Boosting Location-Based Services with a Moving Object Database Engine

Transcription

1 Boosing Locaion-Based Services wih a Moving Objec Daabase Engine ABSTRACT Nikos Pelekis Dep of Informaics Univ. of Piraeus, Hellas npelekis@unipi.gr Composiion of emporal and spaial properies of real world objecs in a unified daa framework resuls ino Moving Objec Daabases (MOD). MODs are able o process, manage and analyze discreely or coninuously changing spaio-emporal daa. This paper presens HERMES Moving Daa Carridge, which provides MOD funcionaliy o OpenGIS-compaible sae-of-hear Objec-Relaional DBMS. HERMES is designed o be used as a pure emporal or a pure spaial sysem, however, is main applicaion is o suppor modeling and querying of moving objecs. A relevan collecion of absrac daa ypes (ADT) and heir corresponding operaions are defined, developed and provided as a daa carridge exending SQL-like query languages wih MOD semanics. The usefuleness of he resuling query language is demonsraed by developing an applicaion on op of his framework, which builds and visualizes he resuls of a palee of spaio-emporal queries ha have been proposed in he lieraure as an advanced Locaion-Based Services (LBS) benchmarking framework for he evaluaion of MOD engines. Caegories and Subjec Descripors: H.2.4 [Daabase Managemen]: Sysems General Terms: Design Keywords: HERMES, Moving Objec Daabases, Locaion-Based Services, Daa Carridge, Benchmark Queries. 1. INTRODUCTION Spaial daabase research has focused on supporing he modeling and querying of geomeries sored in a daabase. On he oher hand, emporal daabases have focused on exending he knowledge kep abou he curren sae of he real world o include he pas, in he wo senses of he pas of he real world (valid ime) and he pas saes of he daabase (ransacion ime). Abou a decade effors aemp o achieve an appropriae kind of ineracion beween boh sub-areas of daabase research. Spaioemporal daabases are he oucome of he aggregaion of ime and space ino a single framework [15], [1], [16], [10]. Permission o make digial or hard copies of all or par of his work for personal or classroom use is graned wihou fee provided ha copies are no made or disribued for profi or commercial advanage and ha copies bear his noice and he full ciaion on he firs page. To copy oherwise, or republish, o pos on servers or o redisribue o liss, requires prior specific permission and/or a fee. MobiDE 06, June 25, 2006, Chicago, Illinois, USA. Copyrigh 2006 ACM /06/ $5.00. Yannis Theodoridis Dep of Informaics Univ. of Piraeus, Hellas yheod@unipi.gr As delineaed in he review papers jus cied, a serious weakness of exising approaches is ha each of hem deals wih few common characerisics found across a number of specific applicaions. Thus, he applicabiliy of each approach o differen cases fails on spaio-emporal behaviors no anicipaed by he applicaion used for he iniial model developmen. The aim of his paper is o describe a robus framework capable of aiding a spaio-emporal daabase developer in modeling, consrucing and querying a daabase wih objecs ha change locaion, shape and size, eiher discreely or coninuously in ime. Objecs ha change locaion coninuously are much more difficul o accommodae in a daabase in conras o discreely changing objecs. Supporing boh ypes of spaio-emporal objecs (he so-called moving objecs) is one of he challenges adoped by his paper. In paricular, we presen an inegraed and comprehensive design of moving objec daa ypes in he form of a daa carridge, called HERMES Moving Daa Carridge (HERMES-MDC). HERMES-MDC is he core componen of he objec-relaional par of he HERMES sysem archiecure [14]. HERMES provides he funcionaliy o consruc a se of moving, expanding and/or shrinking geomeries, modeled as sequences of simple coninuous funcions ha obain hyposasis when projeced o he spaial domain a a specific insan associaed wih of ime. Each one of hese geomeries is cased wih a se of mehods ha faciliae he carridge user o query and analyze spaio-emporal daa. Embedding his funcionaliy offered by HERMES-MDC in he daa manipulaion language of an OpenGIS-compaible sae-of-he-ar objecrelaional DBMS, one obains a moving objec query language ha ouperforms relaed work, in erms of