Scalable Spatio-temporal Continuous Query Processing for Location-aware Services

Transcription

1 Slle Sptio-temporl Continuous uery Proessing for Lotion-wre Servies iopeng iong Mohme F. Mokel Wli G. Aref Susnne E. Hmrush Sunil Prhkr Deprtment of Computer Sienes, Purue University, West Lfyette, IN Astrt Rel-time sptio-temporl query proessing nees to effetively hnle lrge numer of moving ojets n ontinuous sptio-temporl queries. In this pper, we use shre exeution s mehnism to support slility in lotion-wre servers. Our min ie is to mintin query tle tht stores informtion out ontinuous sptio-temporl queries. Then, nswering sptio-temporl queries is strte s sptil join mong the moving ojets n queries. Three query join poliies re propose iming to minimize the ost of the join opertion uner the shre exeution prigm, nmely the Clok-triggere Join Poliy, the Inrementl Join Poliy, n the Hot Join Poliy. We introue the onept of No-Ation Region tht is use in onjuntion with the hot join poliy. We propose lgorithms tht lulte the No-Ation region for ojets n queries. Experimentl performne emonstrtes tht the No-Ation region is more effiient thn other pprohes when use long with the hot join poliy. Experiments lso emonstrte tht the hot join poliy outperforms the lok-triggere join poliy n the inrementl join poliy in terms of oth I/O n CPU osts. Introution Comining the funtionlity of personl lotor tehnologies, glol positioning systems (GPSs), wireless n ellulr telephone tehnologies, n informtion tehnologies enles new environments where virtully ll ojets of interest n etermine their lotions. These tehnologies re the fountion for pervsive lotion-wre environments n servies. This work ws supporte in prt y the Ntionl Siene Fountion uner Grnts IIS-9, EIA-997, IIS , IIS-9, EIA-999, n NSF -CCR. Lotion-wre environments hve the following istinguishe hrteristis: () A lrge numer of ojets n lrge numer of queries intereste in these ojets, () Most of the queries issue to the lotionwre server re ontinuous sptio-temporl queries. Unlike snpshot queries tht re evlute only one, ontinuous queries require ontinuous evlution s the query result eomes invli with the hnge of informtion, n () ueries s well s ojets hve the ility to e sttionry or moving. Thus lotionwre server shoul hve the ility to support wie vriety of ontinuous sptio-temporl queries, e.g., sttionry queries on moving ojets, moving queries on sttionry ojets, n moving queries on moving ojets. By employing the shre exeution prigm [, 7,, ] in lotion-wre servers, the prolem of onurrently evluting set of ontinuous sptiotemporl queries is strte into sptil join. The min ie is to group the set of ontinuous sptiotemporl queries in one tle lle the query tle. Then, the query tle is joine with nother tle tht ontins the lotions of moving ojets. Thus, inste of hving n evlution pln per query, we hve only one shre query evlution pln for ll queries. In this pper, we fous on relizing the join opertion of the shre exeution prigm to support ll mutility vritions of ontinuous sptio-temporl queries. We propose three join poliies tht im to minimize the numer of omputtions. In ition, we propose the notion of No-Ation Region, whih is the region tht n ojet or query n move insie without ffeting the ltest reporte result of ny ontinuous query. No-Ation Regions re utilize to minimize the require join opertions in shre exeution query pln. Although our fous is on ontinuous sptiotemporl rnge queries, the ies n onepts re pplile to other kins of ontinuous sptio-temporl queries. The ontriutions of this pper re summrize s follows:

2 . We utilize the shre exeution of sptio-temporl queries to hieve slility in terms of lrge query n ojet numers, n strt the prolem of evluting multiple ontinuous sptiotemporl rnge queries to the sptil join prolem.. We propose three join poliies; the Clok-triggere Join Poliy, the Inrementl Join Poliy, n the Hot Join Poliy tht join set of sptio-temporl ojets with set of sptio-temporl queries. The three join poliies fit with the shre exeution prigm.. We propose the onept of No-Ation Region tht generlizes the onepts of vliity region [] n sfe region []. The No-Ation region onept is use in onjuntion with the Hot Join Poliy to minimize the numer of join opertions.. We provie omprehensive set of experiments tht show the performne of the propose join poliies. In ition, we show tht utilizing No- Ation regions is more effiient thn utilizing vliity regions or sfe regions. The rest of the pper is orgnize s follows: Setion gives some preliminries tht re use throughout the pper. In Setion, we introue the shre exeution prigm tht is use s mens for hieving slility in lotion-wre servers. Setion proposes three join poliies tht fit with the shre exeution prigm. Setion 5 provies n extensive set of experiments to stuy the performne of the propose join poliies n No-Ation regions. In Setion, we highlight relte work for ontinuous sptio-temporl query