Scaling Location-based Services with Dynamically Composed Location Index

Transcription

1 Scaling Location-based Sevices with Dynamically Composed Location Index Bhuvan Bamba, Sangeetha Seshadi and Ling Liu Distibuted Data Intensive Systems Laboatoy (DiSL) College of Computing, Geogia Institute of Technology Abstact Pefomance and scalability of location-based sevices (LBSs) ae cucial to the wide deployment of mobile entepise systems. Location queies ae a fundamental capability of LBSs. Conventional appoaches to location quey pocessing have been centeed on an object-centic achitectue whee static and moving objects ae pocessed unde a unified famewok though an object index o quey index. In this pape, we identify and exploit the pefomance benefit of a location-centic famewok by pomoting a clean sepaation of location quey pocessing ove static objects fom quey pocessing ove moving objects. We show the pefomance benefits of teating locations as fist class citizens instead of objects. Concetely, we develop a fedeated location indexing scheme fo pocessing location queies ove static objects and maintain a gid-based object index fo pocessing queies ove moving objects. Ou expeimental esults demonstate that the location-centic famewok enables highly efficient pocessing of diffeent types of location queies in a mobile envionment, pevails unde all types of quey wokloads compaed to the object-centic appoaches, and in some scenaios it equies as low as only 6% of the IOs equied by a coesponding object index fo quey evaluation. 1 Intoduction Location queies can be classified into two majo categoies depending on the motion popeties of the taget objects being queied. The fist class of location queies consists of location queies ove static objects. An example of such location queies is show me the locations of all gas stations within 5 miles. In this example, the quey issue is called the focal object of the quey and may be a dive on the oad o a pedestian on foot. The second class of location queies compises of location queies ove moving objects. An example of such queies is find all customes who ae looking fo cabs and ae within five miles of my cuent position. In this example both the taget objects of the quey and the issue of the quey ae mobile uses. Most existing eseach effots to date have been dedicated to spatial and tempoal methods fo indexing objects o indexing queies [14, 16, 1, 4]. Even though some indexing techniques such as TPR-tee [16] have shown highe effectiveness in indexing moving objects than static objects, few studies povide an in-depth undestanding of the potential pefomance benefit of sepaating the indexing ove static objects fom the indexing fo moving objects. We show that a clean sepaation of quey pocessing ove static objects fom quey pocessing ove moving objects povides significant pefomance gains fo scaling the pocessing of queies ove a mixed wokload of both types of objects. Pocessing equiements fo evaluating queies ove static objects ae significantly diffeent fom those fo queies ove moving objects. Fo example, queies ove static objects ae typically issued by mobile clients on the move. The taget objects of the queies ae static objects, but the spatial quey ange changes as the quey issue (i.e., the focal object of the quey) moves on the oad. Thus, the set of static objects to be etieved fom the database is highly dependent on the motion behavio and the cuent location of the quey focal object. In contast, queies ove moving objects need to continuously tack the positions of moving objects in the vicinity of the focal object. The ability to efficiently tack the pecise positions of the taget moving objects is citical fo pocessing such queies in tems of both esult quality and system pefomance. Beaing these obsevations in mind, we develop a location indexing famewok to advocate a clean sepaation of static objects fom moving objects in tems of both spatial indexing stuctue and location quey pocessing. By pomoting locations as fist class citizens, we show that the location indexing famewok enables scaling of locationbased sevices. Concetely, we popose to build a location index fo managing all the static objects in tems of thei geogaphical locations in the eal wold. Ou expeimental evaluation shows that ou location indexing famewok can povide fast access capability with low maintenance cost compaed to existing object indexing schemes. Thee ae seveal factos fo such pefomance gains. Fist, location index is seved as a pimay clusteed index, in the sense that all static objects stoed on disk ae odeed by thei locations instead of thei object identifies, thus equiing fewe disk IOs compaed to the existing object indexing schemes. Second, managing moving objects, thei location

