WITH the continued advances in mobile computing and

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1 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 18, NO. 5, MAY Prcessing Mving Queries ver Mving Objects Using Mtin-Adaptive Indexes Bugra Gedik, Student Member, IEEE Cmputer Sciety, Kun-Lung Wu, Senir Member, IEEE, Philip S. Yu, Fellw, IEEE, and Ling Liu, Senir Member, IEEE Abstract This paper describes a mtin-adaptive indexing scheme fr efficient evaluatin f mving cntinual ueries (MCQs) ver mving bjects. It uses the cncept f mtin-sensitive bunding bxes (MSBs) t mdel mving bjects and mving ueries. These bunding bxes autmatically adapt their sizes t the dynamic mtin behavirs f individual bjects. Instead f indexing freuently changing bject psitins, we index less freuently changing bject and uery MSBs, where updates t the bunding bxes are needed nly when bjects and ueries mve acrss the bundaries f their bxes. This helps decrease the number f updates t the indexes. Mre imprtantly, we use predictive uery results t ptimistically precalculate uery results, decreasing the number f searches n the indexes. Mtin-sensitive bunding bxes are used t incrementally update the predictive uery results. Furthermre, we intrduce the cncepts f guaranteed safe radius and ptimistic safe radius t extend ur mtin-adaptive indexing scheme t evaluating mving cntinual k-nearest neighbr ðknnþ ueries. Our experiments shw that the prpsed mtin-adaptive indexing scheme is efficient fr the evaluatin f bth mving cntinual range ueries and mving cntinual knn ueries. Index Terms Mving bject databases, spati-tempral indexing, cntinual ueries. æ 1 INTRODUCTION WITH the cntinued advances in mbile cmputing and psitining technlgies, such as GPS [16], lcatin management has becme an active area f research. Several research effrts have been made t address the prblem f indexing mving bjects r mving bject trajectries t supprt efficient evaluatin f cntinual spatial ueries. Our fcus in this paper is n mving cntinual ueries ver mving bjects (MCQs fr shrt). There are tw majr types f MCQs: mving cntinual range ueries and mving cntinual k-nearest neighbr ueries. Efficient evaluatin f MCQs is an imprtant issue in bth mbile systems and mving bject tracking systems. Research n evaluating range ueries ver mving bject psitins has s far fcused n static cntinual range ueries [19], [11], [3]. A static cntinual range uery specifies a spatial range tgether with a time interval and tracks the set f bjects that lcate within this spatial regin ver the given time perid. The result f the uery changes as the bjects being ueried mve ver time. Althugh similar, a mving cntinual range uery exhibits sme fundamental differences when cmpared t a static cntinual range uery. A mving cntinual range uery has an assciated mving bject, called the fcal bject f the uery [7]; the spatial regin f the uery mves cntinuusly as the uery s fcal bject mves. Mving cntinual ueries intrduce a new challenge in indexing, due mainly t the highly dynamic nature f bth ueries and bjects. MCQs have different applicatins, such as envirnmental awareness, bject tracking and mnitring, lcatin-based. B. Gedik and L. Liu are with the Cllege f Cmputing, Gergia Institute f Technlgy, 801 Atlantic Drive, Atlanta, GA {bgedik, lingliu}@cc.gatech.edu.. K.-L. Wu and P.S. Yu are with the IBM T.J. Watsn Research Center, 19 Skyline Drive, Hawthrne, NY {klwu, psyu}@us.ibm.cm. Manuscript received 6 Jan. 2005; revised 7 Sept. 2005; accepted 25 Oct. 2005; published nline 17 Mar Fr infrmatin n btaining reprints f this article, please send t: tkde@cmputer.rg, and reference IEEECS Lg Number TKDE services, virtual envirnments, and cmputer games, t name a few. Here is an example f a mving cntinual uery, MCQ 1 : Give me the psitins f thse custmers wh are lking fr taxis and are within five miles (f my lcatin at each instant f time r at an interval f every minute) during the next 20 minutes, psted by a taxi driver n the rad. The fcal bject f MCQ 1 is the taxi n the rad. Anther example is MCQ 2 : Give me the number f friendly units within a five-mile radius arund me during the next tw hurs, psted by a sldier euipped with mbile devices marching in the field, r a mving tank in a military setting. The fcal bject f MCQ 2 is the sldier marching in the field r the mving tank. Different specializatins f MCQs can result in interesting classes f MCQs. One is called mving cntinual ueries ver static bjects, where the target bjects are statinary bjects in the uery regin. An example f such a uery is MCQ 3 : Give me the lcatins and names f the gas statins ffering gasline fr less than $1.20 per galln within 10 miles, during the next half an hur, psted by a driver f a mving car, where the fcal bject f the uery is the car n the mve and the target bjects are the gas statins within 10 miles with respect t the lcatin f the car. Anther interesting specializatin is the s called static cntinual ueries ver mving bjects, where the ueries are psed with static fcal bjects r withut fcal bjects. An example uery is MCQ 4 : Give me the list f AAA vehicles that are currently n service call in dwntwn Atlanta (r five miles frm my ffice lcatin), during the next hur. Nte that these specializatins f MCQs are cmputatinally easier t evaluate. Our fcus in this paper is the evaluatin f MCQs in their mst general frm, such as MCQ 1 and MCQ 2. Due t freuent updates t the index structures, traditinal indexing appraches built n mving bject psitins generally d nt wrk well fr MCQs [19], [11]. In rder t tackle this prblem, several researchers have intrduced alternative appraches based n the idea f indexing the /06/$20.00 ß 2006 IEEE Published by the IEEE Cmputer Sciety

2 652 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 18, NO. 5, MAY 2006 parameters f the mtin functins f the mving bjects [12], [20], [24], [1]. They effectively alleviate the prblem f freuent updates t the indexes, as the indexes need t be updated nly when the parameters change. These appraches are mstly based n R-tree-like structures and prduce time-parameterized minimum bunding rectangles that enlarge cntinuusly [20], [24], [19]. As a cnseuence f enlarged bunding rectangles, the search perfrmance can deterirate ver time and the index structures may need t be recnstructed peridically [19], [20]. As far as update csts are cncerned, appraches based n time-parameterized rectangles [20], [24] can prvide excellent perfrmance. Hwever, they are nt sufficient fr prcessing MCQs. This is because they d nt supprt incremental reevaluatin f ueries and the cntinual nature f these ueries dictates that the same ueries must be reevaluated at freuent intervals. Thus, there is a need fr new methds that can evaluate these MCQs incrementally. In this paper, we describe a mtin-adaptive indexing (MAI) scheme fr efficient prcessing f mving cntinual ueries ver mving bjects. It uses the cncept f mtinsensitive bunding bxes (MSBs) t mdel bth mving bjects and mving ueries. Instead f indexing freuently changing bject psitins, we index less freuently changing bject-and-uery MSBs, where updates t the bunding bxes are needed nly when bjects and ueries mve acrss the bundaries f their bxes. This helps decrease the number f updates perfrmed n the indexes. Hwever, the main use f MSBs is t facilitate incremental prcessing f MCQs. We prvide tw techniues t reduce the csts f uery reevaluatin and search n the MSB indexes. First, we ptimistically precalculate uery results and incrementally maintain such predictive uery results under the presence f bject mtin changes. MSBs are used t cntrl the amunt f precmputatin t be perfrmed fr calculating the predictive uery results and t decide when the results need t be updated. Secnd, we supprt mtin-adaptive indexing. We autmatically adapt the sizes f MSBs t the changing mtin behavirs f the crrespnding individual bjects. By adapting t mvingbject behavir at the granularity f individual bjects, the mving ueries can be evaluated faster by perfrming fewer IOs. Furthermre, we extend the MAI apprach t the evaluatin f mving cntinual k-nearest neighbr ueries, by intrducing the cncepts f guaranteed safe radius and ptimistic safe radius that are used t leverage the mving cntinual range ueries fr answering knn ueries. Other interesting cntributins f this paper are the develpment f an analytical mdel fr estimating the cst f mving uery evaluatin and the use f analytical mdels t guide the setting and the adaptatin f several system parameters fr ur prpsed indexing scheme. The prpsed mtin-adaptive indexing scheme is independent f the underlying spatial index structures by design. In the experiments reprted in this paper, we use bth R -trees and statically partitined grids fr measuring the perfrmance f ur indexing scheme. Our experimental results shw that the mtin-adaptive indexing scheme is efficient fr the evaluatin f bth mving cntinual range ueries and mving cntinual k-nearest neighbr ueries. We reprt a series f experimental perfrmance results fr different wrklads, including scenaris based n skewed bjectand-uery distributin, and demnstrate the effectiveness f ur mtin-adaptive indexing scheme thrugh cmparisns with ther alternative indexing appraches. The rest f the paper is rganized as fllws: We discuss the previus wrk in the literature related t uerying and indexing mving bject psitins in Sectin 2. Sectin 3 gives an verview f the basic cncepts and the system mdel. Sectin 4 describes the mtin-adaptive indexing scheme fr efficient evaluatin f mving range ueries. Sectin 5 extends the slutin t the efficient evaluatin f mving knn ueries. Sectin 6 reprts varius perfrmance results t illustrate the effectiveness f the prpsed apprach. We cnclude with a summary in Sectin 7. 2 RELATED WORK Research n mving bject indexing can be bradly divided int tw categries, based n 1) the current psitins f the mving bjects and 2) the trajectries f the mving bjects. Our wrk belngs t the first categry. An essential study dealing with the prblem f indexing and uerying mving bject trajectries can be fund in [18]. Cntinual ueries are used as a useful tl fr mnitring freuently changing infrmatin [25], [14]. In the spatial databases dmain, cntinual ueries are emplyed fr cntinuusly uerying mving bject psitins. Mst f the wrk n cntinual ueries ver mving bject psitins is either n static cntinual ueries ver mving bjects [19], [11], [12], [3], [21], [29], [30] r n mving cntinual ueries ver static bjects [23], [22]. Nne f the these wrks has addressed the prblem f mving cntinual ueries ver mving bjects. In [19], velcity-cnstrained indexing and uery indexing (Q-index) have been prpsed fr efficient evaluatin f static cntinual range ueries. The same prblem is studied in [11]; hwever, the fcus is n in-memry structures and algrithms. In [20], TPR-tree, an R-tree-based indexing structure, is prpsed fr indexing the mtin parameters f mving bjects by using time-parameterized rectangles and answering ueries using this index. TPR -tree, an extensin f TPR-tree-ptimized fr ueries that lk int the future (predictive), is described in [24]. Nte that even thugh TPR-related indexes [20], [24] supprt mving ueries, these mving ueries are predefined regins in the spati-tempral dmain. They are nt the mving cntinual ueries, such as MCQ 1 and MCQ 2, discussed in this paper. Recently, newer indexing schemes that imprve upn the perfrmance f TPR-trees have been intrduced, such as STRIPES [17] and the B þ -tree-based indexing techniue f [10]. Nevertheless, the fcus f these wrks is n develping search-and-update-efficient indexing structures fr managing mving bject lcatins and they d nt have special mechanisms t supprt cntinual ueries, whereas ur fcus is n develping a lgical indexing scheme that leverages already existing indexing structures t supprt efficient prcessing f MCQs thrugh incremental evaluatin. Advanced indexing structures can be integrated int ur MAI apprach by replacing the R -tree-based bject-and-uery indexes we emply. In [2], efficient uery evaluatin techniues fr nearestneighbr (k ¼ 1) and reverse-nearest-neighbr ueries are develped fr mving ueries ver mving bjects. CNN [23] gives an algrithm fr precalculating k-nearest neighbrs with a line segment representing the cntinuus mtin f the uery; hwever, the target bjects are assumed t be static. In [32], techniues based n bjectnly indexing and uery-nly indexing are prpsed t evaluate mving cntinuus knn ueries ver mving bjects. Hwever, the slutin is exclusive t knn ueries. In cntrast, ur apprach supprts range and knn ueries