proessing. Finlly, Setion 7 onlues the pper. Preliminries. Lotion-wre Environment Moel In this setion, we riefly introue the Pervsive Lotion Awre Computing Environments Projet (PLACE); projet eing evelope t Purue University [, ]. Lotion-etetion evies (e.g., GPS evies) provie the ojets with their geogrphi lotions. Ojets onnet iretly to regionl servers tht hnle the inoming t n proess time-ritil sptio-temporl queries. Regionl servers ommunite with eh other, s well s with higher level repository servers. The PLACE server keeps trk of sttionry ojets (e.g., gs sttions) s well s moving ojets (e.g., rs). Moving ojets upte their lotion in the PLACE server every T seons. An ojet is onsiere sttionry t the time intervl [T i, T j ] if the server oes not reeive ny upte from o uring this intervl. Moving ojets hve the ility to issue sttionry or moving sptio-temporl queries. To ope with the ontinuous nture of sptio-temporl queries, the PLACE server uptes the nswer of ontinuous sptio-temporl query every T seons.. Sptio-temporl uery Types Unlike tritionl n sptil queries, in sptiotemporl queries, oth ojets n query regions my hnge their lotions over time. In this setion, we lssify the sptio-temporl queries se on the mutility of oth ojets n queries. Moving ueries on Sttionry Ojets. uery regions re moving, while ojets re sttionry. An exmple of this tegory is As I m moving in ertin trjetory, show me ll gs sttions within miles of my lotion. Sttionry ueries on Moving Ojets. uery regions re sttionry, while ojets re moving. An exmple of this tegory is How mny truks re within the ity ounry?. Moving ueries on Moving Ojets. Both query regions n ojets re moving. An exmple of suh queries is As I (the sheriff) m moving, mke sure tht the numer of polie rs within miles of my lotion is more thn ertin threshol. Shre Exeution The min ie ehin shre exeution is to group ll ontinuous sptio-temporl queries in query tle T. In ition, we keep trk of ll the moving ojets in n ojet tle OT tht ontins the reent lotions of moving ojets. Then, the evlution of set of ontinuous sptio-temporl queries is strte s sptil join etween the moving ojets tle OT (tle of points) n the moving queries tle T (tle of query retngles) where the join preite is the ontinment (i.e., fin ll pirs of (p, r) of points n retngles where the point p is ontine in the retngle r). Figure gives the exeution plns of two simple ontinuous sptio-temporl queries, : Fin the ojets insie region R, n : Fin the ojets insie region R. Eh query performs file sn on

3 Ojet uery Ojet uery Ojet uery Selet ID Where lotion insie R Selet ID Where lotion insie R Sptil Join File Sn File Sn File Sn File Sn Hot Col Hot Col Moving Ojets Moving Ojets Moving Ojets Moving ueries R R () CJP () IJP () HJP () Lol query pln for two rnge queries () A glol shre pln for two rnge queries Figure. Illustrtion of join poliies Figure. Shre exeution of ontinuous queries the moving ojet tle followe y seletion filter. With shre exeution, we hve the exeution pln of Figure. The tle for moving queries ontins the regions of the rnge queries. Then, sptil join is performe etween the tle of ojets (points) n the tle of queries (regions). The output of the sptil join is split n is sent to the queries. Shre exeution hs een exploite for ontinuous we queries in the NigrC projet [, 7], for ontinuous streming queries in PSoup [5] n [, 5], n for ontinuous sptio-temporl queries [,, ]. However, the reliztion of the join opertion epens on the unerlying pplition. For exmple, in the se of we queries, the join opertion n use tritionl inex strutures. For streming queries, inexes re not ville. In this pper, we re onerne with sptio-temporl queries. Thus the join opertion etween the ojets n queries is sptil join. For sttionry ojets (e.g., gs sttions), the sptil join n e performe using simple R-tree inex [9] on the ojet tle. Then, queries re use to proe the R-tree s rnge queries. In ontrst, if queries re sttionry n the ojets re moving, n inex on the queries, e.g., the -inex [], n e use to inex the queries rther thn the ojets. Then, the ojets re use to proe the query inex to etermine the queries tht re stisfie y eh ojet. If oth ojets n queries re moving, then we n use sptio-temporl ess methos [7] tht support frequent uptes (e.g., the Lzy Upte R-tree (LURtree) [], n the Frequently Upte R-tree (FURtree) []). In this se, the sptil join opertion n e performe with two R-trees s in []. However, if ojets n queries re highly ynmi, then it is more effiient not to use n inex ut use non-inex sptil join (e.g., [9, ]). The SINA frmework [] utilizes gri-se sptil join to join set of ontinuous moving queries with set of moving ojets. Shre Exeution in Lotion-wre Servers In this setion, we fous on the sptil join opertion etween the ojet n query tles. Ielly, the sptil join shoul e reevlute s soon s n ojet or query reports hnge in lotion. However, with lrge numer of uptes from ojets n/or queries, it eomes imprtil to