2 Univese of Discouse MBR M1 q1 Object Index MBR M1 MBR M <pt, MBR> Object Table Object Position ID x1,y1 x,y x15,y15 x3,y3 x3,y3 x35,y35 x5,y5 Fig. 1: Object-Based Modeling Pages updates, and queies ove moving objects using a sepaate object index, consideably educes the etieval and maintenance costs of indexing stuctues fo both static and moving objects. The pocessing efficiency of location queies ove static objects can be geatly enhanced along seveal dimensions, including educed index size, impoved disk locality, and fast seaches at vaying ganulaity of spatial appoximations. Also, by employing a gid-based indexing scheme fo pocessing location queies ove moving objects, we can educe index maintenance cost in the pesence of location updates of moving objects. Speed up fo quey evaluation is achieved by paallel pocessing, specifically using a location index fo queies ove static objects and gid index fo those ove moving objects. Motivation and Poblem Statement We dedicate this section to discuss the motivation fo ou location-centic famewok fo quey pocessing. An example is used to illustate the key diffeences in tems of pocessing equiements between ou location centic famewok and the object-centic appoach, and the potential inefficiencies associated with the object-centic famewok, especially in the context of pocessing location queies ove static objects. Figue 1 shows a set of static objects in the Univese of Discouse U. Data fo each object in U is epesented by a coesponding enty in the object table. In an object-centic famewok, the data maintained in the object table is indexed by the object ID using a R-tee based object index which uses minimum bounding ectangles (MBRs) to index the objects. Conside a location based quey q1 ove this object table as shown in Figue 1. Assuming that an R-Tee based object index exists, the quey etieves a set of index enties that coespond to the list of objects belonging to the egion being queied by q1. Now fo futhe quey pocessing the object enties need to be etieved fom the table using this index on the object ID column. Howeve, since the data oganization on disk is based on object ID athe than spatial locality, the objects being queied, though in close vicinity, may be spead acoss multiple disk pages esulting in highly inefficient disk bandwidth utilization. Fo instance in this example, five objects eside in the egion being queied by q1. Thus as many as fou diffeent disk Univese of Discouse MBR M1 q1 Location Index MBR M1 MBR M <pt, MBR> Location Pages Table Location PositionObjects ID x1,y1 x,y x3,y3 x41,y41 x4,y4 x43,y43 x44,y44 x45,y45 x5,y5 Fig. : Location-Centic Modeling pages may need to be fetched. Futhemoe, if we incopoate moving objects into this model some of the MBRs may need to be split into smalle ones as new mobile objects join the system, not only inceasing the numbe of MBRs to be maintained in the R-Tee based object index and the index seach cost, but also inceasing the maintenance cost of the index since the location updates of moving objects often cause the mobile objects to be moved fom one MBR to anothe. We each the following conclusions fom the above discussion. Fist, when the system needs to maintain an index fo lage numbe of static and moving objects, such maintenance cost can be significant, since each position update of a moving object equies at least one index seach and one update at each of the coesponding index nodes. Second, the spatial locality of the objects is the dominating popety fo both static and moving objects in a mobile envionment. Location queies typically attempt to etieve objects of inteest within a paticula spatial egion in the vicinity of the focal object. Thus static objects o moving objects within cetain spatial vicinity ae typically accessed togethe. Access of static objects is often sepaated fom the access of moving objects due to the fact that location queies ae typically tageted at eithe static objects o moving objects, but aely tageted at both types. Thus mixing static and moving objects in one index is not an optimal solution fo pocessing location queies. Last but not the least, object-based indexing and stoage of static objects fail to captue the spatial locality-based access pattens fo both disk access and pocessing of queies ove static objects. Thus, object indexing and object-based disk management will lead to inefficient etieval of lage numbe of ielevant object tuples in ode to find the taget objects elevant to a location quey. In ode to benefit fom the popeties associated with static objects, we develop a location indexing famewok that cleanly sepaates static objects fom moving objects. The basic pinciples fo making such a clean sepaation include (1) ceating and maintaining sepaate indexing stuctue fo static objects and moving objects; () developing location index to speed up the etieval of static objects whee location is used as the pimay key instead of objects fo both index seach and disk access; and (3) developing a dedicated object indexing stuctue fo managing moving objects.