3 GEDIK ET AL.: PROCESSING MOVING QUERIES OVER MOVING OBJECTS USING MOTION-ADAPTIVE INDEXES 653 TABLE 1 Cmparisn f Mtin-Adaptive Index with Existing Appraches 1. TPR-tree nly supprts mving ueries with predefined paths. 2. CNN has per-result time intervals, nt per-bject. within the same framewrk and uses bject-and-uery indexing at the same time t ptimize the perfrmance fr a large range f parameters that include cases where bjectnly indexing falls shrt, as well as cases where uery-nly indexing is ineffective. The cncept f mving cntinual ueries is t sme extent similar t Dynamic Queries (DQ) [13]. A dynamic uery is defined as a temprally rdered set f snapsht ueries in [13]. This is a lw-level definitin as ppsed t ur definitin f mving cntinual ueries, which is mre declarative and is defined frm the users perspective. The wrk dne in [13] indexes the trajectries f the mving bjects and describes hw t efficiently evaluate dynamic ueries that represent predictable r unpredictable mvement f an bserver. They als describe hw new trajectries can be added when a dynamic uery is actively running. Their assumptins are in line with their mtivating scenari, which is t supprt rendering f bjects in virtual-tur-like applicatins. Our wrk fcuses n realtime evaluatin f mving ueries in real-wrld settings, where the trajectries f the mving bjects are unpredictable and the ueries can ptentially be assciated with mving bjects inside the system. An imprtant feature f ur apprach is its mtin adaptiveness, allwing the uery evaluatin t be ptimized accrding t the dynamic mtin behavir f the bjects. Our experiments have shwn that such mtin-adaptive capability ffers significant perfrmance gain fr evaluating mving ueries ver mving bjects. The mst relevant wrk t urs, in terms f its supprt fr varius types f cntinual spatial ueries discussed in Sectin 1 and its ability t perfrm incremental evaluatin, is the SINA [15] (and its knn extensin SEA-KNN [31]) algrithm that has been develped cncurrently and independently with ur wrk [8]. SINA emplys hashbased indexing techniues fr bth bjects and ueries and generates psitive and negative updates (incrementally) thrugh a three-step prcess cnsisting f hashing, invalidatin, and jining. Hwever, there is an inherent difference between ur apprach and SINA. Specifically, mtin mdeling (described in Sectin 3.2) is integrated int ur apprach, which enables predictive uery results and helps increase the system scalability by reducing the number f lcatin updates received frm the mving bjects. It has been shwn in [4] that the use f linear functins fr mtin mdeling reduces the amunt f updates t ne-third in cmparisn t cnstant functins, fr realistic threshlds. Hwever, SINA wrks n raw lcatin updates in the frm f ðx; yþ crdinate pairs and is nt designed t take advantage f mtin mdeling. On the ther hand, mtin mdeling may intrduce additinal prcessing reuirements n the mving bjects. Frtunately, dead-reckning algrithms fr linear mtin mdeling are simple and can be implemented easily with cheap hardware r sftware. Besides these, the SINA apprach is nt mtin-adaptive like ur MAI apprach, i.e., it des nt ptimize the system based n the mvement characteristics f the individual bjects. In summary, SINA and MAI are different in their assumptins and reuirements with respect t the supprts reuired by the mbile bjects, as well as in terms f the specific techniues they emply fr the purpse f uery evaluatin. Hwever, bth are intended t slve the same high-level prblem f evaluating mving cntinuus ueries ver mving bjects. In [21], a tw-level architecture is prpsed, where there exist lcatin preprcessrs between the mving bjects and the database. The lcatin updates are prpagated t the database nly when the bjects crss bundaries f their hash buckets, which are fixed. The database is aware f nly the hash buckets and des nt knw exact psitins f bjects within the buckets. Sme ueries have t be prpagated t lcatin preprcessrs that have the exact infrmatin. Ging further in this directin, in [3], [7], and [9], tw-level architectures that push the lcatin filtering t mbile units were described. Table 1 summarizes the cmparisn f ur MAI apprach with sme f the existing appraches. Our apprach is the mst universal in handling varius types f cntinual ueries and has many desirable system prperties, such as incremental evaluatin f ueries and mtin adaptatin. 3 THE SYSTEM MODEL The basic elements f ur system mdel are a set f mving r statinary bjects and a set f mving r static cntinual (range r knn) ueries. A fundamental challenge we address in this paper is t study what kind f indexing scheme can efficiently answer the mving ueries. Fast evaluatin is critical fr prcessing mving ueries as it nt nly imprves the freshness f the uery results by enabling mre freuent reevaluatin, but als increases the scalability f the system by enabling timely evaluatin f a large number f mving ueries ver a large number f mving bjects.

4 654 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 18, NO. 5, MAY Basic Cncepts and Prblem Statement We dente the set f mving r statinary bjects as O, where O ¼ O m [ O s and O m \ O s ¼;. O m dentes the set f mving bjects and O s dentes the set f statinary bjects. We dente the set f mving r static ueries as Q, where Q ¼ Q m [ Q s and Q m \ Q s ¼;. Q m dentes the set f mving cntinual range ueries and Q s dentes the set f static cntinual range ueries. Since we fcus n mving cntinual ueries in this paper, frm nw n we use mving ueries and mving cntinual ueries interchangeably. Mving Objects. We describe a mving bject m 2 O m by a uadruple: hi ; p; v; a p i. Here, i is the uniue bject identifier, p ¼ðp x ;p y Þ is the current psitin f the mving bject where p x is its psitin in the x-dimensin and p y is its psitin in the y-dimensin, v ¼ðv x ;v y Þ is the current velcity vectr f the bject, and a p is a set f prperties abut the bject. A statinary bject can be mdeled as a special case f mving bject where the velcity vectr is set t zer, 8 s 2 O s ; s :v ¼ð0; 0Þ. Mving Queries. We describe a mving uery m 2 Q m by a uadruple: hi ;i ;r;fi. Here, i is the uniue uery identifier, i is the bject identifier f the fcal bject f the uery, r defines the shape f the spatial uery regin bund t the fcal bject f the uery, and f is a Blean predicate, called filter, defined ver the prperties (a p ) f the target bjects f the uery. Nte that, r can be described by a clsed shape descriptin such as a rectangle r a circle. This clsed shape descriptin als specifies a binding pint, thrugh which it is bund t the fcal bject f the uery. In the rest f the paper, we assume that a mving cntinual uery specifies a circle as its range with its center serving as the binding pint and we use r t dente the radius f the circle. A static spatial cntinual range uery can be described as a special case where the uery either has n fcal bject r the fcal bject is a statinary bject. Namely, 8 s 2 Q s ; s :i ¼ null _ s :i 2 O s. We assume that a static cntinual range uery specifies a rectangle r a circle as its range. Befre we give an verview f ur apprach, we first review three basic types f indexing techniues fr evaluating mving range ueries ver mving bjects and discuss their advantages and inherent weaknesses. Object-Only Indexing (OI). In the bject-nly indexing apprach, a spatial index is built n the bject psitins. Each time a new bject psitin is received, the bject index is updated. At each uery evaluatin phase, all ueries are evaluated against the bject index. An inherent drawback f the basic bject-nly indexing apprach is the reevaluatin f all ueries against the bject index regardless f whether r nt the bject psitin changes are f interest t the uery. Object-nly indexing is pen t ptimizatins that can decrease the number r cst f the updates n the bject index (see velcity-cnstrained indexing in [19] and TPR-trees in [20]). Query-Only Indexing (QI). In the uery-nly indexing apprach, a spatial index is built n the spatial regins f the ueries. Each time a new uery psitin (the psitin f the uery s fcal bject) is received, the uery index is updated. At each uery evaluatin phase, each bject psitin is evaluated against the uery index and the ueries that cntain the bject s psitin are determined. Nte that this has t be dne fr every bject as ppsed t ding it nly fr bjects that have mved since the last uery evaluatin phase. This is due t the fact that underlying ueries are ptentially mving. This significantly decreases the effectiveness f uery-nly indexing apprach, althugh in the cntext f static cntinual range ueries it has been shwn that a uery index may imprve perfrmance significantly [19], [29], [30]. Object-and-Query Indexing (OQI). In the bject-anduery indexing apprach, tw spatial indexes are built, ne fr the bject psitins and anther fr the spatial regins f the ueries. Each time an bject psitin is received, the bject index is updated. Similarly, each time a new uery psitin (the psitin f a uery s fcal bject) is received, the uery index is updated. At each uery evaluatin phase, each new bject psitin is evaluated against the uery index and the ueries that cntain the bject s psitin are determined. Then, the uery results are updated differentially. Similarly, at each uery evaluatin phase, each new uery psitin is evaluated against the bject index and the new result f the uery is determined. The OQI apprach evaluates bject psitins against the uery index nly fr thse bjects that have changed their psitins since the last uery evaluatin phase, as ppsed t all the bjects reuired by the uery-nly indexing apprach. The OQI apprach als evaluates ueries against the bject index nly fr thse ueries that have mved since the last uery evaluatin phase, as ppsed t all the ueries reuired by the bject-nly indexing apprach. Althugh the OQI apprach incurs a higher cst due t the maintenance f an additinal index structure, it is pen t a wider range f ptimizatins t reduce the cst and it des nt have certain restrictins f the bject-nly indexing r uery-nly indexing apprach. 3.2 Overview f the Prpsed Slutin Cgnizant f the prs and cns f the abve three basic indexing schemes, we prpse a mtin-adaptive indexing scheme fr efficient prcessing f mving ueries ver mving bjects. We use the cncept f mtin-sensitive bunding bxes t mdel the dynamic behavir f bth mving bjects and mving ueries. Such bunding bxes are nt updated unless the psitin f a mving bject r the spatial regin f a mving uery exceeds the brders f its bunding bx. Instead f indexing freuently changing bject psitins r spatial regins f mving ueries, we index less freuently changing mtin-sensitive bunding bxes. This significantly decreases the number f update peratins perfrmed n the indexes. Our indexing scheme maintains bth an index f bject-based mtin-sensitive bunding bxes (dented as Index msb ) and an index f uery-based mtin-sensitive bunding bxes (dented as Index msb ). Mre imprtantly, t address the prblem f increased search cst due t freuent evaluatin f ueries, we emply tw ptimizatin techniues: 1) predictive uery results and 2) mtin-adaptive indexing. Query results are ptimistically precmputed in the presence f bject mtin changes, with the amunt f precmputatin t be perfrmed cntrlled by the mtin-sensitive bunding bxes. The sizes f the mtin-sensitive bunding bxes are dynamically adapted t the changing mtin behavirs at the granularity f individual bjects, allwing mving ueries t be evaluated faster by perfrming fewer IOs. Fig. 1 gives a radmap f methds applied fr MCQ evaluatin. In the rest f this sectin, we describe the mtinmdeling and mtin update generatin, which prvides the fundatin fr mtin-sensitive bunding bxes and predictive uery results.