ontinuously reevlute the sptil join. Thus, we propose three join poliies tht im to provie prtil reliztion of the shre exeution prigm in lotion-wre servers.. POLIC I: Clok-triggere Join Poliy We inlue this si poliy for omprison purposes. The min purpose of the Clok-triggere Join Poliy (CJP, for short) is to voi the ontinuous reevlution of sptio-temporl queries. In the CJP poliy, we reevlute the sptil join every T seons. Thus, for ny evlution time T i, ny hnge in the ojets n/or the queries lotion informtion will not tke effet until the next evlution time T i+ = T i +T. The sptil join is reevlute every T seons y joining ll the reors from the ojet tle with ll the reors from the query tle. A lrger vlue of T woul result in hving long perios of outte results. However, smller vlues of T my result in n exessive numer of omputtions. Typilly, the intervl T is roun one minute [] or 5 seons []. A mjor rwk in the CJP poliy is tht t time T i+, CJP joins ll ojets with ll queries even if most of the ojets n queries i not hnge their lotions from T i.. POLIC II: Inrementl Join Poliy The Inrementl Join Poliy, IJP for short, ims to voi the rwks of the CJP poliy y voiing the reomputtion of the sptil join for ojets n queries tht o not report ny hnge of informtion from the previous evlution time. Figure

4 e f () Snpshot t time T () Snpshot t time T Figure. Exmple of IJP skethes the IJP poliy. The white prts in the ojet n query tles inite the set of ojets n queries tht o not hnge their lotions from the lst evlution time. The she prts in the tles inite the set of ojets n queries tht hnge their lotions from the lst evlution time. Then, the sptil join is performe in two steps: () The set of moving ojets is joine with the set of sttionry queries, () The set of moving queries is joine with ll ojets (sttionry n moving). Notie tht in the first opertion, moving ojets re joine with only sttionry queries. This is minly to voi uplitions in join results tht woul result from the seon opertion where moving queries re joine with moving ojets. Figure gives n exmple of set of ojets n queries. uery n ojets n re the only moving query n moving ojets, respetively, uring the time intervl [T, T ]. Aoring to IJP, n (moving ojets) re joine with, (sttionry queries). In this step, is e into s query result. Then in Step (), (moving query) is joine with, n (ll ojets)., re elete from s query result n is e into s result in this step.. POLIC III: Hot Join Poliy The Hot Join Poliy (HJP, for short) is n enhnement from the inrementl join poliy. At every evlution time T i, moving entities re lssifie into two tegories, nmely, ol n hot entities. An entity is ientifie s ol if its movement hs no effet on the sttus of ny query nswer. On the ontrry, if the entity s movement my use hnges to some query nswers, the entity is ientifie s hot. In orer to ientify n entity s eing hot or ol, we introue the notion of No-Ation Region for eh entity. A No- Ation region is region tht the ojet or the query (tully, the entroi of the query) n move insie without ffeting the ltest result of ny ontinuous An entity is either n ojet or ontinuous query. e f query. At every evlution time, we ientify moving ojet/query s hot if the ojet/query moves out of the former lulte No-Ation region. Otherwise, the ojet/query is ientifie s ol. Figure gives sketh of HJP. The white prts in the ojet n query tles represent the set of ojets n queries tht i not report lotion uptes from the lst evlution time. The she prts mrke s Hot in the tles represent move entities tht eme hot, while the she prts mrke s Col represent move entities tht remin ol. At every evlution time, HJP exeutes the following steps: () Ctegorize every move entity s hot or ol y ompring the entity s urrent position with the former ompute No-Ation region; () The set of hot ojets is joine with ll queries. During this step, the No-Ation region of eh hot ojet is reompute; () The set of hot queries is joine with ll ojets. During this step, the No-Ation region of eh hot query is reompute. We fous on the prolem of omputing the No- Ation regions for ojets n queries in HJP. In the se of moving queries on sttionry ojets, ol n hot entities pply only to queries. So HJP lultes No-Ation regions only for queries. In Setion.., we propose n effiient lgorithm for omputing retngulr No-Ation region for every query. In the ontext of sttionry queries on moving ojets, the onept of ol n hot entities pply only to ojets n it is nturl to ompute No-Ation region for eh ojet. We isuss the lgorithm tht omputes retngulr No-Ation region for eh ojet in Setion... In Setion.., we further introue the notion of Aptive No-Ation regions to el with moving queries on moving ojets, n propose n lgorithm to lulte ptive No-Ation regions. Setion 5 emonstrtes tht the propose No-Ation region lgorithms outperform other lgorithms, e.g., the Vliity Region lgorithm [] n the Sfe Region lgorithm [] when use in onjuntion with HJP... Clulting No-Ation Regions for ueries A No-Ation region is to e use insie HJP for ientifying hot or ol entities. In this setion, we propose n lgorithm for omputing the No-Ation region of eh query in the ontext of moving queries on sttionry ojets. Assume tht entities n move only long xis iretions. Movement in ny other iretion n e projete to movements in oth x- n y-xis iretions. Our lgorithm etermines the mximum istnes