3 Ou location indexing famewok offes seveal advantages. Fist, it offes significant pefomance gains by sepaating opeations ove moving objects fom the etieval of static objects. Second, the location indexing famewok encouages highe level of paallel pocessing since queies ove static objects can be pocessed independently fom queies ove moving objects, leading to anothe level of pefomance and thoughput enhancement. Figue displays ou appoach fo location-centic modeling of static objects. Ou appoach fist divides the entie univese of discouse into spatial egions based on factos such as spatial locality, object density and page size. The example in Figue displays a simple gid-based division of the egion. The static object data is oganized in a location-centic manne with spatial locality of objects being mapped to locality of the data on the disk. By enabling the use of spatial locality to access static object data on disk, we impove quey pocessing by making moe efficient use of disk bandwidth. Fo example, as shown in Figue, the data fo the five objects elevant to quey q1 can now be etieved in a single page fetch. Amed with these insights fo location-dependent data, we next descibe ou famewok fo modeling and indexing static data. 3 Location-Centic Famewok In this section we descibe ou appoach towads modeling and indexing location-dependent data in tems of location tuples athe than object tuples. Ou appoach modifies the object-based modeling and indexing appoach to emphasize on modeling static objects with thei location as the pimay key instead of object identifies. As a esult, each elevant location in ou model has one o moe static objects associated with it. A location-centic model fo static objects equies: (1) modeling object tuples as location tuples and, () constucting a location index to efficiently answe queies associated with static objects. 3.1 Location Centic Data Modeling Ou location-centic famewok stoes and etieves static objects in tems of thei spatial locations. In ode to uniquely identify the static objects using thei spatial locations, we build a gid-based ovelay on top of the geogaphical aea of inteest, namely the Univese of Discouse, and use this gid-based layout to detemine the static objects that can be stoed and etieved togethe. The task of ceating a location table consists of the following steps. Step 1 - Detemining gid patition paametes: The fist step in building a location table is to detemine the gid patition paamete β, which detemines the size of each cell depending on the maximum numbe of locations pemitted in a single cell. In geneal, the gid may consist of cells of diffeent sizes dependent upon the distibution of locations of inteest in the Univese of Discouse. Aeas in the Univese of Discouse, which have highe density of elevant locations, will need to be divided into smalle cells to ensue that the numbe of locations in each cell does not L1 R1 R3 L8 R5 L L5 L7 L4 GS1 GS GS3 R L3 R6 L6 R4 L9 Gas Station L5L7 R3 R4 R-Tee R1 R Movie Theate Restauant R5 R6 L4L9 L1 L L8 L3L6 MT1 MT MT3 RE1 RE RE3 Root Node Intemediate Node Leaf Node Location Tuple L Location Tuple L1 Seconday B Tee Index Fig. 3: Location Index An Example exceed the system-defined maximum limit. The decision on the cell size is based on a numbe of factos, including the density distibution of the static objects, the page size of the disk access, the size of a location tuple, to name a few. The goal is to accommodate the data elated to all location points within one cell in a single disk page. We efe eades to ou technical epot [1] fo a discussion on detemining the appopiate values fo the gid cell size. Step - Obtaining elevant locations: Location can efe to a position o a spatial egion. In ou famewok, each location enty in the location table efes to a spatial egion epesented in tems of gid cell. Each enty in the location table is uniquely identified by its location ID and may efe to multiple static objects. We scan the static object table and obtain elevant locations in tems of the gid cell in which they eside. Step 3 - Geneating location identifies: In the next step, we map each location enty to a single cell on the gid and assign a location identifie (lid) to uniquely identify the list of locations within each cell. Each location in a single cell is assigned a unique lid, with all locations belonging to a paticula cell being assigned location identifies in sequential ode. The ode of the location identifies will also detemine the ode in which the tuples ae aanged on disk. Note that odeing of the tuples is impotant fo efficient etieval of static object data as discussed in section. Step 4 - Associating objects with each location: In the final step, all static objects associated with a location enty in the location table ae assigned to the location. We stoe the object identifie oid and associated values fo othe attibutes of the static objects as vectos elated to this paticula location tuple. In case of skewed distibutions, we can constuct a quadtee-based stuctue instead of gid stuctue. Also, if a paticula location tuple has a lage numbe of associated objects leading to an oveflow, we can ceate an oveflow table and povide a pointe to this oveflow table which will stoe the list of objects associated with this location. 3. Location Index In this section we give a detailed desciption of the vaious aspects of the location index. The design of ou location indexing scheme follows a numbe of basic pinciples. Fist, we model spatial locations in tems of two dimen-

