Efcient SafeRegion Construction for Moving TopK Spatial Keyword Queries Weihuang - Pdf

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Efcient SafeRegion Construction for Moving TopK Spatial Keyword Queries Weihuang

thueducn liguoliangfengjh tsinghuaeducn tanklcompnusedusg ABSTRACT Many realworld applications have requirements to support moving spatial keyword queries For example a tourist look sfortop seafood restaurants while walking in a city She will continu

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Efcient SafeRegion Construction for Moving TopK Spatial Keyword Queries Weihuang






Presentation on theme: "Efcient SafeRegion Construction for Moving TopK Spatial Keyword Queries Weihuang"— Presentation transcript:

0 10 20 30 40 50 60 70 80 90 100 1 5 10 15 20 Server elasped time(ms)k Sense-Approximate Sense-IncreIntersection (a)ServerElapsedTime 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 1 5 10 15 20 Client elasped time(ms)k Sense-Approximate Sense-IncreIntersection (b)ClientElapsedTime 0 10 20 30 40 50 1 5 10 15 20 Transmission(Byte)k Sense-Approximate Sense-IncreIntersection (c)CommunicationCost 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 1 5 10 15 20 Frequencyk Sense-Approximate Sense-IncreIntersection (d)UpdateFrequencyFigure9:Sense-IncreIntersectionvs.Sense-Approximate(varying,California) 0 100 200 300 400 500 600 700 1 5 10 15 20 Server(ms)k MSK Sense (a)ServerElapsedTime 0.001 0.01 0.1 1 10 1 5 10 15 20 Client(ms)k MSK Sense (b)ClientElapsedTime 1 10 100 1000 10000 1 5 10 15 20 Transmission(Byte)k MSK Sense (c)CommunicationCost 0 0.01 0.02 0.03 1 5 10 15 20 Frequencyk MSK Sense (d)UpdateFrequencyFigure11:Comparisonwithstate-of-the-artmethod(varying,California) 0 100 200 300 400 500 600 700 1 5 10 20 50 Server elasped time(ms)Velocity(m/s) MSK Sense (a)ServerElapsedTime 0.001 0.01 0.1 1 10 1 5 10 20 50 Client elasped time(ms)Velocity(m/s) MSK Sense (b)ClientElapsedTime 1 10 100 1000 10000 1 5 10 20 50 Transmission(Byte)Velocity(m/s) MSK Sense (c)CommunicationCost 0 0.01 0.02 0.03 1 5 10 20 50 FrequencyVelocity(m/s) MSK Sense (d)UpdateFrequencyFigure12:Comparisonwithstate-of-the-artmethod(varyingvelocity,California)ingstructurestoimprovetheperformance.Wealsodevel-opedincrementalalgorithmstoecientlycomputethesaferegion.Wehaveimplementedourproposedtechniquesandexperimentalresultsshowthatourmethodsigni“cantlyout-performsstate-of-the-artapproaches.Acknowledgement.ThisworkwaspartlysupportedbytheNa-tionalNaturalScienceFoundationofChinaunderGrantNo.61003004,NationalGrandFundamentalResearch973ProgramofChinaunderGrantNo.2011CB302206,andaprojectofTsinghuaUniversityun-derGrantNo.20111081073,andtheNExTResearchCenterŽfundedbyMDA,Singapore,underGrantNo.WBS:R-252-300-001-490.9.REFERENCES[1]Y.-Y.Chen,T.Suel,andA.Markowetz.Ecientqueryprocessingingeographicwebsearchengines.InConference,pages277…288,2006.[2]G.Cong,C.S.Jensen,andD.Wu.Ecientretrievalofthetop-kmostrelevantspatialwebobjects.,2(1):337…348,[3]J.Fan,G.Li,L.Zhou,S.Chen,andJ.Hu.Seal:Spatio-textualsimilaritysearch.,5(9):824…835,2012.[4]I.D.Felipe,V.Hristidis,andN.Rishe.Keywordsearchonspatialdatabases.In,pages656…665,2008.[5]B.GedikandL.Liu.Mobieyes:Distributedprocessingofcontinuouslymovingqueriesonmovingobjectsinamobilesystem.In,pages67…87,2004.[6]B.Gedik,K.-L.Wu,P.S.Yu,andL.Liu.Motionadaptiveindexingformovingcontinualqueriesovermovingobjects.In,pages427…436,2004.[7]R.Hariharan,B.Hore,C.Li,andS.Mehrotra.Processingspatial-keyword(sk)queriesingeographicinformationretrieval(gir)systems.In,page16,2007.[8]H.Hu,J.Xu,andD.L.Lee.Agenericframeworkformonitoringcontinuousspatialqueriesovermovingobjects.InSIGMODConference,pages479…490,2005.[9]G.Li,J.Xu,andJ.Feng.Desks:Direction-awarespatialkeywordsearch.In,pages459…470,2012.[10]J.Lu,Y.Lu,andG.Cong.Reversespatialandtextualknearestneighborsearch.InSIGMODConference,pages349…360,2011.[11]B.Martins,M.J.Silva,andL.A.Ribeiro.Indexingandrankingingeo-irsystems.In,pages31…34,2005.[12]S.Nutanong,R.Zhang,E.Tanin,andL.Kulik.Thev*-diagram:aquery-dependentapproachtomovingknn,1(1):1095…1106,2008.[13]S.B.RoyandK.Chakrabarti.Location-awaretypeaheadsearchonspatialdatabases:semanticsandeciency.InSIGMODConference,pages361…372,2011.[14]Z.SongandN.Roussopoulos.K-nearestneighborsearchformovingquerypoint.In,pages79…96,2001.[15]Y.TaoandD.Papadias.Time-parameterizedqueriesinspatio-temporaldatabases.InSIGMODConference,pages334…345,2002.[16]Y.Tao,D.Papadias,andQ.Shen.Continuousnearestneighborsearch.In,pages287…298,2002.[17]D.Wu,M.L.Yiu,C.S.Jensen,andG.Cong.Ecientcontinuouslymovingtop-kspatialkeywordqueryprocessing.In,pages541…552,2011.[18]B.Yao,F.Li,M.Hadjieleftheriou,andK.Hou.Approximatestringsearchinspatialdatabases.In,pages545…556,[19]D.Zhang,Y.M.Chee,A.Mondal,A.K.H.Tung,andM.Kitsuregawa.Keywordsearchinspatialdatabases:Towardssearchingbydocument.In,pages688…699,2009.[20]J.Zhang,M.Zhu,D.Papadias,Y.Tao,andD.L.Lee.Location-basedspatialqueries.InSIGMODConference,pages443…454,2003.[21]R.Zhong,J.Fan,G.Li,K.L..Tan,andL.Zhou.Location-AwareInstantSearch.In,2012.[22]Y.Zhou,X.Xie,C.Wang,Y.Gong,andW.-Y.Ma.Hybridindexstructuresforlocation-basedwebsearch.In,pages155…162,2005. 