5 Proeure NoAtionRegionCl(q, Oset) Begin //Input: the query q n the ojet set Oset; //Output: the No-Ation region of q.. Divie the t spe into nine non-overlppe regions with s ounries n ounry extensions.. D e,s,w,n = INF INIT. //D e,s,w,n re the mximum istnes q n move in the est, south, west or north iretions, respetively.. For eh ojet o in Oset: () Bse on whih region o lies t, ompute e(o, q), s(o, q), w(o, q) n n(o, q); // e(o, q), s(o, q), w(o, q) n n(o, q) re the mximum istnes tht q n move in the est, south, west or north iretions, respeively, efore o my hnge q s nswer. () D e = min(d e, e(o, q)); D s = min(d s, s(o, q)); D w = min(d w, w(o, q)); D n = min(d n, n(o, q));. q s No-Ation region is forme y the retngle (q.x - D w, q.y - D s, q.x + D e, q.x + D n), where q is the entroi of q. //Assume q is represente y (q.xlow, q.ylow, q.xhigh, q.yhigh). En. Figure. Pseuo oe for omputing the No- Ation region of query query q n move in every xis iretion with the gurntee tht no ojet will enter or leve q s query region. Let D e, D s, D w n D n enote suh mximum istnes in the est, south, west or north iretions, respetively. For simpliity, let D i e ny one of the ove four istnes. Then q s No-Ation region is onstrute s retngle surrouning the entroi of q with extents eing D i istnes in the orresponing xis iretions. It remins to show how to ompute the four D i vlues. Figure gives the pseuo oe for omputing the No-Ation region for query q. The whole spe is ivie into nine non-overlppe regions y q s ounries n ounry extensions (Step in Figure ). These regions re mrke s E, S, W, N, C, SE, SW, NW n NE. Figure 5() gives n exmple with one moving query n six sttionry ojets f. Figure 5() illustrtes how s ounries n their extensions ivie the t spe. Let e (o, q), s (o, q), w (o, q), n (o, q) e the mximum istne tht query q oul move towrs the est, south, west, north iretions, respetively, efore q enounters the ojet o The letters E, S, W, N n C inite the regions in the est, south, west, north or Centrl iretions, respetively. () lx l NW ly () () NW Dw W SW D e f D s N D n C S NE E SE e W SW f N C S D D n w De D s () NE E e Centroi of Figure 5. Exmple for omputing the No- Ation region of query tht my hnge q s nswer. We use i (o, q) to refer the ove four vlues. Then D e (D s, D w, D n ) of q is the miniml vlue of e (o, q) ( s (o, q), w (o, q), n (o, q)) mong ll ojets, respetively. Depening on the region, e (o, q), s (o, q), w (o, q) n n (o, q) vlues re ompute in ifferent wys. For n ojet o, if o lies in region C, e (o, q)( s (o, q), w (o, q), n (o, q)) is the shortest istne etween o n q s est (south, west, north) ounry. If o lies in region W, w (o, q) is the shortest istne etween o n q s west ounry, n e (o, q), s (o, q) n n (o, q) re ssigne to infinity sine o oul not e hit y ounries of q if q moves towrs the est, south or north iretions. Similrly, if o lies in the regions E, S or N, then e (o, q), s (o, q) or n (o, q), respetively, is the shortest istne etween o n q s est, south or north ounry, n ll other three vlues re ssigne to infinity. In the se o is in ny orner region, i.e., in SE, SW, NW or NE, our lgorithm omputes the four (o, q) istnes s follows. Assume tht there is vetor l pointing from the vertex of q tht is nerest to o. Then l is the shortest pth from q to o. Projeting l to the x- n y-xes, we get the two projete vetors l x n l y. If l x > l y, epening on the iretion of l x, e (o, q) or w (o, q) vlue is set to l x. If l x = l y, epening on the iretion of l x n l y, two of the four i (o, q) vlues re set to l x. All the other unssigne i (o, q) vlues re set to infinity. For exmple, onsier the ojet in Figure 5(). In Figure 5(), l is the shortest pth from to o. Sine l x > l y (>) n the iretion for l x is to the west, w (, ) is set to SE

