinterestedinstudyingthesalesofnauticalgoodsinstoreslocatedincitiescrossedbyrivers.ShecouldfirstquerytheGIS,toobtainthecitiesofinterest.SheprobablyhasstoredsalesinadatacubecontainingadimensionStoreorGeographywithcityasadimensionlevel.Shewouldneedto“manually”selectthecitiesofinterest(i.e.,theonesreturnedbytheGISquery)inthecube,tobeabletogoonwiththeanalysis(inthebestcase,anad-hoccustomizedmiddlewarecouldhelpher).Ofcourse,shemustrepeatthisforeachqueryinvolvinga(geographic)dimensioninthedatacube.Figure1.TwooverlayedlayerscontainingcitiesandriversinNorthAmerica.Onthecontrary,GIS/Datawarehousingintegrationcanprovideamorenaturalsolution.Thesecondpartofthissurveyisdevotedtospatio-temporaldatawarehousingandOLAP.Movingobjectsdatabases(MOD)havebeenreceivingincreasingattentionfromthedatabasecommunityinrecentyears,mainlyduetothewidevarietyofapplicationsthattechnologyallowsnowadays.Trajectoriesofmovingobjectslikecarsorpedestrians,canbereconstructedbymeansofsamplesdescribingthelocationsoftheseobjectsatcertainpointsintime.AlthoughthereFigure2.TwooverlayedlayerscontainingstatesinNorthAmericaandvolcanoesinthenorthernhemisphere.existmanyproposalsformodelingandqueryingmovingobjects,onlyasmallpartofthemaddresstheproblemofaggregationofmovingobjectsdatainaGIS(GeographicInformationSystems)scenario.Manyinterestingapplicationsarise,involvingmovingobjectsaggregation,mainlyregardingtrafficanalysis,truckfleetbehavioranalysis,commutertrafficinacity,passengertrafficinanairport,orshoppingbehaviorinamall.BuildingtrajectorydatawarehousesthatcanintegratewithaGISisanopenproblemthatisstartingtoattractdatabaseresearchers.Finally,theMODsettingisappropriatefordataminingtasks,andwealsocommentonthisinthepaper.Inthispaper,wefirstprovideabriefbackgroundonGIS,datawarehousingandOLAP,andareviewofthestate-of-the-artinspatialOLAP.Afterthis,wemoveontostudyspatio-temporaldatawarehousing,OLAPandmining.WethenprovideadetailedanalysisofthePietframework,aimedatintegratingGIS,OLAPandmovingobjectdata,andconcludewithacomparisonbetweenthisproposal,andtheHermesdatacartrridgeandtrajectorydatawarehousedevelopedinthecontextoftheGeoPKDDproject(InformationabouttheGoePKDDprojectcanbefoundathttp://www.geopkdd.eu).ASHORTBACKGROUNDGISIngeneral,informationinaGISapplicationisdividedoverseveralthematiclayers.Theinformationineachlayerconsistsofpurelyspatialdataontheonehand,thatiscombinedwithclassicalalpha-numericattributedataontheotherhand(usuallystoredinarelationaldatabase).Twomaindatamodelsareusedfortherepresentationofthespatialpartoftheinformationwithinonelayer,thevectormodelandtherastermodel.ThechoiceofmodeltypicallydependsonthedatasourcefromwhichtheinformationisimportedintotheGIS.TheVectorModel.ThevectormodelisusedthemostincurrentGIS(Kuper&Scholl,2000).Inthevectormodel,infinitesetsofpointsinspacearerepresentedasfinitegeometricstructures,orgeometries,like,forexample,points,polylinesandpolygons.Moreconcretely,vectordatawithinalayerconsistsinafinitenumberoftuplesoftheform(geometry,attributes)whereageometrycanbeapoint,apolylineorapolygon.Thereareseveralpossibledatastructurestoactuallystorethesegeometries(Worboys,1995).TheRasterModel.Intherastermodel,thespaceissampledintopixelsorcells,eachonehavinganassociatedattributeorsetofattributes.Usually,thesecellsformauniformgridintheplane.Foreachcellorpixel,thesamplevalueofsomefunctioniscomputedandassociatedtothecellasanattributevalue,e.g.,anumericvalueoracolor.Ingeneral,informationrepresentedintherastermodelisorganizedintozones,wherethecellsofazonehavethesamevalueforsomeattribute(s).Therastermodelhasveryefficientindexingstructuresanditisverywell-suitedtomodelcontinuouschangebutitsdisadvantagesincludeitssizeandthecostofcomputingthezones.SpatialinformationinthedifferentthematiclayersinaGISisoftenjoinedoroverlayed.Queriesrequiringmapoverlayaremoredifficulttocomputeinthevectormodelthanintherastermodel.Ontheotherhand,thevectormodeloffersaconciserepresentationofthedata,independentontheresolution.Forauniformtreatmentofdifferentlayersgiveninthevectorortherastermodel,inthispaperwetreattherastermodelasaspecialcaseofthevectormodel.Indeed,conceptually,eachcellis,andeachpixelcanberegardedas,asmallpolygon;also,theattributevalueassociatedtothecellorpixelcanberegardedasanattributeinthevectormodel.DataWarehousingandOLAPTheimportanceofdataanalysishasincreasedsignificantlyinrecentyearsasorganizationsinallsectorsarerequiredtoimprovetheirdecision-makingprocessesinordertomaintaintheircompetitiveadvantage.WesaidbeforethatOLAP(OnLineAnalyticalProcessing)(Kimball,1996;Kimball&Ross,2002)comprisesasetoftoolsandalgorithmsthatallowefficientlyqueryingdatabasesthatcontainlargeamountsofdata.Thesedatabases,usuallydesignedforread-onlyaccess(ingeneral,updatingisperformedoff-line),aredenoteddatawarehouses.Datawarehousesareexploitedindifferentways.OLAPisoneofthem.OLAPsystemsarebasedonamultidimensionalmodel,whichallowsabetterunderstandingofdataforanalysispurposesandprovidesbetterperformanceforcomplexanalyticalqueries.Themultidimensionalmodelallowsviewingdatainann-dimensionalspace,usuallycalledadatacube(Kimball&Ross,2002).Inthiscube,eachcellcontainsameasureorsetof(probablyaggregated)measuresofinterest.Thisfactualdatacanbeanalyzedalongdimensionsofinterest,usuallyorganizedinhierarchies(Cabibbo&Torlone,1997).ThreetypicalwaysofOLAPtoolsimplementationexist:MOLAP(standingformultidimensionalOLAP),wheredataisstoredinproprietarymultidimensionalstructures,ROLAP(relationalOLAP),wheredataisstoredin(object)relationaldatabases,andHOLAP(standingforhybridOLAP,whichprovidesbothsolutions.InaROLAPenvironment,dataisorganizedasasetofdimensiontablesandfacttables,andweassumethisorganizationintheremainderofthepaper.ThereareanumberofOLAPoperationsthatallowexploitingthedimensionsandtheirhierarchies,thusprovidinganinteractivedataanalysisenvironment.WarehousedatabasesareoptimizedforOLAPoperationswhich,typically,implydataaggregationorde-aggregationalongadimension,calledroll-upanddrill-down,respectively.Otheroperationsinvolveselectingpartsofacube(sliceanddice)andreorientingthemultidimensionalviewofdata(pivoting).Inadditiontothebasicoperationsdescribedabove,OLAPtoolsprovideagreatvarietyofmathematical,statistical,andfinancialoperatorsforcomputingratios,variances,ranks,etc.Itisanacceptedfactthatdatawarehouse(conceptual)designisstillanopenissueinthefield(Rizzi&Golfarelli,2000).MostofthedatamodelseitherprovideagraphicalrepresentationbasedontheEntity-Relationship(E/R)modelorUMLnotations,ortheyjustprovidesomeformaldefinitionswithoutuser-orientedgraphicalsupport.Recently,MalinowskyandZimányi(2006)proposetheMultiDimmodel.ThismodelisbasedontheE/Rmodelandprovidesanintuitivegraphicalnotation.Alsorecently,Vaisman(Vaisman,2006a,2006b)introducedamethodologyforrequirementelicitationinDecisionSupportSystems,arguingthatmethodologiesusedforOLTPsystemsarenotappropriateforOLAPsystems.TemporalDataWarehousesTherelationaldatamodelasproposedbyCodd(1970),isnotwellsuitedforhandlingspatialand/ortemporaldata.Dataevolutionovertimemustbetreatedinthismodel,inthesamewayasordinarydata.Thisisnotenoughforapplicationsthatrequirepast,present,and/orfuturedatavaluestobedealtwithbythedatabase.Inreallifesuchapplicationsabound.Therefore,inthelastdecades,muchresearchhasbeendoneinthefieldoftemporaldatabases.Snodgrass(1995)describesthedesignoftheTSQL2TemporalQueryLanguage,anupwardcompatibleextensionofSQL-92.Thebook,writtenasaresultofaDagstuhlseminarorganizedinJune1997byEtzion,Jajodia,andSripada(1998),containscomprehensivebibliography,glossariesforbothtemporaldatabaseandtimegranularityconcepts,andsummariesofworkaround1998.Thesameauthor(Snodgrass,1999),inotherwork,discussespracticalresearchissuesontemporaldatabasedesignandimplementation.RegardingtemporaldatawarehousingandOLAP,MendelzonandVaisman(2000,2003)proposedamodel,denotedTOLAP,anddevelopedaprototypeandadatalog-likequerylanguage,basedona(temporal)starschema.Vaisman,Izquierdo,andKtenas(2006)alsopresentaWeb-basedimplementationofthismodel,alongwithaquerylanguage,calledTOLAP-QL.Eder,Koncilia,andMorzy(2002)alsoproposeadatamodelfortemporalOLAPsupportingstructuralchanges.Althoughtheseefforts,littleattentionhasbeendevotedtotheproblemofconceptualandlogicalmodelingfortemporaldatawarehouses.SPATIALDATAWAREHOUSINGANDOLAPSpatialdatabasesystemshavebeenstudiedforalongtime(Buchmann,Günther,Smith,&Wang,1990;Paredaens,VanDenBussche,&Gucht,1994).Rigauxetal.(2001)surveyvarioustechniques,suchasspatialdatamodels,algorithms,andindexingmethods,developedtoaddressspecificfeaturesofspatialdatathatarenotadequatelyhandledbymainstreamDBMStechnology.AlthoughsomeauthorshavepointedoutthebenefitsofcombiningGISandOLAP,notmuchworkhasbeendoneinthisfield.VegaLópez,Snodgrass,andMoon(2005)presentacomprehensivesurveyonspatiotemporalaggregationthatincludesasectiononspatialaggregation.Also,Bédard,Rivest,andProulx(2007)presentareviewoftheeffortsforintegratingOLAPandGIS.Asweexplainlater,efficientdataaggregationiscrucialforasystemwithGIS-OLAPcapabilities.ConceptualModelingandSOLAPRivest,Bédard,andMarchand(2001)introducedtheconceptofSOLAP(standingforSpatialOLAP),aparadigmaimedatbeingabletoexplorespatialdatabydrillingonmaps,inawayanalogoustowhatisperformedinOLAPwithtablesandcharts.TheydescribethedesirablefeaturesandoperatorsaSOLAPsystemshouldhave.Althoughtheydonotpresentaformalmodelforthis,SOLAPconceptsandoperatorshavebeenimplementedinacommercialtoolcalledJMAP,developedbytheCentreforResearchinGeomaticsandKHEOPS,see/en/jmap/solap.jsp.Stefanovic,Han,andKoperski(2000)andBédard,Merret,andHan(2001),classifyspatialdimensionhierarchiesaccordingtotheirspatialreferencesin:(a)non-geometric;(b)geometrictonon-geometric;and(c)fullygeometric.Dimensionsoftype(a)canbetreatedasanydescriptivedimension(Rivestetal.,2001).Indimensionsoftypes(b)and(c),ageometryisassociatedtomembersofthehierarchies.MalinowskiandZimányi(2004)extendthisclassificationtoconsiderthatevenintheabsenceofseveralrelatedspatiallevels,adimensioncanbeconsideredspatial.Here,adimensionlevelisspatialifitisrepresentedasaspatialdatatype(e.g.,point,region),allowingthemtolinkspatiallevelsthroughtopologicalrelationships(e.g.,contains,overlaps).Thus,aspatialdimensionisadimensionthatcontainsatleastonespatialhierarchy.Acriticalpointinspatialdimensionmodelingistheproblemofmultiple-dependencies,meaningthatanelementinonelevelcanberelatedtomorethanoneelementinalevelaboveitinthehierarchy.Jensen,Kligys,Pedersen,andTimko(2004)addressthisissue,andproposeamultidimensionaldatamodelformobileservices,i.e.,servicesthatdelivercontenttousers,dependingontheirlocation.Thismodelsupportsdifferentkindsofdimensionhierarchies,mostremarkablymultiplehierarchiesinthesamedimension,i.e.,multipleaggregationpaths.Fullandpartialcontainmenthierarchiesarealsosupported.However,themodeldoesnotconsiderthegeometry,limitingthesetofqueriesthatcanbeaddressed.Thismeansthatspatialdimensionsarestandarddimensionsreferringtosomegeographicalelement(likecitiesorroads).MalinowskiandZimányi(2006)alsoproposeamodelsupportingmultipleaggregationpaths.Pourabbas(2003)introducesaconceptualmodelthatusesbindingattributestobridgethegapbetweenspatialdatabasesandadatacube.Theapproachreliesontheassumptionthatallthecellsinthecubecontainavalue,whichisnottheusualcaseinpractice,astheauthorexpresses.Also,theapproachrequiresmodifyingthestructureofthespatialdatatosupportthemodel.Noimplementationispresented.Shekhar,Lu,Tan,Chawla,&Vatsavai(2001)introducedMapCube,avisualizationtoolforspatialdatacubes.MapCubeisanoperatorthat,givenaso-calledbasemap,cartographicpreferencesandanaggregationhierarchy,producesanalbumofmapsthatcanbenavigatedviaroll-upanddrill-downoperations.SpatialMeasures.Measuresarecharacterizedintwowaysintheliterature,namely:(a)measuresrepresentingageometry,whichcanbeaggregatedalongthedimensions;(b)anumericalvalue,usingatopologicalormetricoperator.Mostproposalssupportoption(a),eitherasasetofcoordinates(Bédardetal.,2001;Rivestetal.,2001;Malinowski&Zimányi,2004;Bimonte,Tchounikine,&Miquel,2005),orasetofpointerstogeometricobjects(Stefanovicetal.,2000).Bimonteetal.