5 GEDIK ET AL.: PROCESSING MOVING QUERIES OVER MOVING OBJECTS USING MOTION-ADAPTIVE INDEXES 655 Fig. 1. Radmap f methds applied fr mving uery evaluatin. Mtin Mdeling. Mdeling mtins f mving bjects fr predicting their psitins is a cmmnly used methd in mving bject indexing [27], [12]. In reality, a mving bject mves and changes its velcity vectr cntinuusly. Mtin mdeling uses apprximatin fr predictin. Cncretely, instead f reprting their psitin updates each time they mve, mving bjects reprt their velcity vectr and psitin updates nly when their velcity vectrs change and this change is significant enugh. (This techniue is knwn as dead reckning [5].) In rder t evaluate mving ueries between the last update reprting and the next update reprting, the psitins f the mving bjects are predicted using a simple linear functin f time. Given that the last received velcity vectr f an bject is v, its psitin is p and the time its velcity update was recrded is t, the future psitin f the bject at time t þ t can be predicted as p þ t v. We use a linear mtin functin in this paper, since it is the cmmnly used mdel in mving bject databases [28]. We refer readers t [1] fr a study f nnlinear mtin mdeling fr mving bject indexing. Predictin-based mtin mdeling decreases the amunt f infrmatin sent t the uery-prcessing engine by reducing the freuency f psitin reprting frm each mving bject. Furthermre, it allws the system t ptimistically precmpute future uery results. Belw, we briefly describe hw the mving bjects generate and send their mtin updates t the server, where the uery evaluatin is perfrmed. Mtin Update Generatin. In rder fr the mving bjects t decide when t reprt their velcity vectr and psitin updates, they need t peridically cmpute if their velcity vectrs have changed significantly. Cncretely, at each time step, a mving bject samples its current psitin and calculates the difference between its current psitin and the psitin predicted by the dead-reckning algrithm based n the last mtin update it reprted t the server. In case this difference is larger than a specified threshld, say, D, the new mtin functin parameters are relayed t the server. Fig. 2 prvides an illustratin. The path f a mving bject is depicted with a slid line, where its path predicted by the server is depicted with a dashed line. The small suares n the slid line represent the current psitins sampled by the mving bject at each time step, and the small circles n the dashed line represent the psitins the server predicts the bject t be at in each f the crrespnding time steps. Fig. 2. Mtin-update generatin. 4 EFFICIENT EVALUATION OF MOVING CONTINUAL RANGE QUERIES In this sectin, we describe the mtin-adaptive indexing scheme fr efficient prcessing f mving range ueries ver mving bjects. We first describe the cncept f mtin-sensitive bunding bxes, and then discuss the mechanisms used fr cmputing predictive uery results, and utline the mtin-adaptive apprach fr determining the sizes f mtin sensitive bunding bxes. In additin, we prvide an verview f the algrithms used fr creating and maintaining the mtin-adaptive indexes, an analytical mdel fr IO estimatin, and the cncrete mechanism that adaptively determines the bunding-bx sizes based n the dynamically changing mtin behavirs f mving bjects and mving ueries. 4.1 Mtin-Sensitive Bunding Bxes Mtin-sensitive bunding bxes (MSBs) can be defined fr bth mving ueries and mving bjects. Given a mving bject m, its assciated MSB is calculated by extending the psitin f the bject alng each dimensin by ð m Þ times the velcity f the bject in that directin. Given a mving uery m, the MSB f the mving uery is calculated by extending the minimum bunding bx f the uery alng each dimensin by ð m Þ times the velcity f the fcal bject f the uery in that directin (see Fig. 3 fr illustratins). Let Rectðl; mþ dente a rectangle with l and m as any tw endpints f the rectangle that are n the same diagnal. Let signðxþ dente a functin ver a vectr x, which replaces each entry in x with 1 if it is greater than r eual t 0, with -1 therwise. Then, we define the MSB fr a mving Fig. 3. Mtin sensitive bunding bxes (MSBs).

6 656 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 18, NO. 5, MAY 2006 Fig. 4. Impact f MSBs and predictive uery results n uery evaluatin cst. bject and the MSB fr a mving uery with fcal bject f as fllws: 8 2 O m ;MSBðÞ ¼Rectð:ps; :ps þ ðþ:velþ 8 2 Q m ;MSBðÞ ¼Rectð f :ps :radius w s ; f :ps þ ðþ:vel þ :radius w s Þ; where w s dentes the sign functin signð:velþ. Fr each mving uery, its MSB is calculated and used in place f the uery s spatial regin in the uery-based MSB index, that is Index msb. Similarly, fr each mving bject, its MSB is calculated and used in place f the bject s psitin in the bject-based MSB index, that is, Index msb. An imprtant feature f indexing mtin-sensitive bxes f mving bjects and mving ueries is the fact that an MSB is nt updated unless the uery s spatial regin r the bject s psitin exceeds the brders f its mtin-sensitive bunding bx. When this happens, we need t invalidate the MSB. As a result, a new MSB is calculated and the Index msb r the Index msb is updated. This apprach reduces the number f update peratins perfrmed n the spatial indexes and, thus, decreases the verall cst f updating the spatial indexes (Index msb and Index msb ). It is als crucial t nte that, using MSBs des nt intrduce any inaccuracy in the uery results, because we stre the mtin functin f the bject r the uery tgether with its MSB inside the spatial index. Althugh maintaining MSB indexes increase the cst f searching the index due t higher verlap f spatial bjects being indexed, fr apprpriate values f the and parameters, the verall gain in the search cst due t the use f MSBs is significant, thanks t the incremental prcessing capabilities MSBs prvide in cnjunctin with predictive uery results. Cncretely, when a uery has nt invalidated its MSB and has nt changed its velcity vectr, then the predictive results f the uery are valid with regard t the bjects fr which n MSB invalidatins r velcity vectr changes have taken place. In case sme f the bjects had MSB invalidatins r velcity vectr changes, ueries are nt cmpletely reevaluated. A uery is cmpletely reevaluated nly when it has invalidated its MSB r it has changed its velcity vectr. We will discuss the details f uery evaluatin in greater depth in Sectin 4.3. In summary, the incremental prcessing f ueries helps minimize the verall search cst and cmpensates fr the small increase in the per peratin index search cst due t the use f MSBs. Fig. 4 summarizes the impact f using MSBs n the uery evaluatin in terms f update and search cst. Furthermre, MSBs prvide the fllwing three advantages: 1. As ppsed t appraches that alter the implementatin f traditinal spatial indexes fr decreasing the update cst (like TPR-tree [20] r VCI index [19]), mtin-sensitive bunding bxes reuire almst n significant change t the underlying spatial index implementatin. 2. They frm a basis fr deciding fr which bjects t precalculate uery results with respect t a uery (see Sectin 4.3). 3. By perfrming size adaptatin at the granularity f individual bjects, they lead t significant reductins in IO cst (see Sectin 4.4). In rder t fully utilize the advantages made pssible by MSBs in terms f uery evaluatin cst, we need mechanisms fr dynamically determining the mst apprpriate values f the and parameters based n the mtin behavir f mving bjects and mving ueries. 4.2 Predictive Query Results n a Per-Object Basis It is well-knwn that ne way f reducing IO and imprving efficiency f evaluating mving ueries is t precalculate future results f the cntinual ueries. This apprach has been used successfully in the cntext f cntinual mving knn ueries ver static bjects [23]. Mst existing appraches t precalculating uery results assciate a time interval with each uery that specifies the valid time fr the precalculated results. One prblem with peruery-based predictin in the cntext f mving ueries ver mving bjects is the fact that a change n the mtin functin f any f the mving bjects may cause the invalidatin f sme f the precalculated results. This mtivates us t intrduce predictive uery results, where the predictin is cnducted n per-bject basis. Given a uery, its predictive uery result differs frm a regular uery result in the sense that each bject in the predictive uery result has an assciated time interval indicating the time perid in which the bject is expected t be included in the uery result. We dente the predictive uery result f uery 2 Q by PQRðÞ. Each entry in a predictive uery result takes the frm h; ½t s ;t e Ši. We call the entry assciated with bject 2 O in PQRðÞ the predictive uery result entry f bject with regard t uery, and the interval ½t s ;t e Š assciated with bject the valid predictin time interval f the predictive uery result entry. Calculating the valid predictin time intervals is dne as fllws: Given a static cntinual range uery and a mving bject with its mtin functin, it is straightfrward t calculate the intersectin pints f the uery s spatial regin and the ray frmed by the mving bject s trajectry (See case I in Fig. 5). Similarly, t calculate the intersectin pint f a mving uery and a mving r nnmving bject (assuming that we nly cnsider mving ueries with circle- shaped spatial regins), we need t slve a uadratic functin f time. Frmally, let 2 Q be a uery with fcal bject f 2 O m, let 2 O be an bject, and let Distða; bþ dente the Euclidean distance between the tw pints a and b. We can calculate the time interval in which the bject is expected t be in the result set f uery by slving the frmula: Distð f :p þ t f :v; :p þ t :vþ m :r: Fig. 5 illustrates three different cases that arise in the calculatin f the predictin-time interval fr each perbject-based predictive uery result entry.