6 n e (, ), s (, ), n (, ) re set to infinity. Oserve tht efore q s ounry hits o, q nees to move t lest l x long l x s iretion or l y long l y s iretion. By onsiering only the projete istnes only, the ove tehnique vois omplex omputtions. Initilly, ll the four D vlues re ssigne to infinity. (Step in Figure ). These vlues re then upte y the four (o, q) vlues of every ojet(step in Figure ). Figure 5() illustrtes the vlues of (o, q) (in otte lines) n the finl D vlues (in soli lines). Then, the No-Ation region of q is onstrute s retngle surrouning the entroi of q with D istnes s extents in the orresponing xis iretions (Step in Figure ). In Figure 5(), the she re represents the No-Ation region of. Prtilly, ojets tht re fr from q hve little effet on q s No-Ation region. Only the ojets ner query q nee to e proesse. An expne query q from q serves s pre-filter efore omputing the No- Ation region. Hene, only the ojets insie q re onsiere. In tht se the initil D vlues re set s the istnes etween q n q in the orresponing xis iretions... Clulting No-Ation Region for Ojets In the se of sttionry queries on moving ojets, No-Ation region is ompute for eh ojet. Here we pt the lgorithm in Setion.. to ompute No-Ation region for ojet in ontrst to queries. We reefine e (o, q), s (o, q), w (o, q) n n (o, q) to e the mximum istne tht ojet o n move towrs the est, south, west, n north iretions, respetively, efore o nees hek for nswer hnges with ny ontinuous query. Eh sttionry query q ivies the t spe into nine regions. Then, the four i (o, q) vlues re etermine similrly s in Setion... The only ifferene is tht the present w (o, q) is equivlent to the former e (o, q) in omputing query s No-Ation region euse now o is moving to q, n not the reverse. Similrly, the present e (o, q), n (o, q), s (o, q) re equivlent to the former w (o, q), s (o, q), n (o, q) vlues, respetively. Let D e, D s, D w, D n e the miniml e (o, q), s (o, q), w (o, q), n (o, q) vlues mong the queries. Then D i vlues re etermine y heking o ginst nery sttionry queries. After etermining the D vlues, the ojet No-Ation region is forme s retngle whose lower-left n upper-right vertexes re (o.x D w, o.y D s ) n (o.x + D e, o.y + D n ). Figure gives n exmple tht omputes the No-Ation region for n ojet o with four sttionry queries () D D n w D D D n e w D e o o D s D s () Figure. Computing the No-Ation region of n ojet to surrouning o. The ompute four D vlues re showe in Figure () n the No-Ation region is forme s the she region in Figure ()... Clulting Aptive No-Ation Regions A No-Ation region is stti n is not pplile in the se of moving queries on moving ojets. In this setion, we exten the notion of No-Ation region to Aptive No-Ation Region tht n e use in HJP to ientify hot or ol entities where oth ojets n queries re moving. Aptive No-Ation regions re lulte for oth ojets n queries. For spe limittions, we only isuss ptive query No-Ation regions. An ptive query No-Ation region is the sme s regulr query No-Ation region exept tht the ptive one my hnge its shpe over time. We mke n ssumption tht the mximum veloity V mx mong ll ojets is known. Assume tht t time t, the No- Ation region for query q is ompute using the proeure N oationregioncl(q, Oset) in Figure. After some time t + t, the No-Ation region is invli euse ojets my hve move towrs q even when q i not move. By hnging the size of No-Ation region, the query No-Ation region n e revlite t time t+ t. During the time intervl t, the istne n ojet moves oes not exee the istne D mx =V mx t. This suggests tht if the former No-Ation region shrinks t ll xis iretions y D mx, we get onservtive No-Ation region. Then, if the entroi of q remins in the upte No-Ation region, q is onsiere ol query with respet to the time t+ t. q is onsiere hot query if q s entroi lies out of the upte No-Ation region. The lgorithm for omputing ptive query No- Ation regions is liste in Figure 7. Figure gives n exmple for omputing ptive No-Ation region

7 Proeure AptiveNARegionCl(q, Oset, t urrent) Begin //Input: the query q, the ojet set Oset n urrent time t urrent; //Output: the upte ptive No-Ation region of q. //D e,s,w,n re efine s in Proeure NoAtionRegionCl(q, Oset); t reent is the timestmp when the No-Ation region of q ws reently ompute or upte. t reent equl to mens q s No-Ation region ws never ompute.. If (t reent is ) then {ompute q s No-Ation region s in Proeure NoAtionRegionCl(q, Oset); store D e, D s, D w, D n; store oorintes of q s urrent entroi C; store t reent = t urrent; return;}. D mx = V mx (t urrent - t reent).. D e = D e - D mx; D s = D s - D mx; D w = D w - D mx; D n = D n - D mx;. if ny of D e, D s, D w, D n, then { q s No-Ation region is set to null; t reent = ; return;} 5. q s No-Ation region is upte s the retngle (C.x - D w, C.y - D s, C.x + D e, C.y + D n); store D e, D s, D w, D n; store t reent = t urrent; return; En. Figure 7. Pseuo oe for omputing ptive query No-Ation region for query. In Figure (), the query retngle of is rwn s soli line n the initil No-Ation region of with respet to four moving ojets to t time step is rwn s she re. Assume tht V mx is one xis unit per one time step. Figure () n Figure () show the upte No-Ation region t time steps n, respetively. The entroi of remins in the upte No-Ation region t time step n, so is ol n vois heking for nswer hnges. Figure () shows tht t time step, the entroi of hs move out of the upte No-Ation region, so eomes hot. In this se, must hek for nswer uptes n reomputes new No-Ation region se on s urrent position. 