4 sional geogaphical coodinates and extend the R-tee data stuctue [5] to model locations as fist class citizens. Fo example, leaf nodes in ou R-tee based location index efe to a set of locations instead of a set of objects. Second, we build the R-tee based location index bottom up though soting ectangles and meging neaby ectangles to fom a hieachical indexing tee stuctue. Thee ae seveal ways to sot the MBR ectangles, such as tee-based vaiations [5,, 18, 3, 17] and methods that use space filling cuves [9, 7]. Accoding to [9], two dimensional Hilbet cuve though centes only (D-c Hilbet) achieves the best clusteing among all space filling cuve algoithms. In this algoithm, each data ectangle is epesented by its cente only. The Hilbet value of the cente is the Hilbet value of the ectangle. The thid design pinciple fo building a high pefomance location index is to balance the access latency to all locations. We build a location index in thee steps. Figue 3 illustates the building of a location index by example. Step 1 - Detemining MBRs associated with each location: The fist step in building a location index fo fast etieval of static objects is to detemine the MBR associated with each location identifie. Figue 3 displays a set of locations (L1, L,, L9), whee each location is epesented by its MBR. A location can be a egion of any shape and be appoximated by its MBR. Step - Constucting R-tee: By soting the MBRs fo locations, an R-tee is constucted bottom up fo indexing the unique locations. The leaf nodes in the R-tee stuctue contain enties of the fom pt,mbr, whee pt is a pointe efeing to a paticula location enty and M BR is the minimum bounding ectangle enclosing this location. Intemediate level nodes contain enties of the fom childpt,mbr, whee childpt is a pointe to a lowe level node in the R-tee and MBR is a egion enclosing the MBRs fo all enties in the child node. Step 3 - Adjusting leaf node pointes: Some leaf nodes may have locations associated with a lage numbe of static objects (hundeds o thousands of offices, stoes, estauants, fo example). One way to handle this situation is to ceate a seconday index ove some othe attibute associated with the static objects at this location, speeding up the access to these objects. The attibute that is fequently used in the filte conditions of location queies is a natual candidate to build such a seconday index. Fo example, in Figue 3 location L7 has a lage numbe of buildings associated with it. In this step, a second level B-tee index is constucted ove the attibute Associated Business fo the static objects associated to the L7 location, allowing us to access these objects in alphabetical ode of thei Associated Business. The pointes fo leaf nodes efeing to such locations ae diected at the oot node of the seconday B- tee index ove the static objects. Fo othe locations in the leaf nodes like L1 o L, which have only a few objects associated with each location, the leaf node points to the location tuple that contains these objects. In geneal seconday B-tee indices ae maintained fo locations with lage num-! "#! "# ' $% &# ( )*+ Fig. 4: Dynamically Composed Location Index be of static objects. The decision is pimaily based on the tade-offs involved in maintaining B-tee indices and the advantage gained in quey pefomance. Ou cuent simulato constucts B-tee indices fo those locations that ae associated with moe than a specified numbe of objects. An update on the location index equies a seach on the R-tee index to fist locate the elevant location which needs to be updated. The list of objects o the B-tee index on the objects is then appopiately updated. Note that the R- tee index is fixed and ideally no locations ae added to o emoved fom the index. 3.3 Dynamic Composition of Location Index The location indexing appoach poposed above can be used to index all elevant locations of inteest in the entie wold. This equies engineeing modifications to enable the system to handle queies efficiently. It is impossible to handle all locations of inteest in a single LI; multiple LIs ae equied to handle the vast magnitude of locationdependent data that is geneated. In ode to answe queies efficiently, it is impotant to build a dynamically composed location index (DCLI) fom seveal smalle LIs. This is handled by engineeing the DCLI as a hieachical stuctue whee we index locations with inceasing esolution in a hieachical manne. Due to space constaints, we biefly explain ou methodology fo constucting a DCLI. The oot node of the DCLI epesents all elevant locations of inteest in the entie wold. The next level in this hieachical stuctue epesents the diffeent continents which ae futhe divided accoding to the geogaphical extent of counties. Lage counties will be divided accoding to natual geogaphical boundaies; fo example, USA can be futhe epesented by the states at the next level of the DCLI. The geogaphical division can be futhe pefomed by splitting states into counties, cities and so on till we ae able to identify a egion with has a easonable numbe of locations of inteest which can be inseted in a single LI. In ode to diect queies to the appopiate LI, we maintain a hashmap which stoes a hash of the path to the LI beginning at the oot node of the hieachical stuctue (the Wold node). Each hash key fo a paticula path is mapped to the oot node of the LI fo the end point of the path. Fo example, the path Wold Euope V atican City is hashed and stoed as a key in