7 GEDIK ET AL.: PROCESSING MOVING QUERIES OVER MOVING OBJECTS USING MOTION-ADAPTIVE INDEXES 657 Fig. 5. Calculating intervals. The predictive uery results are precalculated n a perbject basis and the result entries are crrect unless the mtin functin f the fcal bject f a uery r the mtin functin f the mving bject assciated with the uery result entry have changed within the valid predictin-time interval. As a result, there are tw key uestins t answer in rder t effectively use the predictive uery results in evaluating MCQs: Predictin: Fr each mving uery, shuld we perfrm predictin n all mving bjects? If nt, hw d we determine fr which bjects we shuld d predictin? Obviusly, we shuld nt perfrm predictin fr bjects that are far away frm the spatial regin f the uery within a perid f time, as the predicted results are less likely t hld until thse bjects reach t the prximity f the uery. Invalidatin: When and hw t update the predictive results? This can be referred t as the invalidatin plicy fr perbject-based predictin. The predictive uery results may be invalid and, thus, need t be updated when the mtin functin f a mving uery r the mtin functin f a mving bject changes. In additin, the predictive results may need t be refreshed when the bjects in the predictive uery results have mved away frm the prximity f the uery r when the bjects that did nt participate in the predictin have entered the prximity f the uery. 4.3 Determining Predictive Query Results Using MSBs MSBs are used t effectively determine fr which bjects we shuld perfrm result predictin with respect t a uery (answering the first uestin listed in Sectin 4.2). Cncretely, fr a given uery, bjects whse MSBs intersect with the uery s MSB are cnsidered as ptential candidates f the uery s predictive result. Fig. 6 gives an illustratin f hw predictive uery results integrate with mtinsensitive bunding bxes. Cnsider the mving uery 1 with its uery MSB and fur mving bjects 1 ; 2 ; 3 ; and 4 as shwn in Fig. 6. In the figure, 1 is the fcal bject f uery 1 and the ther three mving bjects, 2 ; 3 ; and 4 are assciated with their bject MSBs. At time t 0, nly bjects 2 and 3 are subject t uery 1 s PQR, as their MSBs intersect with the uery s MSB. Hwever, the valid predictin time interval f bject 3 with regard t uery 1 is empty because there is n such time interval during which 3 is expected t be inside the uery result f 1. Thus, bject 3 shuld nt be included in the PQR f uery 1.At sme later time t 1, bject 2 and uery 1 remain inside their MSBs. Hwever, bjects 3 and 4 have changed their MSBs. As a result, bjects 2 and 4 becme ptential candidates f uery 1 s PQR at time t 1. Since 2 has nt changed its MSB, it remains included in 1 s PQR. By applying the valid predictin time interval test n 4, we btain a nnempty time interval with respect t 1, during which 4 is expected t be included in the uery result. Thus, 4 is added int the PQR f 1. In rder t achieve an IO-efficient slutin, the MSB sizes shuld be adjusted such that the PQRs are calculated fr a sufficiently large set f bjects t take advantage f precmputatin. Hwever, result predictin shuld nt be perfrmed fr bjects that are far away frm a uery, and, thus, are likely t invalidate their PQRs befre becming f interest t the uery. We use and parameters t adjust the MSB sizes n a per-bject/uery basis t ptimize this trade-ff. The details are given in Sectin Mtin-Adaptive Indexing We have described the main ideas and mechanisms used in ur mtin-adaptive indexing scheme. In this sectin, we describe mtin-adaptive indexing as a uery evaluatin techniue that integrates the ideas and mechanisms presented s far fr efficient prcessing f mving ueries ver mving bjects. Fig. 6. An illustratin f hw PQRs integrate with MSBs.

8 658 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 18, NO. 5, MAY 2006 Fig. 7. Mtin update prcessing Prcessing Mving Queries: An Overview The evaluatin f mving ueries is perfrmed thrugh uery evaluatin phases executed peridically with regular time intervals f P s (scan perid) secnds. We build tw spatial MSB indexes, Index msb fr the bjects and Index msb fr the ueries. Index msb stres MSBs f the bjects accmpanied by the assciated mtin functins as data. Static bjects have pint MSBs. Similarly, Index msb stres the MSBs f the ueries accmpanied by the assciated mtin functins f the fcal bjects f the ueries and their radii as data. Static ueries have MSBs eual t their minimum bunding rectangles and they d nt have assciated mtin functins. We create and maintain tw tables, a mving bject table and a mving uery table. They stre infrmatin regarding the mving bjects and mving ueries. The static ueries and static bjects are included in the spatial MSB indexes but nt in the tw tables. The peridic evaluatin is perfrmed by scanning these tables at each uery evaluatin phase and perfrming updates and searches n the spatial indexes as needed in rder t incrementally maintain the uery results as bjects and the spatial regins f the ueries mve. Detailed descriptins f the tw tables are given belw: Mving Object Table (MOT): An MOT entry is a tuple ði ;i ; p; v; t; B msb ;P cm ;V ch Þ and stres infrmatin regarding a mving bject. Here, i is the mving bject identifier, i is the uery identifier f the mving uery whse fcal bject s identifier is i, i is null if n such mving uery exists, p is the last received psitin, v is the last received velcity vectr f the mving bject, t is the time stamp f the mtin updates (p and v) received frm the mving bject, B msb is the MSB f the mving bject, P cm is an estimate n the perid f cnstant mtin f the bject, and V ch is a Blean variable indicating whether the bject has changed its mtin functin since the last uery evaluatin phase. Mving Query Table (MQT): An MQT entry is a tuple ði ; p; v; r; t; B msb ;P cm ;V ch Þ and stres infrmatin regarding a mving uery. Here, i is the mving uery identifier; p and ~v are the last received psitin and the last received velcity vectr f the uery s fcal bject, respectively; t is the time stamp f the mtin updates (~p and ~v) received frm the fcal bject, r is the radius f the mving uery s spatial regin, B msb is the MSB f the mving uery, P cm is an estimate f the perid f cnstant mtin f the bject, and V ch is a Blean variable indicating whether r nt the fcal bject has changed its mtin functin since the last uery evaluatin phase. Nte that the infrmatin in MQT is t sme extent redundant with respect t MOT. Hwever, the redundant infrmatin is reuired during the mving uery table scan. Withut redundancy, Fig. 8. General view f uery evaluatin. we wuld need t lk them up frm the mving bject table, which culd be cstly. The MOT and MQT table entries are updated whenever new mtin updates are received frm the mving bjects. The P cm entries are updated using a simple weighted running average. The details are given in Algrithm 1 (Fig. 7). Assuming that mving bjects decide whether r nt they shuld send new mtin updates at every P mu secnds (called the mtin update perid), ne f ur aims is t perfrm a single uery evaluatin phase in less than P mu secnds in rder nt t miss any mtin updates, i.e., having P s P mu. If, under the available resurces, a given implementatin f MAI is unable t perfrm the uery evaluatin with P s P mu satisfied, then the uery evaluatin perid P s has t be increased, i.e., uery evaluatin has t be perfrmed less freuently. Since the effects f mtin updates are reflected in the uery results during the next uery evaluatin step, false psitives and false negatives arise between uery reevaluatins mre freuently fr larger P s values. Hwever, this prblem is nt specific t MAI. In general, when the available resurces are nt sufficient t handle all ueries and psitin updates in real time, false psitives and negatives will temprarily arise in the uery results. When we have P s P mu, then it is at least guaranteed that n mtin updates are missed. Althugh the mving bject and uery tables increase the strage reuirements f the prpsed slutin, fr mst cases the server already cntains tables crrespnding t all bjects and all ueries. The bject table may cntain detailed infrmatin abut varius bject attributes and the uery table may cntain attributes f the ueries. In the wrst case, where all f the bjects and all f the ueries are mving, we can expect the size f the database t duble due t the inclusin f MOT and MQT. Hwever, we feel that such an increase is acceptable when the imprvement in perfrmance is cnsidered. Fig. 8 gives an verall sketch f the uery evaluatin prcess. At each uery evaluatin phase, we need t perfrm uery table scan and bject table scan. The scan algrithms presented in the next sectin describe hw these tw tasks are perfrmed The Scan Algrithms At each uery evaluatin phase, tw scans are perfrmed. The first scan is n the mving bject table, MOT, and the secnd scan is n the mving uery table, MQT. The aim f the MOT scan is t update the Index msb and t incrementally update sme f the uery results by perfrming searches n the Index msb. The aim f the MQT scan is t update the Index msb and t recalculate sme f the uery results by perfrming searches n the Index msb.

9 GEDIK ET AL.: PROCESSING MOVING QUERIES OVER MOVING OBJECTS USING MOTION-ADAPTIVE INDEXES 659 Fig. 9. Object table and uery table scans. MOT Scan. During the MOT scan, when prcessing an entry, we first check whether the assciated bject f the entry has invalidated its MSB (using p; v; t; and B msb )r changed its mtin functin since the last uery evaluatin perid (based n V ch ). (See Fig. 9a.) If nne f these has happened, we prceed t the next entry withut perfrming any peratin n the spatial MSB indexes. Otherwise, we first update the Index msb. In case there is an MSB invalidatin, a new MSB is calculated fr the bject and the Index msb is updated. The value used fr calculating the new MSB is selected adaptively, using jvj and P cm (see Sectin fr further details). If there has been a mtin functin change, the data assciated with the entry f the bject s MSB in the Index msb is als updated. Once the Index msb is updated, tw searches are perfrmed n the Index msb. First, using the ld MSB f the bject, the Index msb is searched and all the ueries whse MSBs intersect with the ld MSB f the bject are retrieved. The bject is then remved frm the results f thse ueries (if it is already in). Then, a secnd search is perfrmed with the newly calculated MSB f the bject, and all ueries whse MSBs intersect with the new MSB f the bject are retrieved. Fr all thse ueries, result predictin is perfrmed against the bject. Last, the uery result entries btained frm the predictin with nnempty time intervals are added int their assciated uery results. MQT Scan. During the MQT scan, when prcessing a uery entry we first check whether the assciated uery f the entry has invalidated its MSB (using p; v; r; t; and B msb ) r its fcal bject has changed its mtin functin since the last uery evaluatin phase (based n V ch ). (See Fig. 9b) If nne f these has happened, we prceed t the next entry withut perfrming any peratin n the spatial indexes. Otherwise, we first update the Index msb. In case there is an MSB invalidatin, a new MSB is calculated fr the uery and the Index msb is updated. The value used fr calculating the new MSB is selected adaptively, using jvj and P cm (see Sectin fr details). If there has been a mtin functin change, the data assciated with the entry f the uery s MSB in the Index msb is als updated. Once the Index msb is updated, a single search is perfrmed n the Index msb with the newly calculated MSB f the uery. All bjects whse MSBs intersect with the new uery MSB are retrieved. Fr all thse bjects, result predictin is perfrmed against the uery. The predictive uery result entries with nnempty time intervals are added int the uery result and all ld uery results are remved. Nte that after the MOT scan, all results are crrect fr the ueries whse MSBs are nt invalidated and whse fcal bjects have nt changed their mtin functins. Fr ueries that have invalidated their MSBs r whse fcal bjects have changed their mtin functins, the uery results are recalculated during the MQT scan. Therefre, all f the uery results are up-t-date after the MQT scan, given that MOT scan is perfrmed first. The rder f the scans can be reversed with sme minr mdificatins. Between uery reevaluatins, false psitives and negatives may arise in the uery results. False psitives may nly arise fr bjects and ueries whse mtin functins