941 10 100 1000 10000 1 5 10 15 20 Server elasped time(ms)k Non-Cache Cache-based (a)California 10 100 1000 10000 1 5 10 15 20 Server elasped time(ms)k Non-Cache Cache-based (b)BeijingFigure7:Evaluationoncache-basedtechnique 1 10 100 1000 10000 1 5 10 15 20 Server elasped time(ms)k Sense-Intersection Sense-IncreIntersection Sense-Approximate (a)California 1 10 100 1000 10000 1 5 10 15 20 Server elasped time(ms)k Sense-Intersection Sense-IncreIntersection Sense-Approximate (b)BeijingFigure8:EvaluationofcomputingmodelonserverSense-ApproximateWefurthercompareApproximateintermsofaverageserverelapsedtime,aver-ageclientelapsedtime,averagecommunicationcost(bytes)andtheupdatefrequencywhichistheratioofthenum-berofqueriesissuedtotheservertothetotalnumberofqueries.Theclientissuedaqueryforeachpointinatra-jectory.ForSense-Approximate,tocalculateweset=1000.Figure9showstheresultsbyvaryingDuetothespaceconstraints,weonlyshowtheresultsontheCaliforniadataset.OntheBeijingdataset,wegotsimilarre-sults.WecanseethatSense-Approximatetooklessservertimeasitusesanapproximatemethodtocomputethesaferegion.AlthoughSense-Approximateinvolvedmoreclienttime,itonlytookabout0.006millisecondswhichisnegli-Sense-Approximateinvolvedmorecommunicationoverheadsinceitneedstointersecthyperbolasandellipseswhichresultsinmorevertexes.Sense-Approximatelargerupdatefrequencyasitestimatedthesaferegionwhichismuchsmallerthantherealsaferegion.Tofurthercomparethetwomethods,weevaluatetheservertimeandcommunicationcostinatimewindow(Wedonotcomparetheclienttimeasitisnegligible).Inourexperiments,thetimewindowsis10minutes.Wecom-paredthetotalserverelapsedtimetoanswerthequeriesinthewindow.Figure10showstheresults.WecanseeSense-Approximatetooklessservertimethan,especiallyforlargervalues.ThisisbecauseSense-Approximateestimatesthesaferegionsandreducesthecomputationtime.Sense-Approximatevolvednearlythesamecommunicationoverheadwith,especiallyforalarge.Thisisbe-causeourapproximatemethodhasbetterapproximationratioforlarger,sinceitenlargesthespaceforlarger6.4Comparisonwithstate-of-the-artmethodAsthestate-of-the-artmethodMSK[17]onlysupport-sthead-hocrankingfunctionasdiscussedinSection2.2,weextendtosupportthesamerankingfunctionandcomparewithit.Figure11showstheresultsbyvarying.Wecanseethatourmethodsigni“-cantlyoutperformsMSKintermsofservertime,clienttime,andcommunicationcost.Themainreasonisasfollows.Forservertime,weusepolarcoordinatestorepresentthesafe 0 5000 10000 15000 20000 1 5 10 15 20 Server elasped time(ms)k Sense-Approximate Sense-IncreIntersection (a)ServerTime 0 1000 2000 3000 4000 5000 1 5 10 15 20 Transmission(Byte)k Sense-Approximate Sense-IncreIntersection (b)CommunicationCostFigure10:Sense-IncreIntersectionvs.Sense-Approximate(for10minutes,California)region,whichismuchmoreecientthantheapproximatebasedmethod.Forthecommunicationcost,MSKneedstoreturnsomeobjectstoavoidinvolvingfalsenegatives.ThatisalsowhytheclienttimeofMSKismuchlargerthan:besidescheckingwhetherthecurrentlocationisinsaferegion,theclienthastoexamineeveryreturnedobjects.andMSKnearlyachievethesameupdatefrequencyastheygeneratesimilarsaferegion.TheonlydierenceisthatMSKapproximatesthesaferegionsusingpolygonsandourmethodcomputestheexactones.Figure12showstheresultsbyvaryingvelocity.Wecanseethatourmethodstillsigni“cantlyoutperformsMSKintermsoftheservertime,clienttime,andcommunicationcost.7.RELATEDWORKTherehavebeenmanystudiesonspatialkeywordsearch[9,7,22,19,18,10,13,1,3,21].Felipeetal.[4]addressed-nearest-neighborproblemwhichreturnsobjectsthatcontainthequerykeywordsandareneartothequeryloca-tion.TheyproposedIR-treebyaddingsignature“lestoR-treenodes.Congetal.[2]proposedtheIR-treewhichcansupportIR-basedrankingfunctions.Zhouetal.[22]andHariharanetal.[7]studiedrange-basedspatialkey-wordsearch,which,givenarectangleandasetofkeywords,“ndsallrelevantanswersthatarelocatedintherectangle.Zhangetal.[19]studiedcollectivekeywordsearch,which“ndsasetofobjectsthatcontainallthequerykeywords.Luetal.[10]studiedreversespatialandtextualneighborsearch.Lietal.[9]studieddirection-awaresearchbyconsideringdirections.Obviouslytheseproblemsared-ierentfromours.Wuetal.[17]studiedmovingspatialkeywordsearch.Howevertheyonlysupportedad-hocrankingfunctions(Sec-tion2.2).Insteadourmethodadoptsageneralrankingfunc-tion.Whenweadaptedourmethodtosupporttheirfunc-tions,ourmethodsigni“cantlyoutperformstheirapproachintermsofbotheciencyandcommunicationcost.Continuousquerieshaveattractedmuchattentionwiththepopularityoflocation-basedservices.Foracontinuousquery,thequerypositionwasmovingwhiletheobjectscanbestatic[15,14,16]ormoving[6,8,5].Weconsidertheformercase.Toavoidrepeatedlyissuingqueries,thesaferegionbasedmethodwasproposed[20,12].Howeverthesestudiesonlyconsideredspatialinformationanddidnottakeintoaccounttextualdescriptions.8.CONCLUSIONInthispaperwehavestudiedthemovingtop-keywordsearchproblem.Foreachquerysubmittedtotheserver,besidesgeneratingtop-answerswealsoconstructeditssaferegion.Weproposedtousehyperbolastorepresen-tthesaferegion.Toecientlycalculatethesaferegion,wedevisedeectivepruningtechniquesandutilizedindex- 940 