5 ou hashmap. The value fo this key points to the database seve which stoes the LI fo the egion Vatican City. This mapping enables us to diect all queies to the appopiate LI based on the egion of inteest fo the quey. 4 Location Quey Evaluation In this section we descibe ou appoach fo evaluating diffeent types of location queies, simultaneously discussing the concepts associated with each situation. We povide evaluation techniques fo two epesentative types of location queies: Moving Location Queies ove Static Objects and Moving Location Queies ove Moving Objects. In ode to handle moving queies, updating positions of mobile objects is essential fo the pecision and feshness of quey esults. Howeve, fequent updates to the database seve ae expensive in tems of both communication costs and CPU and Disk IO costs fo update pocessing and index maintenance at the database seve. A numbe of techniques have been poposed to handle the location update of mobile objects, which attempt to balance the contasting equiements of pecision of quey esults and limited bandwidth usage. A naive appoach fo updating positions of mobile objects is the peiodical update of object positions in which each moving object epots its cuent position afte an inteval of time. Howeve, this appoach suffes fom low pecision. Moeove, the appoach also leads to a heavy load on the database seve as motion updates to the seve may need to be synchonized in ode to compute quey esults consistently. Modeling motions of the moving objects fo pedicting thei positions is anothe commonly used method in moving object indexing [1]. Motion modeling uses appoximation fo pedicting the position of a moving object based on its available motion paametes using techniques such as dead eckoning. The disadvantage with dead eckoning aises fom the fact that the method is based on estimation, each object needs to sample its motion paametes at egula intevals and may not necessaily epot all updates as soon as they occu. Anothe poblem with these methods is that they might exclude some elevant esults. 4.1 Moving Object Indexing The objective of designing a moving object index is to find a data stuctue that can effectively captue the dynamics of moving objects in tems of thei position changes and be capable of etieving moving objects in a specified location efficiently. We popose to use a gid based index stuctue with pe-defined cells to model and tack the movement of mobile objects. Concetely, we divide the Univese of Discouse in which mobile objects move fom one location to anothe into a numbe of cells of size α. Each moving object will map its cuent position to a paticula gid cell in which it esides. Thus the system uses the cuent gid cell of the moving object to tack its wheeabout. Each moving object is esponsible fo initiating a position update when it moves fom one α-cell to anothe. The database seve is only awae of the cuent gid cell fo each moving object and pocess location queies ove moving objects using the cuent α-cell as the position fo each moving object. Thee ae seveal advantages of using the gid-based appoach fo building a moving object index. Fist, it does not make any assumptions egading the motion paametes of moving objects. Second, the appoach is guaanteed to etun at least all elevant esults fo a location quey and updates esults as motion updates ae eceived. Last but not the least, motion updates ae asynchonous and each object tigges updates when it moves fom one cell to anothe; as updates do not occu at the same time the load on the database seve is distibuted. 4. Quey Evaluation Pocedue We now biefly descibe the evaluation pocedue fo diffeent types of location queies. Moving Quey ove Static Objects: The pocedue fo evaluation of moving queies ove static objects is illustated by an example displayed in Figue 5(a). A location quey q1 is associated with a focal object; the position of this focal object is denoted using the cuent α-cell in which it is located. This α-cell is displayed using a dak gey cell in the figue. As the actual position of the object may lie anywhee inside this α-cell the bounding box fo the quey compises of the MBR fo cicles with adius (adius of quey) dawn at the fou cones of the α-cell. The light gey aea in the figue displays the bounding box fo the quey q1. Any static objects associated with locations lying inside this bounded egion will fom the answe fo the quey. As long as the focal object of the quey emains inside its α-cell, the quey esult will emain unchanged. When the focal object moves to anothe cell, the quey esults need to be evised as the bounding box fo quey q1 will change. Note that the bounding box and MBR fo the quey ae the same in this case. Moving Quey ove Moving Objects: The pocedue fo evaluating moving queies ove moving objects is illustated by example in Figue 5(b). The MBR fo location quey q in Figue 5(b) is defined in a simila manne as the MBR fo location quey q1 in Figue 5(a). The bounding box BB(q) is the set of α-cells intesecting the MBR of the quey. Any moving objects lying within the bounding box ae potential candidates fo answeing the quey and may be etuned as the esults fo the quey q. Each α-cell is associated with a set of queies that have thei bounding box intesecting with this α-cell. When an object moves fom one α-cell to anothe the set of queies associated with both α-cells may need to be updated. Fo each moving quey ove moving objects, the set of moving objects esiding in its bounding box constitute the esult of the quey. 5 Expeimental Evaluation This section descibes thee sets of expeiments fo evaluating the pefomance and effectiveness of ou location index famewok. The fist set of expeiments analyzes the behavio of the location index. The second set of expeiments exhibits the advantages of location indexing ove ob-