10 660 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 18, NO. 5, MAY 2006 TABLE 2 Symbls and Their Meanings have changed since the last uery evaluatin step. This is because when n mtin updates take place, PQRs are accurate and can predict the departure f bjects frm the uery regins crrectly. On the ther hand, false negatives may take place when sme f the bjects enter int MSBs f sme ueries between uery reevaluatins. This happens mre freuently when P s is large. Since we encurage perfrming uery reevaluatins as freuently as pssible, large P s values are unlikely. 4.5 Setting and Values The and parameters used fr calculating MSBs can be set based n the mtin behavir f the bjects, in rder t achieve mre efficient uery evaluatin. There are tw imprtant characteristics f bject mtins: 1) the speed f the bject and 2) the perid f cnstant mtin f the bject (i.e., the length f the time perid it takes fr the mtin functin t change). Fr instance, fr a uery whse fcal bject changes its mtin functin freuently, it may nt be a gd idea t perfrm t much predictin. Thus, the value fr this uery s MSB shuld be kept smaller. Hwever, fr an bject with high speed, a small value may nt be apprpriate, as it may cause freuent MSB invalidatins. As a result, it is imprtant t design a mtin-adaptive methd that can set the values f and parameters adaptively. A cmmn apprach t runtime parameter setting is t develp an analytical mdel and use it t guide the runtime selectin f the best parameter settings. We develp an analytical mdel fr estimating the IO cst f perfrming uery evaluatin. This mdel is used as the guide t build an ffline cmputed Table, giving the best and values fr different value pairs f speed and perid f cnstant mtin f a mving bject Analytical Mdel fr IO Estimatin We develp an analytical mdel fr estimating the IO cst f perfrming uery evaluatin, i.e., the tw scans perfrmed at each uery evaluatin phase. The frmulatins in this sectin are derived based n the average values fr the speed and the perid f cnstant mtin f a mving bject. Fr the purpse f ffline T able creatin, the assciated speed and perid f cnstant mtin values are taken frm the table cells. Table 2 lists sme f the symbls used in this sectin and their meanings. Let A m dente the average area f a mving bject MSB and A m dente the average area f a mving uery MSB. Denting the average bject speed as V a, based n the definitin f MSBs we have: p A m ¼ðV a = ffiffiffi Þ 2 ; and p A m ¼ðV a = ffiffiffi þ 2 Rm Þ 2 : The derivatin f A m fllws frm the fact that the side f a mving bject MSB has an average size f times the average speed f the bject n the side s directin. Averaging ver all pssible angles fr the velcity vectr, we have A m ¼ðV a Þ p ¼ðV a = ffiffiffi Þ 2 : Z 2 0 j sin xjjcs xj dx The derivatin fr the mving uery MSBs fllw a similar frmulatin, with the exceptin that the diameter f the uery, dented by 2 R m, is als included in the euatin. Let A dente the average size f the bject bunding bxes stred in the Index msb (static bjects are assumed t have a bx with zer area) and A dente the average size f the uery bunding bxes stred in the Index msb. Then, we have ; and A ¼ N m A m þ 1 N m N N A ¼ A m N m N L 2 s : The derivatin f A fllws frm the fact that N m =N fractin f the bjects (that are mving bjects) have an average MSB size f A m and the rest (statinary bjects) have an MSB size f 0. The derivatin f A fllws similarly. Statinary ueries, which frm N m =N fractin f all ueries, have an average MSB size f L 2 s, where L s is the average side length f a static range uery. On the ther hand, mving ueries, that frm N m =N fractin f all ueries, have an average MSB size f A m. Given this infrmatin, the fllwing fur uantities can be analytically derived based n well-studied R-tree cst mdels [26]: nde IO cst during the prcessing f 1. an bject-table entry fr updating the Index msb, C u; 2. an bject-table entry fr searching the Index msb, C s; 3. a uery-table entry fr updating the Index msb, C u; and 4. a uery-table entry fr searching the Index msb, C s. Let N vc dente the expected value f the number f distinct bjects causing velcity change events during ne scan perid and let N vc dente the expected value f the number f distinct ueries causing velcity change events during ne scan perid. If P s =P cm < 1, nly sme f the mving bjects will cause velcity change events. Hence, we have N vc ¼ N m min 1; P s ; and P cm N vc ¼ N m Nvc : N m The derivatin f N vc fllws frm the fact that a mving uery causes a velcity change event nly if its fcal bject causes a velcity change event and that nly N vc=n m fractin f the mving bjects cause velcity change events.

11 GEDIK ET AL.: PROCESSING MOVING QUERIES OVER MOVING OBJECTS USING MOTION-ADAPTIVE INDEXES 661 TABLE 3 A Sampled Subset f the T able frm the Experiment f Fig. 14 in Sectin 6 Fig. 10. (a) Experimental uery evaluatin time and (b) analytical nde IO estimate. Let N bi dente the expected value f the number f bjects causing bx invalidatins during ne scan perid and N bi dente the expected value f the number f ueries causing bx invalidatins during ne scan perid. If P s = < 1, nly sme f the mving bjects will cause bx invalidatins. Similarly, if P s = < 1, nly sme f the mving ueries will cause bx invalidatins. Then, we have N bi min 1; P s N m ; and N bi min 1; P s N m : Let N mt dente the expected value f the number f entries in the bject table that caused velcity change r bx invalidatin events and let N mt dente the expected value f the number f entries in the uery table that caused velcity change r bx-invalidatin events. Assuming that an bject causes a velcity change event independent f whether it has caused an MSB invalidatin and similarly assuming that a uery causes a velcity change event independent f whether it has caused an MSB invalidatin, we have: N mt ¼ N vc N mt ¼ N vc þ Nbi þ N bi Nbi Nbi Nvc ; and N m Nbi : N m Finally, the ttal IO cst fr the peridic scan, C i, can then be calculated, cnsidering that fr an entry f MOT that reuires prcessing due t velcity change r MSB invalidatin, an update n the Index msb and tw searches n the Index msb are needed, and fr an entry f MQT that reuires prcessing due t velcity change r MSB invalidatin, an update n the Index msb and a search n the Index msb are needed: C i ¼ N mt ðc u þ 2 Cs ÞþN mt ðc u þ Cs Þ: ð1þ T able and Adaptive Parameter Selectin The cst functin develped in this sectin has a glbal minimum that ptimizes the IO cst f the uery evaluatin. We build an ffline cmputed Table, which gives the ptimal and values fr different value pairs f bject speed (v) and perid f cnstant mtin (P cm ), calculated using the cst functin we have develped. We implement the T able as a 2D matrix, whse rws crrespnd t different bject speeds and whse clumns crrespnd t different perids f cnstant mtin, and the entries are ptimal ð; Þ pairs. Recall that, as discussed in Sectin 4.4, when we calculate the MSBs f mving bjects and mving ueries, we already have the estimates n perids f cnstant mtin and speeds f all mving bjects including the fcal bjects f the mving ueries. We can decide the best and values t use during MSB calculatin by perfrming a single lkup frm the ffline cmputed T able. Fig. 10a plts the average time it takes t perfrm ne cmplete uery evaluatin phase (labeled as ttal uery evaluatin time) as a functin f and. These values are frm the actual implementatin f mtin-adaptive indexing. Fig. 10b plts the analytical nde IO cunt estimate f perfrming ne uery evaluatin phase as a functin f and. Tw imprtant bservatins can be btained by cmparing these graphs. First, they shw that the IO cst is dminant n the time it takes t perfrm uery evaluatin, as the nde IO cunt graph highly determines the shape f the uery evaluatin time graph. Secnd, the ptimal values f and calculated using the analytical cst functin indeed result in faster uery evaluatin. In Table 3, we give a sampled subset f the Table that is used in the experiment reprted in Fig. 12 f Sectin 6. The actual table cvers a larger range and has a higher reslutin. Each entry in the table is in the frm ð; Þ. We make tw bservatins frm Table 3. First, with increasing bject speeds, the ptimal and values decrease. This is because fr high speeds the and parameters shuld be kept small in rder t avid large MSBs, which will cause high verlap and increase the cst f spatial index peratins. Secnd, with decreasing perid f cnstant mtin, the ptimal and values decrease. This is because large MSBs are undesirable when the predictability is pr (perid f cnstant mtin is small), since they will result in a larger number f invalidated PQRs and thus increased IO cst. We will prvide perfrmance results n the imprvement prvided by the adaptive parameter selectin in Sectin EVALUATING MOVING knn QUERIES WITH MOTION ADAPTIVE INDEXING Mving cntinual k-nearest neighbr ðknnþ ueries ver mving bjects can be evaluated using the main mechanisms emplyed fr mving range uery evaluatin. A mving knn uery is defined similar t a mving range uery, except that instead f a range, the parameter k is specified fr retrieving the k nearest neighbrs f the fcal bject f the uery.