5.2ApproximateMethodThepreviousmethodscomputetheglobalsaferegion,andinthissectionwecomputealocalsaferegion(denotedbywhichisasubsetoftheexactglobalsaferegion().Astheclientslocationsareusuallynotfarawayfromthecurrentquery,wecanusethelocalsaferegiontoapproximatethesaferegion.ThismethodhasabigadvantagethatitisveryecienttocomputethelocalsaferegionandoutperformsthemethodsinSection5.1.Nextwediscussthedetails.WecantransferourrankingfunctioninEquation1intothefollowingform:q,oq,o q,oInthiswaywecanmodeleachobjectasacirclecenterandradiusof q,o)).Then,q,oq,o=maxq,oA}thecirclecenteredatandradiusof.Foranobject,wehaveq,o,whichisequivalenttoq,o,thusifandonlyifthecircleareinside.SimilarlyanobjectifandonlyifthecirclearenotinsideThensupposetheclientmovestolocation.Letdenotethecirclecenteredatandradiusofq,qisinside,foreachobject,ifisinsideisstillatop-answerofisinsideifandonlyifq,qwhichcanbewrittenasq,qObviouslythelocusofsuchpointsisanellipsewithasthetwofocuses,denotedbyq,q.Obviouslyisalocalsaferegion,thatisifisstilltheanswerset.SinceasstatedinLemma10,isnotempty.GivenaqueryanditsanswersetnotemptyandWecanusethepolarcoordinatetorepresentanellipse.isineachellipse,wecantakeastheoriginofthepolarcoordinateandthuscanecientlycomputetheintersectionoftheellipses.Duetospaceconstraints,weomitthedetailsabouthowtousepolarcoordinatestocomputetheintersection.Asthelocalsaferegionissmall,wecanenlargeitasfollows.BasedonEquation8,ifincreases,theeclipsewillbecomelargerandsowillregion.Thuswecantoenlargethesaferegionasfollows(Figure6(b)).denotethecirclecenteredatradiusof.Wecomputetheellipseq,qandregionObviouslyE\fE.ObviouslydominatestheobjectsoutsideSincetheremaybeotherobjectsinvolvedin,weneedtodeterminewhetherdominatestheseobjects.Letdenotethesetofobjectswhosecorrespondingcirclesinsidecirclebutnotinsidedenotethedominantregionofwhichis.WecantakeasalocalsaferegionsinceasformalizedinLemma11.Forany,wehave(2)IfTherearetwochallenges.The“rstoneishowtocompute.Wecan“ndtheobjectsinusinganyspa-tialindexstructures(whichistheobjectswithdistancetobetween).Thenbasedontheseobjects,wecanecientlycomputebasedonthenon-indexbasedalgorithm.Thesecondoneishowtoselect.Ifissmal-l,thelocalsaferegionissmall,andtheclientquerieshavelargeprobabilitiesoutsidetheregion.Ifislarge,therewillbemoreobjectsin,anditwilltakemoretimetocompute.Thusitisatradeotoselectanap-.Wecandeterminethevaluebasedontheclientmovingspeed(e.g.,meter/persecond).Ifweexpectthequerylocationtobestillinthesaferegionafterweset6.EXPERIMENTWeimplementedourproposedtechniquesandcomparedwiththestate-of-the-artmethodMSK[17].Weuseddisk-basedIR-tree[2]astheindextocomputetheanswersandsaferegions.We“xedthepagesizeat4KB.WeusedtworealspatialdatasetscomposedofPOIsinCaliforniaandBeijing.ThedetailsarelistedinTable2.Werandomlygenerated100querytrajectoriesandeachqueryhad2-5keywords.Eachtrajectoryconsisted1,000pointsandthedistancebetweentwoconsecutivepointswere100meters.AlltheexperimentswereimplementedinJavaandconductedonaLinuxserverwithIntel(R)Xeon(R)2.27GHzCPUand4GBRAM.Table2:DataSets dataset #ofobjects #ofdistinctkey-words avg#ofkeywordsperobject California 544,906 132,552 7.39 Beijing 1,056,770 93,543 4.52 6.1EvaluationofCache-basedTechniqueInthissection,weevaluatethecache-basedtechnique.Weimplementedtwoalgorithms,-Indexwithoutcache-indexwithcache,whereweusedtheincrementalintersectionmethods.Figure7showstheresults.Wecanseethatthecache-basedtechniquecansigni“cantlyimprovetheperformance.Forexample,ontheCaliforniadataset,=20,thecache-basedtimereducesthetimefrom1228millisecondsto55milliseconds.ThisisbecausewecanreducelargenumbersofIOsbyusingcachedinformation.6.2EvaluationofComputingAlgorithmsWe“rstevaluateourdierentmethodstocomputethesaferegion.Weimplementedtreealgorithms,intersectionbasedmethod(),incrementalintersection-basedmethod(),andapproximate-basedmethod(Sense-Approximate).Figure8showstheexperimentalresults.WecanseethatSense-ApproximateoutperformThisisbecausehastotraversethetimes.If=1,achievednearlythesameperformance.Sense-Approximatewasbetterthantheothertwometh-odsasitreducesthenumberofdominantregionsandesti-matesthesaferegionsusingsmallernumbersofdominan-tregions.Asisalwaysbetter,nextweonlycompareSense-Approximate 939 4.4DiscussionsCheckingSafeRegionintheClient:Intheclient,weneedtocheckwhetherthecurrentlocationisinasaferegion.Asweuseapiecewisefunctiontorepresentasaferegion,itisveryecienttodothecheckingasfollows.Assumethecurrentlocationisisii+1](1im,).First,wecomputewhichistheanglefromlinetothe-axis.Supposeosej,j+1),1jm.Wecalculate)whichisthedistancefromtotheboundaryofwiththisangle.Therefore,ifisinside,andthusisstillthebestanswer.Otherwise,theclientshouldsendanewquerytotheserver.Supportingotherfunctions:Ourframeworkcanbeex-tendedtosupporttherankingfunctioninEquation3whichwasusedin[17].Dierentfromourrankingfunction,theshapeofthesaferegionofthisfunctioniscomposedofcir-clesandlines.Wecanextendourtechniquestocomputethedominantregionandthesaferegion.Noticethatintheirwork,theyonlyusepolygonstoapproximatecirclesandtheycannot“ndtheexactsaferegion.Howeverwecanusethepolarcoordinatetoecientlycomputetheexactsaferegion.Duetospaceconstraints,weomitthedetails.5.EXTENDINGOURTECHNIQUESTOSUP-PORTTOP-KQUERIESInthissection,weextendourtechniquestosupporttop-queries.Weproposeanintersection-basedmethodinSec-tion5.1andanapproximatemethodinSection5.2.5.1Intersection-basedMethodTocomputethesaferegionforatop-query,anintu-itivewayisto“rstcomputethesaferegionforeachobjec-totheobjectset(denotedbyandthencomputetheirintersection(Wecancomputebyintersectingthedominantre-gionoftoeveryobject.Thuswehave)asstatedinLemma9.Givenaqueryanditsanswerset,thesaferegioncanbecomputedas:Forexample,inFigure6(a),assume=2.Theshadedregionsrespectivelydenote,andthesaferegionfor.ObviouslythesaferegionofistheintersectionofBasedonLemma9,foreachobject,we“rstcom-andthenintersectforevery.Fortheno-indexbasedalgorithm(Algorithm1),wecaneasilycomputebyreplacing.Fortheindex-basedalgorithm(Algorithm2),duringthetraversaloftheindexingstructure,ifweencounteranobjectin,wejustignoretheobject.Ifweencounteranode,weusethesamemethod,regardlessofwhetherthenodecontainsanobjectin.Themainreasonisasfollows.Ifweprunean-ode,allobjectsunderthenodecoverthesaferegion.Thuswecanusethetwoalgorithmstosupporttop-ForexampleinFigure6(a),consider.We“rstcomputethesaferegionfor,i.e.,.D-ierentfrom“ndingthesaferegionfortop-1answer,wedonotneedtocompute.Then,basedonthesafe o1 o2o3 qo4o5o6o7o8o9o10o11o12o13o14o15o16 00.20.40.60.81 (a)Intersection-based o1o2o3o4o5o6o7o8o9o10o11o12o13o14o15o16q 00.20.40.6 (b)ApproximatemethodFigure6:Supportingtop-regionfor,wetraversetheIR-treeagaintocompute.Theintersectionbetweenisthesaferegion.Nextwediscusshowtocomputetheintersectionofregions.Aseachregioniscomposedbyasetofhyperbolas,itisexpensivetocomputetheintersection.Althoughweusethepolarcoordination,dierentregionshavedierentoriginsandwehavetotransfercoordinates.Toalleviatethisproblem,weuseapolygontoapproximatetheregionasfollows.Foreachcurveoftheregion,ifitisconvex,weusethesegmentbetweenitstwoendpointstoapproximateit;ifthecurveisconcave,weusetangentsinsidethesaferegiontoapproximateit.Noticethatifweusetheindex-basedalgorithm,thismethodneedstoaccessthetimes.Ifislarge,theperformancewillbepoor.Toaddressthisissue,weproposeanalternativemethod.Thebasicideaistocomputetheintersectionduringthetraversaloftheindex,weonlyaccesstheindexonce.Beforeintroducingouridea,we“rstde“nethedominantregionofananswersettoanobjectGivenaquery,thedomi-nantregionof)is:whereObviously.Basedonthisconcept,wepro-posetwoincrementalalgorithms.Fortheno-indexmethod,weonlyneedtousetoreplace.Fortheindex-basedmethod,besidesreplacingforanob-,weneedtorede“nehowtopruneanobject(node).Asmaynotbein,weneedtoreselectalocationwhichmustbein.BasedonLemma3,mustbeinThusweuseq,D)and)todopruning.Wecaneasilydeducealowerboundofthedistancefromtotheboundaryofbasedonthetriangleinequality,i.e.,wesetq,D)isthemaximaldistancefromtotheboundary.Then,wecanuseourframeworktocomputethesaferegion.Asarecomplexregionscomposedbyasetofhyperbolas,itisexpensivetocomputetheregion.Toaddressthisissue,weusepolygonstoapproximatetheregionsasdescribedinSection3.Forexample,inFigure6(a),thedashedlinesrepresenttheboundaryofrespectivelyandtheirin-tersectionis.Intheintersectionmethod,wecomputethesaferegion“rstforandthenfor.Instead,ourin-crementalmethod“rstcomputes,andthencalculatestheirintersectiontogetthesaferegion. 938 o1 o2 o3q o4 o5 o6 o7 o8 o9 o10 o11 o12 o13 o14 o15 o16 N1N2N3N4N5N6N7N8N9N10N11N12N13N14 N15 N13N14 N9N10 N11N12 o1o2 N1N2 o3o4 o5o6 o7o8 o9o10 o11o12 o13o14 o15o16 N3N4 N5N6 N7N8 Inv 1 Inv 5 Inv 2 Inv 3 Inv 6 Inv 7 Inv 4 Inv 8 Inv 9 Inv 10 Inv 11 Inv 12 Inv 13 Inv 14 Inv 15 Inv1 Inv2 ··· k1 N13,N14 N9,N10 ··· k2 N13,N14 N9,N10 ··· k3 N13,N14 N9,N10 ··· k4 N13,N14 N9,N10 ··· k5 N13,N14 N9,N10 ··· Inv8 Inv9 Inv10 ··· k1 o1 o3,o4 o6 ··· k2 o1,o2 o4 o6 ··· k3 o1 o3,o4 o5 ··· k4 o1,o2 o4 o6 ··· k5 o2 o3 o5,o6 ··· )MBRs)IR-tree)InvertedFilesFigure4:IR-tree);and(2)where Basedonthesetwonotations,wecande“neasfollows.Case1:)isthemini-maldistancefromtotheboundaryofthewholeplane,denotedbyCase2:0)=min( Case3:=0.)=min( Case4:)=min(max(0 Case5:)=0.Givenanobjectandanode,theabove-deÞnedfunction)satisÞesisanobjectundernodeWecanprovethatisanobjectundernode.Basedonthisfunction,wecanuseindexestoprunenodes(groupsofobjects)andpro-poseanindex-basedmethod.Thepseudo-codeisshowninFigure5.We“rstinitializesimilartothenon-indexalgorithm(line3-4)andcreateanemptypriority(line5).ThenweinserttherootoftheIR-treein(Line6).Wedequeuethetopelementuntil(line8).If,thealgorithmterminates(line9)sincealldominantregionsofremainingobjectscontainthesaferegion.Ifisanode,wegeteachofitschildren,calculateitsdominantregion),andinsertintowithitscorre-sponding)(line10-13).Ifisanobject,weupdateusingtheintersectionbetweenanditsdominantregion(line15)andalsoupdate(line16).4.3Cache-basedImprovementNotethatbefore“ndingthesaferegion,wemustcom-putetheanswerset.Whencomputing,wehavealreadytraversedtheIR-treeandvisitedsomenodesandobject-s.Tocomputethesaferegion,wemaystillneedtovisitsomeofthesenodesandobjects.Forexample,inFigure4,nodeswillbevisitedtwice.Moreimportant-ly,tocomputetheanswersetandthesaferegion,weusethesamekeywordset.Basedontheseobservations,wecancachesomeinformationtoavoidunnecessarycomputation Algorithm2 :Acollectionofobjects:Aquery:SafeRegionbegin =thebestanswerforquery=thewholeplaneboundingall=anemptypriorityqueue;BuildanIR-treeandinsertrootintoisnotempty ();breakisanode eachchild into else14 R=R\tDo,n;15dmax=MaxBD(o,R);16 end17 Figure5:Sense(Index)Algorithmandfacilitatethesaferegioncomputation.Tothisend,wecachethefollowinginformation.(1)Invertedlists:Whenvisitinganode,theanswercompu-tationstepneedstoloadtheinvertedlistsofquerykeywords.Inthesaferegioncomputationstep,wemaystillusesuchinvertedlists,andthuswecancachethem.(2)KeywordMBR:Inordertoget)foranodewehavetouse)(and)).Themostdirectwayistousetheobjectwhichisnearest(andfarthest).HoweverthismethodisinaccuratesincesomeobjectsintheMBRmaycontainnoquerykeywordandthiskindofobjectswillnotaectthesaferegion.Toimprovetheaccuracy,foravisitednodeintheanswercomputationstep,wecomputeandstoretheMBRthatcontainatleastonekeyword,calledkeywordMBR.WeusethekeywordMBRtoestimatethespatialinformationofthisnode.(3)Scorebounds:Foravisitednodeintheanswercompu-tationstep,foreachnodewecancacheitsvirtualtextualandThusduringtheanswercomputationstep,wecachetheaboveinformation.Theninthesaferegioncomputationstep,wecanutilizesuchinformationforpruningandthuscanimprovetheeciency.Thecache-basedmethodhasthefollowingtwoadvantages.First,asIR-treeisadisk-basedstructure,itisexpensivetoaccessnodesmultipletimesfromthediskandthecache-basedmethodcanreducethenum-berofdiskaccesses.Second,wecanestimatethedominantregionforeachobjectmoreaccurately. 937 anobject,let)denotethemin-imumdistancefromtotheboundary.Noticethatif,wehaveasformalizedinLemma6,andthuswecanpruneobjectGivenaregionandobject,ifGivenanobject,nextwediscusshowtocomputetheCase1:isthewholeplane,and)istheminimaldistancefromtothebound-aryoftheplane;Case2:0)isthedistancetotheleftvertexand 2=dist(o,o)+t Case3:=0.isahalf-plane,and Case4:)isthedistancetotherightvertexand 2=dist(o,o)+t Case5:)=0.Case6:).TherewillbenosuchcaseasformalizedinLemma4.AsshowninFigure1, 2=0.MinBD(o4,Do4,o15)=dist(o4,o15) Herewediscusshowtocompute).Letdenotetheintersectionsinamongdomi-nantregionsforeachobjectthathasbeenaddedinto(alsoincludingtheintersectionswiththeboundaryofthewholeplaneandthefourvertexesoftheplaneiftheyareintheregion).Wehave)=maxasstatedinLemma7.Wecaneasilycomputetheintersec-tionsusingthepolarcoordinate.Givenaregioncomputedintheincremen-talalgorithm,wehave)=maxTofacilitatethepruning,weaccessobjectsinascendingordersortedby(o).If,wecanpruneallobjectsafterobject.Basedonthisidea,weintroduceourframeworktocomputethesaferegionandthepseudo-codeisshowninFigure1.We“rstinitializeasthewholeplane(line3-4).Thenwesorttheobjectsbyandcreateapriorityqueue(line5).Wedequeueandgettheobjectwiththeminimalvalue.If,thealgorithmterminates(line8);otherwiseweupdate(line10-11).Forexample,inFigure1,togetthesaferegionofthequery,weinitializeasthewholeplaneandasthedistancefromtothetop-rightcornerof,i.e.,=0.84.Thenwecalculate)foreveryandinsertintothepriorityqueueinorder.The“rstelementinWedequeueitandupdateisstil-l0.84asthetop-rightcornerisstillthefarthestpointto.Nextweprocessobjectsinthesamewayandget27.Forthenextobject,since Algorithm1 :Acollectionofobjects:Aquery:SafeRegionbegin =thebestanswerforquery=thewholeplaneboundingobjectsSortobjectbasedon),andbuildapriorityqueuewiththesortedobjects;isnotempty ();break R=R\tDo,o;10dmax=MaxBD(o,R);11 end12 Figure3:Sense(No-Index)Algorithm(S afe-re gioncon structionformovings patialke ywordqueries),thealgorithmterminates.Thusweonlycomputethedominantregionsfor6objectsandprunetheother9objects.4.2UsingIndexestoImproveOurMethodItisusuallytime-consumingtocompute(o)forallobjectssincetheremaybelargenumbersofobjects.Toaddressthisissue,weutilizespatialstructurestoalleviatetheproblem.Withoutlossofgenerality,weusetheIR-tree[2]asanexample,whichisthestate-of-the-artindextoanswertop-spatialkeywordqueries.Ourmethodcanbeeasilyextendedtosupportotherindexingstructures.IR-treeincorporatesinvertedindexesintoR-treenodes.Foreachleafnode,inadditiontokeepingasetofobjectsintheminimumboundingrectangle(MBR)ofthisnode,foreachkeywordcontainedintheseobjects,italsomaintainsaninvertedlistofobjectsinthenodethatcontainthekeyword.Foreachinternalnode,besideskeepingasetofobjectsunderthisnode,foreachkeyword,italsomaintainsaninvertedlistwhichkeepsalistofitschildrenwhichcontainthekeyword.Figure4showstheIR-treestructure.Thebasicideatousethespatialindextodopruningisasfollows.EachIR-treenodecontainsagroupofobjectsunderthisnode.Wecanestimatethelowerboundofthedominantregionsofobjectsunderthisnode.Iftheesti-mateddominantregioncovers,wecanprunethewholesubtree.AstheIR-treeusesahierarchicalstructure,wecanprunemanyunnecessarynodes.Nextwediscussthedetails.Givenanode,wede“netheminimalbounddistancefornodeandobject,denotedby).Ifisanobjectundernode,wehave,wecanprunenodeThisisbecauseforeachobjectundernode,wehave)asisinside.Thenwediscusshowtode“nethefunction)and)respectivelydenotetheminimalandmaximaldistancefromnodetotheM-BRofnode.Letdenotethesetoftermsunderthisnode.Noticethatforeachterm,itstermfrequen-cyisthelargesttermfrequencyofobjectsunderthisn-odeanditsinversedocumentfrequencyisstill).Let )).Foreachobjectundernode,wehave 936 