flexibiliy, expressiveness and ease of use. One could menion a series of applicaions of HERMES (from he name of he ancien Greek god of Commerce) a various levels in he conex of mobile services. For example, HERMES can be used as a plug-in in elecom daa warehouses ha handle spaioemporal conen. This example refers o offline processing of such hisorical daa. Besides, HERMES suppors he daa managemen of real-ime mobile services, addressing he issues of emerging online applicaions. For insance, imagine a user (raveler, consumer, ec.) moving around a ciy wih a high echnology mobile erminal a hand (e.g. a smarphone or PDA equipped wih a GPS receiver), receiving hins of informaion, commercial spos ec. Moivaed from such kind of applicaion scenarios, recen research has ried o model spaio-emporal daabases using his concep of moving objecs and inegrae hem ino any exensible DBMS [3], [4], [6], [8]. On he oher hand, commercial relaional or objec-relaional daabase sysems offer limied capabiliy of handling his kind of non-radiional daa (objec rajecories, in ime and space). HERMES is he parial

2 realizaion of he above discussed research vision in sae-of-hear Objec-Relaional DBMS. In order o demonsrae he usefulness and applicabiliy of he server-side exensions provided by HERMES we implemen an LBS applicaion on op of his MOD funcionaliy. The general idea is o provide a flexible linkage for a non-exper user o pose a palee of MOD queries ha have been proposed in he lieraure [19] as an advanced (LBS) benchmarking framework for he evaluaion of MOD engines. To he bes of our knowledge, his is he firs work rying o boos LBS uilizing a MOD engine. In he res of he paper, we firs presen our daa ype model inroduced by HERMES-MDC (Secion 2), and hen we propose an appropriae se of operaions for he above ypes ha exend SQL wih MOD semanics (Secion 3). For evaluaion purposes, HERMES-MDC is applied o he previously discussed LBS case sudy (Secion 4). Subsequenly, he paper presens relaed work in he field in comparison wih HERMES-MDC funcionaliy (Secion 5). Finally, he paper winds up and a he same ime poins ou some ineresing fuure research direcions (Secion 6). 2. HERMES MOVING DATA CARTRIDGE In his secion, we design a daa ype model for he endorsemen of exending a query language wih consrucs ha would enable he querying of MODs. We focus on capuring spaio-emporal processes ha change coninuously as his is he mos challenging and also allow us o capure spaio-emporal phenomena ha change in discree seps as a special case of coninuous change. The daa ypes are classified ino wo main caegories. The firs caegory consiss of off-he-shelf base, (saic) spaial and emporal ypes and he second caegory inroduces ypes ha describe moving objecs. 2.1 Base, Temporal and Spaial Types Base ypes are he sandard daabase ypes buil ino mos DBMS, such as ineger, real numbers ec. These ypes form a subse of he aomic lieral ypes needed o define he emporal ypes. Temporal ypes are inroduced by TAU Temporal Lieral Library (TAU- TLL) in [13], which is he componen of HERMES sysem responsible for providing HERMES-MDC wih pure emporal objec-relaional funcionaliy. Basically, his carridge implemens he Time Model, adoped by he TAU Temporal Objec Model [9], and augmens he four emporal lieral daa ypes found in ODMG objec model [2] (namely, Dae, Time, Timesamp and Inerval) wih hree new emporal objec daa ypes (namely, Timepoin, Period and Temporal Elemen). TAU- TLL provides clear semanics abou he ime boundaries, ime order, ime reference, emporal granulariies, and he suppored calendar. On he oher hand, saic spaial ypes are suppored by a daa carridge providing an inegraed se of funcions and procedures ha enable spaial daa o be sored, accessed, and analyzed quickly and efficienly, such as Oracle Spaial [12]. 