5 Performne Evlution In this setion, we evlute the performne of poliies n lgorithms eling with ontinuous queries. Setion 5. esries the experimentl settings. In Setion 5., we stuy n ompre the performne of HJP when No-Ation region lgorithms, vliity region [] n sfe region [] re utilize. In Setion 5., we investigte the performne when the server employs ifferent join poliies. Centroi of () Snpshot t T = Centroi of () Snpshot t T = () Snpshot t T = Centroi of Centroi of () Snpshot t T = Figure. Aptive query No-Ation region exmple 5. Experimentl Settings All experiments re performe on Intel Pentium IV CPU.GHz with 5MB RAM running Linux... If not stte otherwise, the t set onsists of, ojets n, ontinuous rnge queries uniformly istriute in the unit squre. The mximum veloity of entities is set to.7 s in [] n []. uery sizes re ssume to e squre regions of sie.. One time step (or yle) is tken to e 5 seons s in []. At eh time step, pre-set perentge of ojets n/or queries is rnomly hosen to move with pre-ssigne veloities. R-trees re implemente n uilt on oth ojets n queries. For ll our experiments, the pge size is KB n the first two levels of R-trees re ssume to resie in min memory. We fous only on the joining performne n ignore the upting osts of R-trees. 5. Performne of HJP First we stuy the performne when the server is running HJP poliy. Figure 9 ompres the performne when the query No-Ation region lgorithm n the vliity region lgorithm [] re respetively use to ientify hot/ol entities. All ojets re sttionry while ll queries re moving t every yle. Figure 9() plots the reution rte omprison up to yles. The reution rte is the frtion of move entities tht re within their vliity region/sfe region/no- Ation region. One query moves out of No-Ation region/vliity region/sfe region, it remins outsie

8 Reution rte.... Vliity Region No-Ation Region Cyle Exeution time (se).... Vliity Region No-Ation Region Cyle Reution rte.... K s K s.k s Cyle Reution rte.... V<=.7 V<=.5 V<=. Cyle () Reution Rte () Exeution Time () Reution Rte () Reution Rte Figure 9. No-Ation region vs Vliity region Figure. Aptive No-Ation region for ojets Reution rte.... Sfe Region No-Ation Region Cyle () Reution Rte Exeution time (se) Sfe Region No-Ation Region Cyle () Exeution Time Figure. No-Ation region vs Sfe region of tht region from then on. In Figure 9(), there re more queries stying in their vliity region thn in their No-Ation region t every yle, whih is euse the vliity region is more preise thn No-Ation region. However the ifferene in reution rte etween the vliity region n No-Ation region is lower thn 5% within yles. Figure 9() shows the umultive exeution time when using vliity region or No-Ation region for HJP. The exeution time onsists of the time of joining hot queries with ojets n the time of reomputing vliity regions/no-ation regions. The umultive time to ompute the vliity region is out six times higher thn the time to ompute the No-Ation region. This is minly euse t eh yle, queries tht hve move out of their vliity region/no-ation region nee to reompute new vliity region/no-ation region, n the omputtion ost of vliity region is muh higher thn tht of No-Ation region. Figure ompres the performne when the server runs HJP when the ojet No-Ation region lgorithm n the sfe region lgorithm [] re use, respetively. Only retngulr sfe regions re ompre. All queries re sttionry n ll ojets re moving t every yle. Figure () gives omprison of the re- ution rte while the Figure 9() gives the umultive exeution times of HJP. Similr to the omprison with vliity regions, the No-Ation region exhiits reution rte ner tht of sfe region n outperforms the sfe region in terms of the totl exeution time when use in HJP. Figure 9 n Figure emonstrte tht the No- Ation region is more effiient thn vliity region n sfe region when use in HJP ue to the muh smller omputtion ost. So we use No-Ation regions with HJP in lter experiments. Next, we exploit some properties of the ptive No- Ation region. Figure () gives the reution rte of ptive No-Ation regions for ojets when the numer of queries hnges from.k to K. We oserve tht when the numer of queries eomes smller, more ojets re moving insie their ptive No-Ation regions. This is euse when less queries exist in the spe, the ensity of queries eomes lower. Thus, the initil ojet No-Ation region s well s the upte No-Ation regions re generlly lrger. An ojet is more likely to remin in the No-Ation region. Figure () stuies the reltionship etween the reution rte of ptive No-Ation regions for ojets n the mximum veloity V mx of queries. The numer of queries is set to K n V mx vries etween. to.7. In Figure (), the ptive No-Ation region shows etter performne when V mx is smller. This is euse t eh yle, the No-Ation region shrinks in ll iretions y D mx =V mx t. Given tht t is fixe, smller V mx results in smller D mx n thus lrger No-Ation region, so the ojet is more likely to sty in the ptive No-Ation region longer. The performne of Aptive No-Ation regions for queries exhiits similr properties n is omitte here for revity.