3.2SafeRegionInthissection,wediscusshowtorepresentthesaferegion.Givenaquery,supposeitstop-1answeris.Basedonthede“nitionofthedominantregion,obviouslythesaferegionistheintersectionofthedominantregionoftoallotherobjects,i.e.,asformalizedinLemma2.Givenaquery,supposeitstop-1answerisInthisway,after“ndingthetop-1answer,wecomputethedominantregionoftoeachobjectThenwecomputetheintersectionofthesedominantregions.NoticethatthesaferegionisalwaysnotemptyandisinasformalizedinLemma3.Foraquery,thesaferegionisalwaysnotemptyandisinSomereadersmay“ndthatinCase3(thedominantregionisempty.Interestingly,wecanprovethatforthebestanswer,thereisnosuchcase,thatis,Givenaqueryanditsbestanswer,foranyobjectNextwediscusshowtorepresentthesaferegion.Recallthedierentshapesofthedominantregions.Itiseasytorepresentplanes,half-planes,andhalf-lines.Howeveritisnoteasytorepresentahyperbola.Ahyperbolaisatypeofconicsection.InaCartesiancoordinatesystem,itisusual-lyrepresentedbyasecond-degreepolynomialoramatrix.Howeveritisveryexpensivetousesuchmethodsanditisalsoinecienttocomputetheintersection.Toaddressthisissue,weintroducetwoalternativemethods.UsingPolygonstoApproximateaHyperbola:thedistancebetweenahyperbolaanditsasymptotestendsto0whentheyapproachin“nity,wecanuseasymptotestoapproximatehyperbola.Forthedominantregioninside(theshadedregioninFigure2(a)),considerthetwohalf-linesstartingfromthevertexwithdirectionsthesameasthetwoasymptotes.denotetheregioninsidethetwohalf-lines(theshad-edpolygonregioninFigure2(a)).Obviouslyisinthedominantregionandweuseittoapproximatetheregion.Similarlyforthedominantregionoutside(theshadedregioninFigure2(b)),considerthetwohalf-linesstartingfromthecenterwithdirectionsthesameasthetwoasymptotes.Letdenotetheregionoutsidethetwohalf-lines(theshadedpolygonregioninFigure2(b)).ObviouslyisinthedominantregionandweuseittoapproximatetheregionoutsideUsingPolarCoordinatestoDenoteHyperbola:proposetousethepolarcoordinatetorepresentahyperbola.Considertwoobjects.Supposethecorrespondingdominantregionisahyperbola,denotedby.Let)denotethebranchnearby).Letdenotethetwodirectrices.Weconstructacoordinatesys-temwheretheoriginisthemidpointbetween,and-axisisthelinepassing,the-axisistheperpendicularbisectorofsegmentbetween.Thedistancefrom)to-axisis e(Ša Consideranypointinbranch.Letp,ldenotethedistancefromtodirectrixp,oWehave d=dist(p,o dist(p,l+d)=e,wheree=c istheeccentricityasdiscussedinSection3.1.LetdenotetheanglebetweenŠ\n-axis.Wehave.As wehave Thus r+cŠa Wecandeducethat 1Šcos e.whereŠarccos(1 e)arccos(1 Inthisway,wecanusethispolarcoordinaterepresenta-tiontodenote.Similarlyfortheotherbranch 1+cos +arccos( Similarlywecanalsousethepolarcoordinatetorepresenttheplane,half-planes,andhalf-lines.Thekeytousepolarcoordinatetorepresentplane,half-planesorhalf-linesistouseittorepresentlines.Consideringline,wedrawitsperpendicularintersectat.Foranypoint,thedistancefromcanberepresented ,whereistheanglebetweenlines.Notethatweneedtotransferthecoordinate.Inthepolarcoordinate,theneworiginis.Forallotherobjects,theoriginisalways.WeneedtoprovethatisinGivenaquery,ifisthebestanswer,thelocationofmustbeinthesaferegionTocomputetheintersectionamongmultiplepolarequa-tions,weuseapiecewisefunctioninapolarcoordinatewiththeoriginof.Thesaferegioncanberepresentedbyy12m4.COMPUTATIONOFSafeRegionInthissectionwestudyhowtocalculatethesaferegion.4.1FrameworkAnaivemethodtocomputethesaferegionisto“rstcalcu-latethedominantregionsoftoallotherobjectsandthencomputetheirintersection.Toimprovetheperformance,weproposeaneectivepruningtechnique.Thebasicideaisasfollows.Considertwoobjects.If,wecanprune.Noticethatitisusuallyhardtodeterminewhether.Toutilizethisidea,weproposeanalterna-tivemethod.Consideraregion.Foranyobject,wecanpruneobjectandobjectwillnotaectthesaferegion.Toachieveourgoal,therearetwochallenges.The“rstoneishowto“ndsuch.Thesecondoneishowtocheck.Toaddressthe“rstchallenge,weproposeanincrementalcomputationmethod.First,weini-tializethesaferegionastheminimumboundingrect-angleofallpoints.Nextforeachobject,wecompute.If,wepruneobject;otherwiseweup-Nextwediscusshowtocheck.Weintroducetwofunctions.As,let)denotethemaximumdistancefromanypoint.Given 935 ratioofthenumberofobjectsintothatofobjectswhosetextualdescriptionscontain.Foreaseofpresentation,ifthecontextisclear,weuse)and),and)and)interchangeably.FortheexampleinFigure1,assume q,oq,o1,andq,oq,oq,o75andq,oq,oq,o85andq,o23.Thetop-1answerisandthetop-2answerisNoticethatourrankingfunctioniswidelyadoptedinex-istingstudies[2,11].AlthoughWuetal.[17]studiedthemovingtop-spatialkeywordqueryproblem,theyusedaveryad-hocrankingfunctionasde“nedbelow.q,oq,o q,oObviouslyourrankingfunctionismoregeneral.Wewilldiscusshowtosupporttheirrankingfunctionandexperi-mentallycomparewiththeirmethodinSection6.3.REPRESENTATIONMODELFORTOP-1QUERIESInthissection,we“rstintroduceaconceptdominantre-inSection3.1,andthenbasedonthede“nitionwediscusshowtorepresentthesaferegioninSection3.2.3.1DominantRegionGivenaqueryandtwoobjects,,theregionisaregionsuchthatifisintheregion,isabetteranswerthan,asde“nedbelow.Givenaquery,thedomi-nantregionofForexample,inFigure1,thedominantregionofistheregionoutsidethedashedline.Thatisifaqueryintheregion,isabetteranswerthanNextwededucehowtorepresentthedominantregion.We“rstintroducetwonotations. BasedonEquation1,)ifandonlyif.Thuswehave,accordingtoDe“nition4.Basedontherelationshipbetween),wecandeterminetheshapeofthedominantregionasfollows(alsoshowninTable1andFigure2).Case1:).Basedonthetriangleinequal-ity,).If),isalwaystrue,thusthedominantre-gionisthewholeplane.Case2:).Basedonthetrianglein-equality,If),isalwaysfalse,thusthedominantregionisempty.Case3:).BasedonCase2,onlythepointsonthehalf-linestartingfromandwithdirection(denotedbyŠ)satisfyTable1:DominantRegion