12 662 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 18, NO. 5, MAY 2006 A uniue feature f ur mtin-adaptive indexing scheme is its ability t efficiently prcess bth cntinual mving range ueries and cntinual mving knn ueries. Nte that, fr a mbile database system that has t manage bth range MCQs and knn MCQs, slutins that are exclusive t knn ueries will intrduce extra verhead, since the indexes and data structures are nt shared with the range uery evaluatin cmpnent, further exacerbating the prblem f high index maintenance cst in mving bject databases. In cntrast, ur slutin uses a cmmn framewrk t supprt bth range and knn ueries, s that wrklads that are mixtures f knn ueries and range ueries are efficiently handled. In rder t extend the mtin-adaptive indexing develped fr evaluating mving range ueries t the evaluatin f mving knn ueries, we intrduce the cncept f safe radius and tw mechanisms: guaranteed safe radius and ptimistic safe radius. T evaluate knn ueries with the use f safe radii, we need t make the fllwing three changes: 1. During the MQT table scan, when a uery invalidates its MSB r changes its mtin functin, we calculate a safe radius, which is guaranteed t cntain at least k mving bjects until the next time the safe radius is calculated ( is an upper bund fr this time). Then, the knn uery is installed as a standard MCQ with its range eual t the safe radius. 2. Instead f string time intervals in uery result entries, we stre the distance f the bjects frm the fcal bject f the uery as a functin f time. 3. At the end f each uery evaluatin phase, results are srted based n their distances t their assciated fcal bjects by using the distance functins stred within the uery result entries. The tp k result entries are then marked as the current results. The imprtant step here is t calculate a safe radius that will make sure that at least k bjects will be cntained within the safe radius during the next t time units. We prpse tw different appraches t tackle this prblem: the guaranteed safe radius (GSR) and the ptimistic safe radius (OSR). The guaranteed safe radius apprach retrieves the current k nearest neighbrs, and fr each bject in the list calculates the maximum pssible value the distance between the bject and the fcal bject f the uery can take at the end f the next t time units. This can be calculated using the fcal bject s mtin functin and the upper bunds n the maximum speeds f these k nearest neighbr bjects. The maximum f these k calculated distances will give the safe radius. Hwever, there are tw prblems. First, it reuires us t knw the upper bunds n the speeds f mving bjects. Secnd, the calculated safe radius may becme unnecessarily large, negatively affecting the perfrmance. The ptimistic safe radius apprach retrieves the current k nearest neighbrs, and fr each bject in the list calculates the maximum value f the distance between the bject and the fcal bject f the uery can take thrughut the next t time units, assuming that the bjects will nt change their mtin functins during this time. Fr each f the k bjects, this calculatin can be dne using the current mtin functin f the bject and the mtin functin f the uery s fcal bject. The maximum f these k calculated distances will give the safe radius. This apprach guarantees that k bjects will be cntained within the safe radius during the next t time units under the assumptin that the initial set f Fig. 11. Illustratin f ptimistic and guaranteed safe radius calculatin fr 2NN ueries. k nearest neighbrs d nt change their mtin functins during this perid. When using this apprach, if the number f bjects in the result f a knn uery turns ut t be smaller than k, we fall back t the traditinal spatial index knn search plan fr that uery until the next time a new safe radius is calculated. Fig. 11 illustrates hw safe radii are calculated with an example 2NN uery, where the fcal bject is 1 and the tw nearest neighbrs at time t 0 are bjects 2 and 3. The safe radius is calculated t be valid during the next time units. We will prvide the perfrmance cmparisn f guaranteed safe radius (GSR) and ptimistic safe radius (OSR) in Sectin 6. 6 EXPERIMENTAL RESULTS This sectin describes five sets f experiments, which are used t evaluate ur slutin. The first set f experiments cmpares the perfrmance f mtin-adaptive indexing against varius existing appraches. The secnd set f experiments illustrates the advantages f adaptive parameter selectin ver fixed parameter setting n the sizes f bunding bxes. The third set f experiments studies the effect f skewed data and uery distributin n uery evaluatin perfrmance. The furth set f experiments analyzes the scalability f the prpsed apprach with respect t ueries with varying sizes f spatial regins, varying percentages f mving ueries, and varying numbers f bjects. Finally, the fifth set f experiments present the effectiveness f the mtin-adaptive apprach t evaluating mving cntinual knn ueries ver mving bjects. 6.1 System Parameters and Setup In the experiments presented in the rest f the paper, the parameters take their default values listed in Table 4, when nt specified therwise. Based n the default values, 50 percent f the bjects are mving and the remaining 50 percent are static. Similarly, 50 percent f the ueries are mving and the remaining 50 percent are static. Different percentages f mving ueries are studied in Sectin 6.6. Mving ueries are assigned range values frm the list f5; 4; 3; 2; 1g (in miles) using a Zipf distributin with parameter 0.6. Static ueries are assigned side range values frm the list f8; 7; 5; 4; 2g (in miles) using a Zipf distributin with parameter 0.6. The default bject density is taken in accrdance with previus wrk [19], [20]. Objects and ueries are randmly distributed in the area f interest except in Sectin 6.5, where we cnsider skewed distributins. Objects that belng t

13 GEDIK ET AL.: PROCESSING MOVING QUERIES OVER MOVING OBJECTS USING MOTION-ADAPTIVE INDEXES 663 TABLE 4 System Parameters different classes with strictly varying mvement behavirs are cnsidered in Sectin 6.3. The paths fllwed by the bjects are randm, i.e., each time a mtin functin update ccurs, a randm directin and a randm speed are chsen. The bject speeds are selected frm the range ð0; 150Š (in miles/hur) unifrmly at randm. Table 4 gives details f ther imprtant system parameters. We vary the values f many system parameters t study their effects n the perfrmance. Fr R -trees, a 101-nde LRU buffer is used with 4-KByte page size. Branching factr f the internal tree ndes is 100 and the fill factr is 0.5. Relative merits f ur techniues shwn in the rest f the sectin are als valid under scenaris with large buffer sizes (which effectively makes it a main memry algrithm); hwever, we d nt reprt thse results. All experiments are perfrmed using R -trees; except that in Sectin 6.5 a static grid-based spatial index implementatin is used fr cmparisn purpses. We cmpare the perfrmance f mtin-adaptive indexing against varius existing appraches, in terms f uery evaluatin time and nde IO cunts. The appraches used fr cmparisn are brute frce (BF), bjectnly indexing (OI), uery-nly indexing (QI), bject-and-uery indexing (OQI), mtin-adaptive indexing (MAI), and bject indexing with MSBs (OIB). The brute frce calculatin is perfrmed by scanning thrugh the bjects. During the scan, all ueries are cnsidered against each bject in rder t calculate the results. The OI apprach uses an bject index which is updated fr all bjects that have mved since the last uery evaluatin phase 1 and searched fr all ueries in rder t evaluate the uery results. The QI apprach uses a uery index, which is updated fr all ueries that have mved since the last uery evaluatin step and is searched fr all bject psitins in rder t update the uery results incrementally. OQI is a strippeddwn versin f MAI withut MSBs and PQRs. OIBs is similar t pure bject-nly indexing, except that the mtin sensitive bxes are used instead f bject psitins in the spatial index (withut the PQRs). 6.2 Perfrmance Cmparisn Fig. 12 plts the ttal uery evaluatin time fr a fixed number f bjects (50 K) with a varying number f ueries (2.5 K t 20 K). The hrizntal line in the figure represents the scan perid. We cnsider a uery evaluatin scheme as 1. Althugh update-efficient bject indexes exist [20], [24], we shw that their use des nt change ur cnclusin fr large r mderate numbers f ueries, in which cases search cst is the dminant factr. acceptable when the ttal uery evaluatin time is less than the scan perid. Nte that the scan perid, P s, is set t be eual t the mtin update perid, P mu, in this set f experiments. Fig. 13 plts the uery evaluatin nde IO cunt fr the same setup. The nde IO is divided int fur different cmpnents: 1. nde IO due t bject index update, 2. nde IO due t bject index search, 3. nde IO due t uery index update, and 4. nde IO due t uery index search. Each cmpnent is depicted with a different shade in Fig. 13. Several bservatins can be btained frm Fig. 12 and Fig. 13. Fig. 12. Query evaluatin time. Fig. 13. Query evaluatin nde IO.

14 664 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 18, NO. 5, MAY 2006 First, the appraches with an bject index that is updated fr all mving bjects d nt perfrm well when the number f ueries is small. This is clear frm the pr perfrmances f OI and OQI fr 2.5 K ueries, as shwn in Fig. 12. The reasn is straightfrward. The cst f updating the bject index dminates when the number f ueries is small. This can als be bserved by the bejct index update cmpnent f the OI in Fig. 13. Hwever, there are als significant csts fr searching the bject index fr the OI apprach. These csts dminate the ttal IO cst when the number f ueries is large (see the case f 20 K ueries in Fig. 13). This pints ut an imprtant fact: Althugh it is pssible t reduce the cst f updating the bject index (fr instance, by using a TPR-treebased bject index [20], [24]), MAI still perfrms significantly better than such an bejct index-based apprach. Secnd, the appraches with a uery index that is searched fr a large number f bjects d nt perfrm well fr a large number f ueries. This is clear frm the pr perfrmances f QI and OQI fr 20 K ueries, as shwn in Fig. 12. This is due t the fact that the cst f searching the uery index dminates when the number f ueries is large. This can als be bserved by the uery index search cmpnent f the QI in Fig. 13. Nte that, fr a small number f ueries, the nde IO cunt fr QI appears as 0, because the uery index fits int the LRU buffer. Third, the brute frce apprach perfrms relatively well cmpared t OQI and slightly better than OI when the number f ueries is small (2.5 K), as shwn in Fig. 12. Obviusly, BF des nt scale with the increasing number f ueries, since the cmputatinal cmplexity f the brute frce apprach is OðN N Þ, where N is the ttal number f bjects and N is the ttal number f ueries. Althugh OQI seems t be a cnsistent lser when cmpared t ther indexing appraches, it is interesting t nte that the mtin-adaptive indexing is built n tp f it and perfrms better than all ther appraches. Finally, it is wrth nting that nly MAI manages t prvide gd enugh perfrmance t satisfy P s P mu under all cnditins. MAI prvides arund percent savings in uery evaluatin time under all cases when cmpared t the best cmpeting apprach except OIB. Hwever, OIB perfrms reasnably well but fails t scale well with increasing number f ueries when cmpared t the prpsed MAI apprach. 6.3 Effect f Adaptive Parameter Selectin In rder t illustrate the advantage f adaptive parameter selectin, we cmpare mtin-adaptive indexing against itself with static parameter selectin. Fr the purpse f this experiment, we intrduce three different classes f mving bjects with strictly different mvement behavirs. The first class f mving bjects change their mtin functins freuently (average perid f cnstant mtin: 1 minute) and mve slwly (maximum speed: 20 miles/hur). The secnd class f mving bjects pssess the default prperties described in Sectin 6.1. The third class f mving bjects seldm change their mtin functins (avgerage perid f cnstant mtin: 30 minutes) and mve fast (maximum speed: 300 miles/hur). In rder t bserve the gain frm adaptive parameter selectin, we set the and parameters t the ptimal values btained fr mving bjects f the secnd class fr the nnadaptive case. Fig. 14 plts the time and IO cst f uery evaluatin fr MAI and a static parameter setting versin f MAI. The x-axis represents the bject class distributins. Hence, 1:1:1 represents the case where the number f bjects belnging Fig. 14. Perfrmance gain due t adaptive parameter selectin. t different classes are the same. Alng the x-axis, we change the number f bjects belnging t the secnd class. 1:0.25:1 represents the case where the number f bjects belnging t the first class and the number bjects belnging t the third class are bth fur times the number f bjects belnging t the secnd class. Dually, 1:4:1 represents the case where the secnd class cardinality is fur times thse f the ther tw classes. Ttal uery evaluatin times are depicted as lines in the figure and their crrespnding values are n the left y-axis. The nde IO cunts are depicted as an embedded bar chart and their crrespnding values are n the right y-axis. There are tw imprtant bservatins frm Fig. 14. First, we ntice that the adaptive parameter selectin has a clear perfrmance advantage. This is clearly bserved frm Fig. 14, which shws significant imprvement prvided by mtin-adaptive indexing ver static parameter setting in bth uery evaluatin time and nde IO cunt. Secnd, it is imprtant t nte that the bjects belnging t the first class r the third class cannt be ignred even if their numbers are small. Even fr 1:4:1 distributin, where the secnd class f bjects is dminant, we see a significant imprvement with MAI. Nte that bjects belnging t the first and the third class are expensive t handle. The first class f bjects are expensive as they cause freuent mtin updates which in turn causes mre prcessing during MOT and MQT scans. The third class f bjects are als expensive, as they cause freuent MSB invalidatin which instigates mre prcessing during MOT and MQT scans. The fact that bth uery evaluatin time and nde IO cunt are declining alng the x-axis shws that it is bviusly mre expensive t handle the first and the third class f bjects. 6.4 Strage Cst Since MAI uses bth an bject index and a uery index, its strage reuirements are expected t be larger than the strage reuirements f the ther alternatives cnsidered in this sectin. Hwever, given that the prcessing resurces are the limiting factr fr handling cntinuus ueries in the mbile bject mnitring cntext, this increase in the strage cst is acceptable cnsidering the savings in IO cst and uery evaluatin time prvided by MAI. In Fig. 15, we reprt the strage cst f the MAI apprach, relative t ther alternatives, fr three different settings fr the