9 I/O (*) CJP IJP HJP CPU time (ms) Moving perentge of queries(%) 7 5 IJP HJP Moving perentge of queries(%) I/O (*) CJP IJP HJP CPU time (ms) Moving perentge of queries(%) 7 5 IJP HJP Moving perentge of queries(%) () I/O () CPU Time () I/O () CPU Time Figure. Moving queries on sttionry ojets Figure. Moving queries on moving ojets 5. Performne of Join Poliies We ompre the performne when the server runs the three join poliies isusse in this pper. Figure presents the query evlution osts in one evlution yle when the server runs CJP, IJP, or HJP. The perentge of moving queries t every yle vries from % to % while ojets re lwys stti. Both I/O ost n CPU osts re ompre. The I/O ost is mesure s the numer of isk I/Os without ssuming ny uffering effets, n the CPU time is mesure s the time onsume in the memory. For CJP, n R-tree se sptil join lgorithm is implemente []. For IJP n HJP, eh moving (or moving hot) query exploits the ojet R-tree one. Figure () shows the I/O performne of the three poliies. The nive CJP poliy hs onstnt numer of I/O regrless the perentge of moving queries, where every time the whole query tle is joine with the whole ojet tle. As the perentge of moving queries inreses, the numer of I/Os inreses for oth IJP n HJP poliies. However, the reltive enhnement in performne of HJP over IJP inreses. This is euse when more queries re moving, there re more queries remining in the No-Ation region n o not nee to serh the ojet R-tree. Figure () shows the CPU osts for IJP n HJP (CJP is omitte euse its CPU ost is out two orers of mgnitue higher thn the other two). In Figure (), even when onsiering the CPU ost of reomputing the No-Ation region, HJP still hs muh lower CPU ost thn IJP poliy y voiing mny join opertions. The se for sttionry queries on moving ojets exhiits the sme performne trens n is omitte for revity. Figure presents the performne omprison of the three poliies in the se of moving queries on moving ojets. In Figure, the perentge of moving ojets is fixe to % n the perentge of moving queries vries from % to % t every yle. For IJP n HJP, moving (or moving hot) ojets (queries) re use to proe the query (ojet) R-tree. Figure () n Figure () present the I/O n CPU performne, respetively. Agin, CPU ost for CJP is omitte. In oth Figure () n (), HJP hs the lowest I/O n CPU osts euse most of moving entities still remine in their No-Ation region n voi joining osts. The ost sving etween IJP n HJP results from the effet of ptive No-Ation region. Experiments using vrious omintions of perentges of moving ojets n queries re onute, n their results re similr to Figure. We onlue from the experiments tht IJP outperforms CJP for ll omintions of moving n sttionry queries, n HJP outperforms oth IJP n CJP. Relte Work Most of the reserh on ontinuous query proessing in sptio-temporl tses fouses on effiiently evluting one outstning ontinuous query (e.g., see [,,, ]). Conurrent exeution of set of outstning sptio-temporl queries is reently resse for entrlize [, ] n istriute environments [, ]. However, for the entrlize environments [], the fous is only on proessing monitoring queries, e.g., sttionry queries on moving ojets. The Hot Join poliy long with the No-Ation region n support ny non-inexing sptil join (e.g., SINA []) to smrtly hoose the tuples to join. Distriute environments [, ] ssume tht the moving lients hve the pility to shre the proessing with lotion-wre servers. The min ie is to ship some prt of the query proessing own to the moving ojets, while the server minly ts s meitor mong moving ojets. The onept of No-Ation region generlizes the onepts of Vliity region [] n Sfe region []. The Vliity region onept is introue in [] s the re-