6 α α MBR(q1) (a) Moving Quey Static Objects α MBR(q) α BB(q) (b) Moving Quey Moving Objects Fig. 5: Location Quey Evaluation ject indexing fo evaluating queies ove static objects. The thid set of expeiments consides a ealistic envionment compising of static and moving queies ove a set of static and moving objects. 5.1 System Paametes and Setup Fo all ou expeiments, we conside the Univese of Discouse to be a ectangula egion expanding aound 5, sq. miles. Moving o static queies ove moving o static objects ae consideed in each scenaio. Moving queies ae assigned ange values fom the list {1,, 3, 4, 5} miles using a Zipf distibution with paamete.6. Similaly, static queies ae assigned side ange values fom the list {, 3, 4, 6, 8} miles using a Zipf distibution with paamete.6. The above mentioned paametes and default object densities closely follow pevious wok in the aea; objects and queies ae andomly distibuted ove the Univese of Discouse. Moving objects follow andom paths, each motion update will lead to a andom diection and andom speed being chosen fo the object, with object speeds categoized into diffeent values. We conside diffeent classes of moving objects like pedestians (-5 miles/hou), slow moving vehicles (3-6 miles/hou) and fast moving vehicles (7-1 miles/hou). As each object is esponsible fo initiating an update when it moves fom one α-cell to anothe, no infomation egading the motion of the object is equied fo quey evaluation. Both the location index and object index ae R-tee based indices, with a 1 page LRU buffe, each page 4 KBytes in size. Intenal tee nodes have a banching facto of 1 with a fill facto of.7 in ode to optimize pefomance [5]. 5. Location Index vs. Object Index In this set of expeiments we study the advantages of location indexing (LI) ove taditional object indexing (OI). Figue 6(a) plots the size of an OI and the size of the coesponding LI. The simulation setup involves a univese of discouse (UoD) containing 1K static objects. The distibution of static objects in the UoD is vaied so that the aveage numbe of static objects pe location (N static ) inceases fom one to ten. As can be seen in Figue 6(a) inceasing N static does not affect the size of OI as it still needs to index 1K data ectangles. On the othe hand, the size of LI deceases with inceasing N static ; the numbe of ectangles to be indexed by LI deceases, as LI only needs to index (1K/N static ) ectangles. Figue 6(b) plots the total IO opeations equied by both indices as we vay the aveage numbe of static objects pe location. We also vay the numbe of queies (5K-1K) ove the static objects. As can be obseved fom the figue LI, pefoms bette than a coesponding OI ove the static objects. Even with a single object pe location, the location-centic appoach pefoms bette than object-based appoach as etieval of tuples fom the elational table is optimized fo the locationcentic appoach. This is due to the spatial locality of data being mapped to locality of data on disk. Fo N static = 1, bette oganization of data on disk is solely esponsible fo supeio pefomance of LI. As N static inceases, the advantage associated with the LI futhe inceases as seach opeations ae caied out ove a smalle index in case of LI. In fact, with ten objects pe location on an aveage, LI equies only aound 6% of the numbe of IO opeations equied by OI. As the numbe of objects emains the same thoughout the expeiment, the pefomance of OI almost emains the same as we vay N static. Ou simulato can povide appoximations fo disk IOs fo elational data access which is included in the numbe of IOs. The evaluation times fo the same scenaio, as shown in Figue 6(c), show that evaluation ove LI is much faste than evaluation ove OI fo static objects (except fo N static = 1). 5.3 Location Index Pefomance Figue 7 plots the quey evaluation times fo a set of queies ove the location index as the size of the index inceases. The size of the location index is detemined by the numbe of ectangles indexed which depends on the numbe of elevant locations in the UoD. As fo any index stuctue, the quey evaluation pefomance fo the location index declines as the size of the index inceases (Figue 7). The hoizontal lines at t = 3 sec. and t = 6 sec. Evaluation Time (seconds) K Queies 5K Queies 1K Queies Numbe of Indexed Locations (in s) Fig. 7: Evaluation Time vs. Size of Location Index help us benchmak the index pefomance. Depending on the aveage numbe of expected queies the sevice povide may guaantee a cetain Quality of Sevice(QoS), measued in tems of minimum quey evaluation intevals at which use queies can be answeed. Fo example, as can be seen fom the figue, fo a QoS guaantee of t s = 3 sec., if the sevice is expected to handle.5k queies on aveage, then this location index can index aound 115K locations. Howeve, if the sevice is expected to handle 5K queies, the maximum numbe of locations that can be indexed falls to aound 5K.