15 GEDIK ET AL.: PROCESSING MOVING QUERIES OVER MOVING OBJECTS USING MOTION-ADAPTIVE INDEXES 665 Fig. 15. Strage cst f MAI relative t ther alternatives. joj : jqj rati, that are 1:0.01, 1:0.1, and 1:1. We bserve frm the figure that, relative t OI and OIB, MAI has a strage cst f arund three times and 1.25 times fr the case f joj : jqj ¼0:0:01 and arund 2.15 times and 1.35 times fr the case f joj : jqj ¼0:0:1, respectively. Fr the extreme case f joj : jqj ¼ 1: 1, where the number f ueries is eual t the number f bjects, we see that MAI has a strage cst f arund three times and tw times relative t OI and OIB, respectively. In general, the number f ueries is expected t be smaller than the number f bjects. Thus, it is fair t say that MAI has a strage cst that is arund tw times that f a simple bejct index-based apprach. The figure als shws results relative t the QI and QIB appraches. It is bserved that MAI incurs up t five times mre strage cst cmpared t QI, the wrst-case scenari happening when the number f ueries is the smallest, that is joj : jqj ¼ 0: 0:01: Hwever, given the pr perfrmance f QI cmpared t bth OI and MAI, the savings it prvides in terms f strage cst are nt f much value. 6.5 Effect f Data and Query Skewness Our experiments up t nw have assumed unifrm bjectand-uery distributin. In this sectin, we cnduct experiments with skewed data and uery distributins. We mdel skewness using tw parameters, number f ht spts (N h ) and scatter deviatin (d). We randmly pick N h different psitins within the area f interest, which crrespnd t ht-spt regins. When assigning an initial psitin t an bject, we first pick a randm ht-spt psitin frm the N h different ht spts and then place the bject arund the ht-spt psitin using a nrmally distributed distance functin n bth x and y dimensins with zer mean and d standard deviatin. Scatter deviatin d is set t 25 miles in all experiments and the number f ht spts is varied t experiment with different skewness cnditins. Queries als fllws the same distributin with bjects. Fig. 17 shws the bject and uery distributin fr N h ¼ 5 and N h ¼ 30. We als experiment with different spatial indexing mechanisms. We have implemented a static grid-based spatial index, backed up by a B þ -tree with z-rdering [6]. The ptimal cell size f the grid is determined based n the wrklad. The mtivatin fr using a static grid is that with freuently updated data it may be mre prfitable t use a statically partitined spatial index that can be easily updated. Actually, previus wrk dne fr static range ueries ver mving bjects [11] has shwn that using a Fig. 16. Effect f data and uery skewness n perfrmance. static grid utperfrms mst ther well-knwn spatial index structures fr in-memry databases. With this experiment, we als investigate whether a similar situatin exists in secndary strage based indexing in the cntext f MCQs. Fig. 16 plts the ttal uery evaluatin time as a functin f number f ht spts fr different spatial index structures used fr Index msb and Index msb. Nte that the smaller the number f ht spts, the mre skewed the distributin is. Fig. 16 shws that decreasing the number f ht spts uadratically increases the uery evaluatin time. But even fr N h ¼ 5, the uery evaluatin time des nt exceed the uery evaluatin perid. Fig. 16 als shws that R -tree perfrms the best under all cnditins. 6.6 Scalability Study In this sectin, we study the scalability f the prpsed slutin with respect t the varying size f uery ranges, the varying percentage f mving ueries ver the ttal number f spatial ueries, and the varying ttal number f bjects. We first measure the impact f the uery range and the mving uery percentage n the uery evaluatin perfrmance. We use the range factr (r f ) t experiment with different wrklads in terms f different uery ranges. The uery radius and uery side length parameters given in Sectin 6.1 are multiplied by the range factr r f in rder t alter the size f uery regins. Nte that multiplying the range factr by tw in fact increases the area f the uery range by fur. Fig. 18 plts the ttal uery evaluatin time as a functin f mving uery percentage fr different range factrs. As Fig. 17. Query and bject distributin frn h ¼ 5 and N h ¼ 30.

16 666 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 18, NO. 5, MAY 2006 Fig. 18. Effect f uery range and mving uery percentage n perfrmance. shwn in Fig. 18, the scalability in terms f mving uery percentage is extremely gd. The slpe f the uery evaluatin time functin shws gd reductin with increasing percentage f mving bjects. Increasing the range factr shws rughly linear increase (with a multiplier that increases with increasing mving uery percentage, 0.25 t 0.5 fr 0 percent t 100 percent) n the uery evaluatin time. In Fig. 19, we study the effect f the number f bjects n the uery evaluatin perfrmance. Fig. 19 plts the ttal uery evaluatin time as a functin f number f bjects fr different spatial index structures used fr Index msb and Index msb. The number f ueries is set t its default value f 5 K. Frm Fig. 19, we bserve a linear increase in the uery evaluatin time with the increasing number f bjects. The uery evaluatin time fr 200 K bjects is arund fur times the uery evaluatin time fr 50 K bjects fr the R -tree implementatin f Index msb and Index msb, which shws better scalability with increasing number f bjects than the static-grid implementatin. Fig. 20. Ttal uery evaluatin time fr mving cntinual knn ueries. 6.7 Perfrmance Cmparisn fr Cntinual knn Queries We cmpare the perfrmance f MCQ-based mving cntinual knn uery evaluatin against the bject-nly indexing apprach. In bject-nly indexing, the bject index is updated and the knn ueries are evaluated against the updated bject index during each uery evaluatin phase. In this experiment, 10 K bjects are used with the same bject density (N =A) specified in Sectin 6.1, where 50 percent f the bjects are mving with the default mtin parameters frm Sectin 6.1. All ueries are mving cntinual knn ueries and the number f ueries ranges frm 0.5 K t 4 K. The k values f the knn ueries are selected frm the list f5; 6; 7; 8; 9; 10g using a Zipf distributin with parameter 0.6. Fig. 20 plts the ttal uery evaluatin time and Fig. 21 plts the nde IO cunt fr different number f bjects with different appraches. The nde IO cunt is divided int tw cmpnents. The lwer part shws the nde IO due t index searches, where the upper part shws the nde IO due t index updates. Evaluating mving cntinual knn ueries with mtinadaptive indexing shws significant imprvement ver an bject-nly indexing apprach. Between the tw variatins Fig. 19. Effect f number f bjects n perfrmance. Fig. 21. Nde IO cunt fr mving cntinual knn ueries.

17 GEDIK ET AL.: PROCESSING MOVING QUERIES OVER MOVING OBJECTS USING MOTION-ADAPTIVE INDEXES 667 Fig. 22. Range MCQ result accuracy fr knn ueries. f safe radius, OSR (ptimistic safe radius-based apprach) perfrms better than GSR (guaranteed safe radius-based apprach). Object-nly indexing with MSBs (OIB) slightly utperfrms GSR. Hwever, OSR prvides 20 t 40 percent imprvement in ttal uery evaluatin time ver OIB. An interesting statistic is the average result accuracy f the range MCQs used t answer knn ueries, fr GSR and OSR techniues. Cncretely, the rati f the k value specified in the uery t the average number f results in the MCQ used t answer the uery is an imprtant measure t assess the effectiveness f using range ueries as a filtering step in answering knn. In Fig. 22, the range MCQ result accuracy fr knn ueries is pltted as a functin f k fr ptimistic and guaranteed safe radius techniues. The k values used in the figure are in the range ½5; 10Š. Fr k ¼ 5 and with OSR, ne-fifth f the results f a range MCQ cnstitute the result f the assciated knn uery. This means that the size f the result set f the range MCQ is 25 fr a 5NN uery, n the average. Imprtantly, the accuracy f the range MCQs increase with increasing k. Fr instance, fr k ¼ 10 and with OSR, ne-uarter f the results f a range MCQ cnstitute the result f the assciated knn uery. This increasing trend in accuracy is very useful, since the cst f uery evaluatin increases with increasing k and it is imprtant that the range MCQs prvide gd filtering fr such cstly knn ueries. Fig. 22 als shws that GSR perfrms prly cmpared t OSR, having a very lw accuracy value f 6 percent t 8 percent, where k ranges frm 5 t CONCLUSION We have presented a system and a mtin-adaptive indexing scheme fr efficient prcessing f mving ueries ver mving bjects. Our apprach has three uniue features. First, we use the cncept f mtin-sensitive bunding bxes (MSBs) t mdel the dynamic mtin behavir f bth mving bjects and mving ueries and we prmte indexing less freuently changing MSBs tgether with the mtin functins f the bjects, instead f indexing freuently changing bject psitins. This significantly decreases the number f update peratins perfrmed n the indexes. Secnd, we prpse using mtin-adaptive indexing in the sense that the sizes f the MSBs can be dynamically adapted t the mving bject behavir at the granularity f individual bjects. Cncretely, we develp a mdel fr estimating the cst f mving uery evaluatin, and use the analytical mdel t guide the setting and the adaptatin f several system parameters dynamically. As a result, the mving ueries can be evaluated faster by perfrming fewer IOs Finally, we advcate the use f predictive uery results t reduce the number f search peratins t be perfrmed n the spatial indexes. Other imprtant characteristics f ur apprach include the extensin f the mtin-adaptive indexing scheme t the evaluatin f mving cntinual knn ueries thrugh the cncept f guaranteed safe radius and ptimistic safe radius.we reprt a series f experimental perfrmance results fr different wrklads, including scenaris based n skewed bject and uery distributin, and demnstrate the effectiveness f ur mtin-adaptive indexing scheme thrugh cmparisns with ther alternative indexing mechanisms. We have shwn that the prpsed mtin-adaptive indexing scheme is efficient fr evaluatin f bth mving cntinual range ueries and mving cntinual knn ueries. ACKNOWLEDGMENTS This research is partially supprted by grants frm US Natinal Science Fundatin (NSF) CSR, NSF ITR, US Department f Energy SciDAC, an IBM Faculty Award, an IBM SUR grant, and an HP euipment grant. REFERENCES [1] C.C. Aggarwal and D. Agrawal, On Nearest Neighbr Indexing f Nnlinear Trajectries, Prc. ACM Principles f Database Systems (PODS), pp , [2] R. Benetis, C.S. Jensen, G. Karciauskas, and S. Saltenis, Nearest Neighbr and Reverse Nearest Neighbr Queries fr Mving Objects, Prc. Int l Database Eng. and Applicatins Symp. (IDEAS), pp , [3] Y. Cai and K.A. Hua, An Adaptive Query Management Techniue fr Efficient Real-Time Mnitring f Spatial Regins in Mbile Database Systems, Prc. IEEE Int l Perfrmance Cmputing and Cmm. Cnf. (IPCCC), pp , [4] A. Civilis, C.S. Jensen, J. Nenrtaite, and S. Pakalnis, Efficient Tracking f Mving Objects with Precisin Guarantees, Prc. Int l Cnf. Mbile and Ubiuitus Systems (MbiQuitus), pp , [5] R.M. Fujimt, Parallel and Distributed Simulatin Systems. Wiley- Interscience, [6] V. Gaede and O. Gunther, Multidimensinal Access Methds, ACM Cmputing Surveys, vl. 30, n. 2, pp , [7] B. Gedik and L. Liu, MbiEyes: Distributed Prcessing f Cntinuusly Mving Queries n Mving Objects in a Mbile System, Prc. Int l Cnf. Extending Database Technlgy (EDBT), [8] B. Gedik, K.-L. Wu, P.S. Yu, and L. Liu, Mtin Adaptive Indexing fr Mving Cntinual Queries ver Mving Objects, Prc. ACM Cnf. Infrmatin and Knwledge Management (CIKM), [9] S. Ilarri, E. Mena, and A. Illarramendi, A System Based n Mbile Agents fr Tracking Objects in a Lcatin-Dependent Query Prcessing Envirnment, Prc. Int l Wrkshp Database and Expert Systems Applicatins (DEXA), pp , [10] C.S. Jensen, D. Lin, and B.C. Oi, Query and Update Efficient B+-Tree Based Indexing f Mving Objects, Prc. Int l Cnf. Very Large Data Bases (VLDB), pp , [11] D.V. Kalashnikv, S. Prabhakar, S. Hambrusch, and W. Aref, Efficient Evaluatin f Cntinuus Range Queries n Mving Objects, Prc. Database and Expert Systems Applicatins (DEXA), pp , [12] G. Kllis, D. Gunpuls, and V.J. Tstras, On Indexing Mbile Objects, Prc. ACM Principles f Database Systems (PODS), pp , [13] I. Lazaridis, K. Prkaew, and S. Mehrtra, Dynamic Queries ver Mbile Objects, Prc. Int l Cnf. Extending Database Technlgy (EDBT), pp , 2002.