10 gion tht moving query n move freely insie without ffeting its results. The vliity region onept works only for the se of sttionry ojets. The Sfe region onept is introue in [] s the region tht moving ojet n move freely insie without ffeting the result of ny outstning ontinuous query. The Sfe region onept works only with sttionry queries. A similr onept is reently introue s the Sfe perio []. The Sfe perio is ompute for eh moving ojet with respet to every sttionry or moving query. Our propose No-Ation region onept generlizes the other onepts where it works in the se of oth ojets n queries re moving n is slle to lrge numers of moving ojets n queries. 7 Conlusion In this pper, we use shre exeution to proess similr sptio-temporl ontinuous queries. By utilizing shre exeution, the prolem of proessing onurrent ontinuous sptio-temporl queries is strte s sptil join prolem. Three query join poliies (the Clok-triggere Join Poliy, the Inrementl Join Poliy n the Hot Join Poliy) re propose uner the shre exeution prigm. CJP joins ll ojets with ll queries t every evlution time. IJP only heks nswer hnges for move entities n voi joining etween unmove ojets n unmove queries. HJP enhnes over IJP y ignoring move entities tht o not ffet query nswers. The No-Ation region is introue to ientify hot n ol entities in HJP. Effiient lgorithms re propose to ompute No-Ation region for oth ojets n queries. Experiment evlution emonstrtes tht No-Ation region, when use in hot join poliy, is more effiient thn vliity region [] n sfe region []. Experiments ompring ifferent poliies show tht HJP outperforms oth the CJP n IJP join poliies in oth I/O n CPU osts. Referenes [] W. G. Aref, S. E. Hmrush, n S. Prhkr. Pervsive Lotion Awre Computing Environments (PLACE). [] L. Arge, O. Proopiu, S. Rmswmy, T. Suel, n J. S. Vitter. Slle Sweeping-Bse Sptil Join. In VLDB, 99. [] T. Brinkhoff, H.-P. Kriegel, n B. Seeger. Effiient Proessing of Sptil Joins Using R-Trees. In P. Bunemn n S. Jjoi, eitors, SIGMOD, 99. []. Ci, K. A. Hu, n G. Co. Proessing Rnge- Monitoring ueries on Heterogeneous Moile Ojets. In Moile Dt Mngement, MDM,. [5] S. Chnrsekrn n M. J. Frnklin. Streming ueries over Streming Dt. In VLDB,. [] J. Chen, D. J. DeWitt, n J. F. Nughton. Design n Evlution of Alterntive Seletion Plement Strtegies in Optimizing Continuous ueries. In ICDE,. [7] J. Chen, D. J. DeWitt, F. Tin, n. Wng. NigrC: A Slle Continuous uery System for Internet Dtses. In SIGMOD,. [] B. Geik n L. Liu. MoiEyes: Distriute Proessing of Continuously Moving ueries on Moving Ojets in Moile System. In EDBT,. [9] A. Guttmn. R-Trees: A Dynmi Inex Struture for Sptil Serhing. In SIGMOD, 9. [] M. A. Hmm, M. J. Frnklin, W. G. Aref, n A. K. Elmgrmi. Sheuling for shre winow joins over t strems. In VLDB,. [] G. Kollios, D. Gunopulos, n V. J. Tsotrs. On Inexing Moile Ojets. In PODS, 999. [] D. Kwon, S. Lee, n S. Lee. Inexing the Current Positions of Moving Ojets Using the Lzy Upte R-tree. In Moile Dt Mngement, MDM,. [] I. Lzriis, K. Porkew, n S. Mehrotr. Dynmi ueries over Moile Ojets. In EDBT,. [] M.-L. Lee, W. Hsu, C. S. Jensen, n K. L. Teo. Supporting Frequent Uptes in R-Trees: A Bottom-Up Approh. In VLDB,. [5] S. Men, M. Shh, J. M. Hellerstein, n V. Rmn. Continuously ptive ontinuous queries over strems. In SIGMOD,. [] M. F. Mokel, W. G. Aref, S. E. Hmrush, n S. Prhkr. Towrs Slle Lotion-wre Servies: Requirements n Reserh Issues. GIS, Novemer. [7] M. F. Mokel, T. M. Ghnem, n W. G. Aref. Sptiotemporl Aess Methos. IEEE Dt Engineering Bulletin, (),. [] M. F. Mokel,. iong, n W. G. Aref. SINA: Slle Inrementl Proessing of Continuous ueries in Sptio-temporl Dtses. In SIGMOD,. [9] J. M. Ptel n D. J. DeWitt. Prtition Bse Sptil- Merge Join. In SIGMOD, 99. [] S. Prhkr,. i, D. V. Klshnikov, W. G. Aref, n S. E. Hmrush. uery Inexing n Veloity Constrine Inexing: Slle Tehniques for Continuous ueries on Moving Ojets. IEEE Trns. on Computers, 5(),. [] Z. Song n N. Roussopoulos. K-Nerest Neighor Serh for Moving uery Point. In SSTD,. []. To, D. Ppis, n. Shen. Continuous Nerest Neighor Serh. In VLDB,. [] J. Zhng, M. Zhu, D. Ppis,. To, n D. L. Lee. Lotion-se Sptil ueries. In SIGMOD,. [] B. Zheng n D. L. Lee. Semnti Ching in Lotion- Depenent uery Proessing. In SSTD,.