7 Size of Index (KB) Object Index Location Index Avg. Numbe of Static Objects pe Location (a) Index size Numbe of IO Opeations 3 x 15 1 OI - 5K Queies LI - 5K Queies OI - 1K Queies LI - 1K Queies Avg. Numbe of Static Objects pe Location (b) Numbe of IO Opeations Fig. 6: Compaison of Location Index and Object Index Pefomance 5.4 Location Quey Pefomance Evaluation Now we conside a scenaio involving static and moving objects and display that the location-centic famewok outpefoms object-based modeling and indexing fo a mixed wokload compising of moving and static queies. We compae the pefomance of thee diffeent appoaches in this expeiment. The fist appoach is the taditional object indexing appoach, which equies all static and moving objects to be indexed as an object index. The second appoach indexes locations of all static objects using the LI that we have developed; moving objects ae still indexed using a taditional OI. We efe to this appoach as the LOI appoach. Ou thid appoach indexes locations fo all static objects as a LI and maintains an OI ove positions of moving objects using the gid-based famewok descibed in section 4. We call this appoach the LGI appoach. Fo this set of expeiments, we pefom quey evaluation fo a set of K queies ove a UoD having 1K (5% static and 5% moving) objects Detemining α The paamete α detemines the size of the gid cell fo appoximating positions of moving objects. It is impotant to detemine the optimal value of α fo efficient system pefomance. Numbe of IO Opeations 5 x 15 Update IO 4 Seach IO Total IO Alpha Fig. 8: IO Costs with Vaying α Figue 8 displays the update, seach and total IO costs fo diffeent values of α. Fo this expeiment half of the queies ae ove moving objects and the othe half ove static objects. The following conclusions can be eached fom Figue 8. As α inceases the update IO cost fo the system deceases; lage values of α imply objects will have to tavel geate distances to shift α-cells. Fo lage α values, fewe objects ae expected to shift α-cells fo any time inteval, thus leading to fewe updates. Similaly, the seach IO costs ise with inceasing α values due to lage bounding boxes as explained ealie. α is set to the value which balances the update IO and seach Evaluation Time (seconds) OI - 5K Queies LI - 5K Queies OI - 1K Queies LI - 1K Queies Avg. Numbe of Static Objects pe Location (c) Quey Evaluation Time IO costs thus poviding lowest total IO costs. Fo the cuent set of expeiments, we can obseve that α = 4 is the ideal value Pefomance Evaluation Figue 9(a) plots the numbe of IO opeations equied fo quey evaluation, as we vay the faction of queies ove moving objects and exploe the pefomance of the thee indexing appoaches as discussed above. The coesponding quey evaluation times fo all appoaches ae shown in Figue 9(b). Among queies ove moving objects, half of the queies ae static queies ove moving objects and the othe half ae moving queies ove moving objects. The IO opeations consist of thee diffeent components: (a) object index update IO fo moving objects, (b) object index seach IO and (c) location index seach IO. The OI appoach has just the fist two components as it does not suppot a location index. As can be obseved fom the figue LOI appoach woks much bette than the OI appoach and the LGI appoach outpefoms both the OI and LOI appoaches. Even when all queies ae ove moving objects, LOI appoach woks bette as the object index fo moving objects in the LOI appoach is smalle than the object index of the OI appoach. This is because the object index of the OI appoach indexes static as well as moving objects wheeas the object index in the LOI appoach indexes only the moving objects. As only half the objects ae moving objects, this index is oughly half the size of the index of the OI appoach. The seach component of the IO fo the LOI appoach is much lowe than the seach IO equied by the OI appoach. Futhe, as the pecentage of queies ove moving objects deceases, the diffeence in seach IOs equied by LOI appoach and the OI appoach inceases. As all queies ove static objects ae diected to the location index, the seach pefomance of the LOI appoach compaed to the OI appoach impoves as moe queies ae diected to the location index. LOI appoach has lowe update costs too as updates ae equied ove a smalle index compaed to the OI appoach. The LGI appoach, futhe impoves the associated update costs by adopting a gidbased famewok fo handling moving objects. The seach costs fo the LGI appoach ae a little highe than those fo the LOI appoach. This is simply due to the fact that the bounding boxes fo the queies and MBRs fo moving objects using the gid-based famewok ae lage than the coesponding quey bounding boxes and MBRs based on