Cases DominantRegion tdist(o,o) wholeplane t=Šdist(o,o) ŠŠ Šdist(o,o) empty t=0 half-plane(inFigure2) 0dist(o,o) inFigure2) Šdist(o,o) inFigure2) (a)- (b)0Figure2:DominantRegion),thusthedominantregionishalf-ŠCase4:=0.Obviouslythelocusof=0istheperpendicularbisectorofsegment whichpartitionsthespaceintotwohalfplanes.ThedominantregionforisthehalfplanethatcontainsCase5:).Thelocusofpointssatisfy-q,oq,oisahyperbolaasitstwofocusesasprovedinLemma1.Letdenotethehyperbolasatisfyingthebranchnearbythefocus(i.e.,satisfyingdenotethebranchnearbythefocus(i.e.,satisfyingistheperpendicularbisectorofsegment dividetheplaneintofourregionsI,II,III,IVasshowninFigure2.Obviouslyinthiscase,thedominantregionforistheregionoutside(i.e.,regioninFigure2).Case6:0.SimilartoCase5,thedominantregionforistheregioninsideinFigure2).,thelocusofpointssatisfyingisahy-perbolawithasitstwofocuses.ThelocusofpointsisthebranchandthatforisthebranchProof.Duetospaceconstraints,weomitallproofs. AsillustratedinFigure2,isthehyperboladerivedfromisthethecenterof,i.e.,themidpointofsegment .NextwegivethebasicparametersandtheirvaluesofhyperbolaFocusesVertices:Thetwonearestpointslocatedatthetwobranch-Semi-focalLength:Thedistancefromonefocustothecenter,denotedby Semi-majorLength:Thedistancefromonevertextothecenter,denotedby Eccentricity:Theparameterdeterminestheshapeofacurve(forallconiccurves),denotedby a. 934 andcomputethesaferegionsimultaneously.Thusthetimeforcomputingthesaferegioncannotbelarge.Toaddressthisissue,wedevelopecientalgorithmsinSection4.Tosummarize,wemakethefollowingcontributions.Weproposeaneectivemodeltorepresentthesaferegionofamovingtop-spatialkeywordquery.Wedeviseecientincrementalalgorithmstoecientlycomputethesaferegion.Wedevelopeectivepruningtechniquestoreducethecomputationtimeontheserverandtheveri“cationtimeontheclient.Experimentalresultsshowthatourmethodachieveshigheciencyandoutperformsexistingmethods.Therestofthepaperisorganizedasfollows.We“rstformulateourprobleminSection2.AmodeltorepresentthesaferegionisdiscussedinSection3.WedeviseecientalgorithmstocomputethesaferegioninSection4.Section5extendsourtechniquestosupportmovingtop-queries.WeconductexperimentalresultsinSection6andreviewrelatedworkinSection7.Section8concludesthepaper.2.PRELIMINARY2.1ProblemFormulationWeadoptaclient-servermodel.Theservercontainsasetofspatio-textualobjects,.Eachobjectcontainsalocationandtextualdescription,denotedby).Inthepaperweconsidertwo-dimensionalspace,and-coordinate-coordinationtodenotealocation.Weuseasetoftermstodenote.Theclientismovingandcontinuouslyissuesatop-spatialkeywordtotheserver.Queryconsistsofaquerylocation,asetofkeywords,andanintegertorestricttheresultsize,denotedby).Foreaseofpresentation,we“rstde“netheanswerofatop-spatialkeywordquery.Definition1(Top-SpatialKeywordQuery).anobjectsetandaquery,theanswerofatop-spatialkeywordqueryisasubsetof,suchthat(1)Thesizeof,i.e.,,andq,oq,owhereisarankingfunctiontoevaluatetherelevancebetweenaqueryandanobject.Thesmallerthevalueis,themorerelevantistheobjecttothequery.WewilldeÞnetherankingfunctioninSection2.2.Forexample,thereisadatasetasshowninFigure1andatop-spatialkeywordquery=((0).Wecangetundertherankingfunctionde“nedinSection2.2.If=2withthesame,thentheanswersetForamovingtop-spatialkeywordquery,inadditionto“ndingtheanswerset,wealsoneedto“ndaregionforquery.Notethatthesaferegiondependsonthekeywordset,andwedenoteitby).Fora)withanewlocation,iftheanswersetofisthesameasthatof.Thuswecanusetheanswersettoanswer.Ifthecontextisclear,)andareusedinterchangeably.Nextweformallyde“nethesaferegionDefinition2(SafeRegion).Givenanobjectsetandaquery,thesaferegionofquery o1o2 o3qo4o5o6o7o8o9o10o11o12o13o14o15o16 0.60.81 Figure1:Dataset(,numbersinbracketsare)andisanylocation.Forexample,inFigure1,theshadowregioninthecenteristhesaferegionfor=1.Thenbasedontheanswersetandthesaferegion,wede“netheanswerofamovingtop-spatialkeywordquery.(MovingTop-SpatialKeywordQuery)Givenanobjectsetandamovingtop-spatialkeyword.Asthequeryismoving,foreachnewlocation,itsansweris,whereisthetop-resultsetofisthecorrespondingsaferegion.Intheclient-servermodel,foraquery,theclient“rstcheckswhether.Ifyes,istheanswerofqueryotherwisetheclientsubmitsthequerytotheserverwhichreturnstheanswersetandthesaferegionofthequery.InourexampleinFigure1,theserverwillreturntheanswersetandasaferegion(shadedintheFigure).Nexttheclientupdatesitslocationandcheckswhetheritisstill.Ifyes,isstilltheanswer;otherwisetheanswerchangesandtheclientissuesanewquerytotheserver.Existingstudies[2]focusontop-spatialkeywordqueriesandtheyproposeecientalgorithmstocomputetheanswer.Inthispaperweemphasizeonhowtocomputethesaferegionandaddresstheresearchchallengesasdis-cussedinSection1.2.2RankingFunctionGivenaqueryandanobject,tocomputetheirrank-ingscoreq,o),wecombinetheirspatialproximitybe-tween,denotedby),andtheirtextualrelevancybetween,denotedby).Therankingfunctionisde“nedasfollows.q,o)+(1))(1)isatuningparametertotrade-otheimportancebetweenthespatialdistanceandtextualrelevancy.Noticethatintherankingfunction,wenormalize)and)to[01]usingtheirpossiblemaximumvalues.Inthepaper,weusetheEuclideandistance(function)tocomputethespatialdistance()betweentwolocations,andadoptthewell-knownfunctiontoevaluatethetextualrelevancy()asfollows.t,o))(2)t,o)isthetermfrequencyofterm)istheinversedocumentfrequencyofterm,i.e.,the 