(Bimonteetal.,2005)definemeasuresascomplexobjects(ameasureisthusanobjectcontainingseveralattributes).MalinowskiandZimányi(2004)followasimilarapproach,butdefiningmeasuresasattributesofann-aryfactrelationshipbetweendimensions.DamianiandSpaccapietra(2006)proposeMuSD,amodelallowingdefiningspatialmeasuresatdifferentgranularities.Here,aspatialmeasurecanrepresentthelocationofafactatmultiplelevelsof(spatial)granularity.Also,analgebraofSOLAPoperatorsisproposed.SpatialAggregationInlightofthediscussionabove,itshouldbeclearthataggregationisacrucialissueinspatialOLAP.Moreover,thereisnotyetaconsensusaboutacompletesetofaggregateoperatorsforspatialOLAP.Wenowdiscusstheclassicapproachestospatialaggregation.Hanetal.(1998)useOLAPtechniquesformaterializingselectedspatialobjects,andproposedaso-calledSpatialDataCube,andthesetofoperationsthatcanbeperformedonthisdatacube.Themodelonlysupportsaggregationofspatialobjects.PedersenandTryfona(2001)proposethepre-aggregationofspatialfacts.First,theypre-processthesefacts,computingtheirdisjointpartsinordertobeabletoaggregatethemlater.Thispre-aggregationworksifthespatialpropertiesoftheobjectsaredistributiveoversomeaggregatefunction.Again,thespatialmeasuresaregeometricobjects.Giventhatthisproposalignoresthegeometries,querieslike“totalpopulationofcitiescrossedbyariver”arenotsupported.Thepaperdoesnotaddressformsotherthanpolygons,althoughtheauthorsclaimthatothermorecomplexformsaresupportedbythemethod,andtheauthorsdonotreportexperimentalresults.Withadifferentapproach,Rao,Zhang,Yu,Li,andChen(2003),andZhang,Li,Rao,Yu,Chen,andLiu(2003)combineOLAPandGISforqueryingso-calledspatialdatawarehouses,usingR-treesforaccessingdatainfacttables.ThedatawarehouseisthenexploitedintheusualOLAPway.Thus,theytakeadvantageofOLAPhierarchiesforlocatinginformationintheR-treewhichindexesthefacttable.Althoughthemeasuresherearenotonlyspatialobjects,theproposalalsoignoresthegeometricpartofthemodel,limitingthescopeofthequeriesthatcanbeaddressed.Itisassumedthatsomefacttable,containingtheidentifiersofspatialobjectsexists.Finally,theseobjectshappentobepoints,whichisquiteunrealisticinaGISenvironment,wheredifferenttypesofobjectsappearinthedifferentlayers.Someinterestingtechniqueshavebeenrecentlyintroducedtoaddressthedataaggregationproblem.Thesetechniquesarebasedonthecombineduseof(R-tree-based)indexes,materialization(orpreaggregation)ofaggregatemeasures,andcomputationalgeometryalgorithms.Papadias,Tao,Kalnis,andZhang(2002)introducetheAggregationRtree(aR-tree),combiningindexingwithpre-aggregation.TheaR-treeisanR-treethatannotateseachMBR(MinimalBoundingRectangle)withthevalueoftheaggregatefunctionforalltheobjectsthatareenclosedbyit.Theyextendthisproposalinordertohandlehistoricinformation(seethesectiononmovingobjectdatabelow),denotingthisextensionaRB-tree(Papadias,Tao,Zhang,Mamoulis,Shen,and&Sun,2002).Theapproachbasicallyconsistsintwokindsofindexes:ahostindex,whichisanR-treewiththesummarizedinformation,andaB-treecontainingtime-varyingaggregatedata.Inthemostgeneralcase,eachregionhasaB-treeassociated,withthehistoricalinformationofthemeasuresofinterestintheregion.Thisisaveryefficientsolutionforsomekindsofqueries,forexample,windowaggregatequeries(i.e.,forthecomputationoftheaggregatemeasureoftheregionswhichintersectaspatio-temporalwindow).Inaddition,themethodisveryeffectivewhenaqueryisposedoveraqueryregionwhoseintersectionwiththeobjectsinamapmustbecomputedon-thefly