8 Numbe of IO Opeations 14 x OI Update IO OI Seach IO LI Seach IO OILOILGI OI LOILGI OI LOILGI OI LOILGI Pecentage of Queies ove Moving Objects (a) Numbe of IO Opeations Evaluation Time (seconds) Index Update Time Index Seach Time OILOILGI OILOILGI OILOILGI OILOILGI Pecentage of Queies ove Moving Objects (b) Quey Evaluation Time Fig. 9: Quey Evaluation Pefomance exact positions of moving objects. Hence, depending on the value of α, the esult sets in the LGI appoach ae a little lage than the esult sets in the LOI appoach. 6 Related Wok Reseach on object indexing in a mobile envionment has been focused eithe on indexing cuent positions of moving objects [6, 16, 1, 4] o indexing the tajectoies of moving objects [14, 13, 11]. R-tee and its vaiants ae the most commonly used indexing stuctues fo spatio-tempoal indexing of mobile objects. Indexing moving object positions poses poblems due to fequent updates to the object positions. To deal with this poblem [15] poposes indexing queies instead of objects fo evaluating static location queies ove moving objects. Some wok attempts to leveage the advantages associated with object indexing and quey indexing by using both types of indexing to pefom quey evaluation [4]. Wok has also been done to intoduce new indexing stuctues like the TPR-tee [16], B+-tee based indexing [8], tajectoy-based indexing [13], and to make the R-tee moe update efficient [1]. Howeve, all eseach exclusively focuses on update and indexing fo mobile objects. Static objects ae simply consideed to be a special case of moving objects whee its velocity is zeo, and thus ae teated in a simila manne as moving objects in most of the liteatues to date. Ou location index and location-centic famewok exploits the pefomance benefits of sepaating static objects fom moving objects and exhibits significant pefomance gains ove conventional object-centic appoaches. 7 Conclusion We have pesented a location-centic famewok that advocates a clean sepaation of static location data fom moving objects in tems of both indexing stuctue and location quey pocessing. We design a location indexing scheme to manage all static objects of inteest, sepaately fom the moving objects and thei location management. Though expeimental evaluation, we show that ou location-centic famewok has a numbe of advantages ove object-based spatial indexing methods, such as significant gain in pocessing efficiency of location queies though educed index size, impoved disk locality, and fast seaches at vaying ganulaity of spatial appoximations. Acknowledgement This eseach is patially funded by gants fom NSF CISE SGER, CSR, and CybeTust pogam as well as an AFOSR gant, an IBM SUR gant, and an IBM faculty awad. Refeences [1] B. Bamba and L. Liu. Scaling Location-based Sevices with Location Indexing. Technical epot, Geogia Institute of Technology, 6. [] N. Beckmann, H. Kiegel, R. Schneide, and B. Seege. The R -tee: An Efficient and Robust Access Method fo Points and Rectangles. In ACM SIGMOD, 199. [3] J. L. Bentley. Multidimensional Binay Seach Tees Used fo Associative Seaching. CACM, 18(9):59 517, [4] B. Gedik, K.-L. Wu, P. S. Yu, and L. Liu. Motion Adaptive Indexing fo Moving Continual Queies ove Moving Objects. In ACM CIKM, 4. [5] A. Guttman. R-tees: A Dynamic Index Stuctue fo Spatial Seaching. In ACM SIGMOD, [6] H. Hu, J. Xu, and D. Lee. A Geneic Famewok fo Monitoing Continuous Spatial Queies ove Moving Objects. In ACM SIGMOD, pages , 5. [7] H. Jagadish. Linea Clusteing of Objects with Multiple Attibutes. In ACM SIGMOD, pages 33 34, 199. [8] C. S. Jensen, D. Lin, and B. C. Ooi. Quey and Update Efficient B+-Tee Based Indexing of Moving Objects. In VLDB, 4. [9] I. Kamel and C. Faloutsos. On Packing R-tees. In ACM CIKM, [1] G. Kollios, D. Gunopulos, and V. J. Tsotas. On Indexing Mobile Objects. In ACM PODS, [11] I. Lazaidis, K. Pokaew, and S. Mehota. Dynamic Queies ove Mobile Objects. In EDBT,. [1] M. L. Lee, W. Hsu, C. S. Jensen, B. Cui, and K. L. Teo. Suppoting Fequent Updates in R-tees: A Bottom-Up Appoach. In VLDB, 3. [13] J. M. Patel, Y. Chen, and V. P. Chakka. STRIPES: An Efficient Index fo Pedicted Tajectoies. In ACM SIGMOD, 4. [14] D. Pfose, C. S. Jensen, and Y. Theodoidis. Novel Appoaches in Quey Pocessing fo Moving Object Tajectoies. In VLDB,. [15] S. Pabhaka, Y. Xia, D. Kalashnikov, W. Aef, and S. Hambusch. Quey Indexing and Velocity Constained Indexing: Scalable Techniques fo Continuous Queies on Moving Objects. IEEE Tansactions on Computes, 51(1): , Octobe. [16] S. Saltenis, C. S. Jensen, S. T. Leutenegge, and M. A. Lopez. Indexing the Positions of Continuously Moving Objects. In ACM SIGMOD,. [17] H. Samet. The Design and Analysis of Spatial Data Stuctues. Addison-Wesley, 199. [18] T. Sellis, N. Roussopoulos, and C. Faloutsos. The R + -tee: A Dynamic Index fo Multidimensional Objects. In VLDB, 1987.