18 668 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 18, NO. 5, MAY 2006 [14] L. Liu, C. Pu, and W. Tang, Cntinual Queries fr Internet Scale Event-Driven Infrmatin Delivery, IEEE Trans. Knwledge and Data Eng., pp , [15] M.F. Mkbel, X. Xing, and W.G. Aref, SINA: Scalable Incremental Prcessing f Cntinuus Queries in Spati-Tempral Databases, Prc. ACM Special Interest Grup n Management f Data Cnf. (SIGMOD), pp , [16] B.W. Parkinsn, J.J. Spilker, P. Axelrad, and P. Eng, Glbal Psitining System: Thery and Applicatins, Vl. 2. Am. Inst. Aernautics and Astrnautics, [17] J.M. Patel, Y. Chen, and V.P. Chakka, Stripes: An Efficient index fr Predicted Trajectries, Prc. ACM Special Interest Grup n Management f Data Cnf. (SIGMOD), pp , [18] D. Pfser, C.S. Jensen, and Y. Thedridis, Nvel Appraches in Query Prcessing fr Mving Object Trajectries, Prc. Very Large Data Bases Cnf. (VLDB), pp , [19] S. Prabhakar, Y. Xia, D.V. Kalashnikv, W.G. Aref, and S.E. Hambrusch, Query Indexing and Velcity Cnstrained Indexing, IEEE Trans. Cmputers, vl. 51, n. 10, pp , Oct [20] S. Saltenis, C.S. Jensen, S.T. Leutenegger, and M.A. Lpez, Indexing the Psitins f Cntinuusly Mving Objects, Prc. ACM Special Interest Grup n Management f Data Cnf. (SIGMOD), [21] Z. Sng and N. Russpuls, Hashing Mving Objects, Prc. IEEE Mbile Data Management, [22] Z. Sng and N. Russpuls, k-nearest Neighbr Search fr Mving Query Pint, Prc. Symp. Spatial and Tempral Databases (SSTD), [23] Y. Ta, D. Papadias, and Q. Shen, Cntinuus Nearest Neighbr Search, Prc. Int l Cnf. Very Large Data Bases, [24] Y. Ta, D. Papadias, and J. Sun, The TPR -Tree: An Optimized Spati-Tempral Access Methd fr Predictive Queries, Prc. Very Large Data Bases Cnf. (VLDB), [25] D.B. Terry, D. Gldberg, D. Nichls, and B.M. Oki, Cntinuus Queries ver Append-Only Database, Prc. ACM Special Interest Grup n Management f Data Cnf. (SIGMOD), [26] Y. Thedridis, E. Stefanakis, and T. Sellis, Efficient Cst Mdels fr Spatial Queries Using R-Trees, IEEE Trans. Knwledge and Data Eng., vl. 12, n. 1, pp , Jan./Feb [27] O. Wlfsn, Mving Objects Infrmatin Management: The Database Challenge, Prc. Next Generatin Infrmatin Technlgies and Systems, [28] O. Wlfsn, A.P. Sistla, S. Chamberlain, and Y. Yesha, Updating and Querying Databases that Track Mbile Units, Distributed and Parallel Databases, vl. 7, n. 3, pp , [29] K.-L. Wu, S.-K. Chen, and P.S. Yu, Prcessing Cntinual Range Queries ver Mving Objects Using VCR-Based Query Indexes, Prc. Int l Cnf. Mbile and Ubiuitus Systems (MbiQuitus), [30] K.-L. Wu, S.-K. Chen, and P.S. Yu, On Incremental Prcessing f Cntinual Range Queries fr Lcatin-Aware Services and Applicatins, Prc. Int l Cnf. Mbile and Ubiuitus Systems (MbiQuitus), [31] X. Xing, M.F. Mkbel, and W.G. Aref, SEA-CNN: Scalable Prcessing f Cntinuus k-nearest Neighbr Queries in Spati- Tempral Databases, Prc. IEEE Int l Cnf. Data Eng., [32] X. Yu, K.Q. Pu, and N. Kudas, Mnitring K-Nearest Neighbr Queries ver Mving Objects, Prc. IEEE Int l Cnf. Data Eng., Bugra Gedik received the BS degree frm the Cmputer Engineering and Infrmatin Science Department at Bilkent University, Turkey. He is currently a PhD candidate in the Cllege f Cmputing at the Gergia Institute f Technlgy. He cnducts research n varius aspects f distributed data intensive systems, including peer-t-peer cmputing, mbile data management and lcatin-based services, and sensr netwrk cmputing. His research emphasis is n develping systemlevel architectures and techniues t address scalability prblems in distributed infrmatin mnitring services. He was a prgram cmmittee member fr the 22nd IEEE Internatinal Cnference n Data Engineering (ICDE 2006) and received the best paper award at the 23rd IEEE Internatinal Cnference n Distributed Cmputing Systems (ICDCS 2003). He is a student member f the IEEE Cmputer Sciety. Kun-Lung Wu received the BS degree in electrical engineering frm the Natinal Taiwan University, Taipei, Taiwan, and the MS and PhD degreess in cmputer science frm the University f Illinis at Urbana-Champaign. He is with the IBM Thmas J. Watsn Research Center, currently as a member f the Sftware Tls and Techniues Grup. His recent research interests include data streams, cntinual ueries, mbile cmputing, Internet technlgies and applicatins, database systems, and distributed cmputing. He has published extensively and hld many patents in these areas. He is a senir member f the IEEE Cmputer Sciety and a member f the ACM. He was an assciate editr fr the IEEE Transactins n Knwledge and Data Engineering, He was the general chair fr the Third Internatinal Wrkshp n E-Cmmerce and Web-Based Infrmatin Systems (WECWIS 2001). He received a best paper award frm IEEE EEE He is an IBM Master Inventr. Philip S. Yu received the BS degree in electrical engineering frm Natinal Taiwan University, the MS and PhD degrees in electrical engineering frm Stanfrd University, and the MBA degree frm New Yrk University. He is with the IBM Thmas J. Watsn Research Center and is currently the manager f the Sftware Tls and Techniues Grup. His research interests include data mining, Internet applicatins and technlgies, database systems, multimedia systems, parallel and distributed prcessing, and perfrmance mdeling. He has published mre than 430 papers in refereed jurnals and cnferences and hlds r has applied fr mre than 250 US patents. He is a fellw f the ACM and a fellw f the IEEE. He is assciate editr f ACM Transactins n the Internet Technlgy and The ACM Transactins n Knwledge Discvery in Data. He is a member f the IEEE Data Engineering steering cmmittee and is als n the steering cmmittee f the IEEE Cnference n Data Mining. He was the editr-in-chief f IEEE Transactins n Knwledge and Data Engineering ( ) and als served as an assciate editr f Knwledge and Infrmatin Systems. He will serve as the general chair f the 2006 ACM Cnference n Infrmatin and Knwledge Management and the prgram chair f the 2006 jint cnferences f the Eighth IEEE Cnference n E-Cmmerce Technlgy (CEC 06) and the Third IEEE Cnference n Enterprise Cmputing, E-Cmmerce and E- Services (EEE 06). He served as the general chair f the 14th IEEE Intl. Cnference n Data Engineering and the general c-chair f the Secnd IEEE Internatinal Cnference n Data Mining. He received an Outstanding Cntributins Award frm IEEE Internatinal Cnference n Data Mining in 2003 and als an IEEE Regin 1 Award fr "prmting and perpetuating numerus new electrical engineering cncepts" in He is an IBM Master Inventr. Ling Liu is an assciate prfessr at the Cllege f Cmputing at Gergia Institute f Technlgy. There, she directs the research prgrams in Distributed Data Intensive Systems Lab (DiSL), examining research issues and technical challenges in building large-scale distributed cmputing systems that can grw withut limits. Their wrk has included peer-tpeer cmputing, data-grid cmputing, and enterprise cmputing systems. She has published mre than 150 internatinal jurnal and cnference articles. Her research grup has prduced a number f sftware systems that are either pen surce r directly accessible nline, amng which the mst ppular nes are WebCQ and XWRAPElite. Mst f Dr. Liu s current research prjects are spnsred by NSF, DE, DARPA, IBM, and HP. She is n the editrial bard f several internatinal jurnals, such as IEEE Transactins n Knwledge and Data Engineering, Internatinal Jurnal f Very Large Database Systems (VLDBJ), and Internatinal Jurnal f Web Services Research. She has chaired a number f cnferences as a prgram cmmittee chair, a vice prgram cmmittee chair, r a general chair. She is a member f the IEEE