933 EfÞcientSafe-RegionConstructionforMovingTop-KSpatialKeywordQueriesWeihuangHuangGuoliangLiKian-LeeTanJianhuaFengDepartmentofComputerScienceandTechnology,TsinghuaNationalLaboratoryforInformationScienceandTechnology(TNList),TsinghuaUniversity,Beijing,ChinaDepartmentofComputerScience,SchoolofComputing,NationalUniversityofSingapore,Singaporehuangwh10@mails.thu.edu.cn;liguoliang,fengjh@tsinghua.edu.cn;tankl@comp.nus.edu.sgABSTRACTManyreal-worldapplicationshaverequirementstosupportmovingspatialkeywordqueries.Forexampleatouristlook-sfortop-seafoodrestaurantsŽwhilewalkinginacity.Shewillcontinuouslyissuemovingqueries.Howeverexist-ingspatialkeywordsearchmethodsfocusonstaticqueriesanditcallsforneweectivetechniquestosupportmov-ingquerieseciently.Inthispaperweproposeaneectivemethodtosupportmovingtop-spatialkeywordqueries.Inadditionto“ndingtop-answersofamovingquery,wealsocalculateasaferegionsuchthatifanewquerywithalocationfallinginthesaferegion,wecandirectlyusetheanswersettoanswerthequery.Tothisend,weproposeaneectivemodeltorepresentthesaferegionanddeviseecientsearchalgorithmstocomputethesaferegion.Wehaveimplementedourmethodandexperimentalresultsonrealdatasetsshowthatourmethodachieveshigheciencyandoutperformsexistingmethodssigni“cantly.CategoriesandSubjectDescriptorsH.2.8[DatabaseApplications]:SpatialdatabasesGeneralTermsAlgorithms,Design,Experimentation,PerformanceKeywordsMovingTop-SpatialKeywordQueries,SafeRegion1.INTRODUCTIONLocationbasedservices(LBS)haveattractedsigni“cantattentionfrombothindustryandacademiccommunitiesinrecentyears,thankstothemodernmobilephonesandnewInternettechnologies.Manyexistingsystemsprovideuserswithlocation-awaresearchexperiencesbasedonusersloca-tionwhichcanbeeasilygottenfromGPSdevicesequippedinmodernmobilephones.Recentlytherearemanystudiesonlocationbasedservicesandmostofthemaddressthespatialkeywordsearchprob-lem[9,4,2,7],which,givenasetofspatio-textualobjectsPermissiontomakedigitalorhardcopiesofallorpartofthisworkforpersonalorclassroomuseisgrantedwithoutfeeprovidedthatcopiesarenotmadeordistributedforproÞtorcommercialadvantageandthatcopiesbearthisnoticeandthefullcitationontheÞrstpage.Tocopyotherwise,torepublish,topostonserversortoredistributetolists,requirespriorspeciÞcpermissionand/orafee.October29ÐNovember2,2012,Maui,HI,USA.Copyright2012ACM978-1-4503-1156-4/12/10...$15.00.withalocationandtextualdescription(e.g.,pointsofinter-estandgeo-taggeddocuments)andatop-spatialkeywordquerywithalocationandasetofkeywords,“ndstop-vantanswers.Howevertheyfocusprimarilyonstaticqueriesandcannotsupportmovingquerieseciently.Noticethatmanyreal-worldapplicationshaverequirementstosupportmovingspatialkeywordqueries.Forexample,ahousewifeisdrivingtoasupermarketandmaywantto“ndthetop-carparkingplacesŽnearthesupermarket.Sincesheisdriving,herquerylocationiscontinuouslychanging.Asanotherexample,atouristlookingforthetop-2Žwhilewalkinginacitywillrequireamovingquery.Althoughwecanextendexistingmethodstosupportmovingqueriesbyrepeatedlyissuingmultiplequeries,thesemethodshavethefollowinglimitations.First,itincreasesthecommunicationcostbetweentheclient(theuserwhois-suesthequery)andtheserver(thesystemthatprovidesthesearchservice),andalsowastesthebandwidthintransmis-sion.Second,itaggravatesthesystemburdenduetoissuingmultiplerepeatedqueries.Toaddressthisproblem,inthispaperweemphasizeonecientlysupportingmovingtop-spatialkeywordqueries.Weadoptaclient-servermodel.Theclientismovingandcontinuouslyissuesaspatialkeywordquerytotheserver.Theserverreturnsthetop-answersofthequery,aswellasasaferegionoftheanswerset(Wewillformallyde“nethesaferegioninSection2).Thenbeforetheclientissuesanewqueryatanotherlocation,itwill“rstcheckwhetherthenewlocationisstillinthesaferegion.Ifyes,itcanreusetheanswerset;otherwisetheclientneedstoissueaquerywiththenewlocationtotheserver.Obviouslyourmethodnotonlyavoidsunnecessarycommunicationcostbutalsoreducesthesystemburden.NoticethatalthoughWuetal.[17]studiedthemovingtop-spatialkeywordquery,theyusedanad-hocrankingfunction(seeSection2).Incontrast,weuseawidelyadoptedrankingfunction[2,11].Dierentfromexistingstudies[2,4]whichfocusoncom-putingtheanswersetofaquery,weemphasizeonhowtocomputethesaferegion.Thereareseveralresearchchal-lenges.First,howtorepresentthesaferegion?Tradition-alstudiesonspatialdata(withouttextualdescription)useVoronoidiagramstorepresentthesaferegion,whichcanbepre-computedandmaterializedforecientonlinequeryprocessing.Howeversaferegioninourproblemdependsonquerykeywordsandcannotbematerialized.Toaddressthisissue,weproposeaneectiverepresentationmodelinSection3.Second,howtocomputethesaferegion?Foraqueryissuedtotheserver,weneedto“nditsanswerset 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