2.2 Moving Types As discussed in [20], he daa obained from moving poin objecs is similar o a sring, arbirary oriened in 3D space, where wo dimensions correspond o 2D (x-, y-) plane and one dimension corresponds o ime. Insead of a sring and due o discreizaion, a MOD sores and manipulaes a 3D polyline represening he rajecory of he objec (i.e., a sequence of 3D line segmens, where each segmen represens he coninuous developmen of he moving objec during sampled locaions). This idea is exended by HERMES-MDC in a way ha a moving poin can be defined as a sequence of differen ypes of simple funcions. The general idea is o decompose he definiion of each moving ype ino several definiions, one for each of he simple funcions, and hen compose hese sub-definiions as a collecion o define he moving ype. Each one of he sub-definiions corresponds o a so-called uni moving ype. In order o define a uni moving ype, we need o associae a period of ime wih he descripion of a simple funcion ha models he behavior of he moving ype in ha specific ime period. Based on his approach, wo real-world noions are direcly mapped o our model as objec ypes, namely ime period and funcion. The firs concep (called Period<SEC> in TAU-TLL erminology [13]) implies a closedopen ime inerval (i.e. [b, e), where b is he beginning and e is he ending poin of he period) wih granulariy a he second level (oher granulariies are also suppored i.e. minue, hour ec). The second concep is an objec ype, named Uni_Funcion, defined as a riple of (x, y) coordinaes ogeher wih some addiional moion parameers. The firs wo coordinaes represen he iniial (x i, y i ) and ending (x e, y e ) coordinaes of he sub-moion defined, while he hird coordinae (x c, y c ) corresponds o he cenre of a circle upon which he objec is moving. Wheher we have consan, linear or arc moion beween (x i, y i ) and (x e, y e ) is implied by a flag indicaing he ype of he simple funcion. Since we require ha HERMES manages no only hisorical daa, bu also online and dynamic applicaions, we furher le a Uni_Funcion o model he case where a user currenly (i.e., a an iniial imepoin) is locaed a (x i, y i ) and moves wih iniial velociy v and acceleraion a on a linear or circular arc roue. Figure 1 depics a poin moving wih differen kind of funcions along subsequen emporal periods. yy' xx ' ε [1, 2) -> Lin ea r m ove m e n ε [2, 3) -> A rc m o ve m e n ε [3, 4) -> C on s m o ve m en ε [4, 5) -> Lin ea r m ove m e n Figure 1 Moving Poin wih various ypes of movemen In he case of arc moions, following he caegorizaion of realisic arc moions iniially discussed in [23], we classify hem according o he quadran he moion akes place and moion heading (clockwise or counerclockwise). Figure 2 illusraes one of he possible eigh cases (e.g. quadran I - clockwise direcion). φ Figure 2 Moion on a circular arc '

3 For consan and linear moions, he inerpolaion of a moving poin s locaion in an inermediae imepoin is sraighforward. For arc moions, here is need of some rigonomeric calculaions. For he case of Figure 2 he necessary operaions are illusraed in Eq. 1. Following a similar process, we develop all kinds of arc funcions in each quadran and direcion. ARC _1( ) ( x, y ) = ( x S L = 2 R Sin( ) 2 R 1 2 S = v + a 2 π 1 yc yi S φ = + Sin ( ) 2 R 2 R + L Cos, y φ ι + L Sinφ) v 0, [ i, e), φ (, + ) Consequenly, Uni_Funcion is defined as follows: ι Eq. 1 Definiion 1: Uni_Funcion = d x i :double, y i :double, x e :double, y e :double, x c :double, y c :double, v:double, a:double, flag:typeoffuncion, where Π TypeOfFuncionΤ={ CONST, PLNML_1, ARC_<1..8> } Combining Uni_Funcion and Period<SECOND> objec ypes ogeher, he mos primiive and simples uni objec ype is defined, namely Uni_Moving_Poin. This is a fundamenal ype since all he successor uni ypes are defined based upon i. As such, Definiion 2: Uni_Moving_Poin = d p: Period SEC, m: Uni_Funcion Following his, we define wo uni moving ypes direcly based on Uni_Moving_Poin, namely Uni_Moving_Circle and Uni_ Moving_Recangle. As i is easily inferred, hese wo objec ypes model circular and recangular geomery consrucs ha change heir posiion and/or exen over ime. Uni_Moving_Circle consiss of hree Uni_Moving_Poin objecs, represening he hree poins (f, s, ) needed o define a valid circle. In he same way, Uni_Moving_Recangle is composed of wo Uni_Moving_Poin objecs, modeling he lower-lef (ll) and upper-righ (ur) poin needed o define a valid recangle. An inuiive consrain is ha ime periods during which hese uni poins are moving mus be equal. More formally, Definiion 3: Uni_Moving_Circle = d { f: Uni_Moving_Poin, s: Uni_Moving_Poin, : Uni_Moving_Poin equal (f.p, s.p,.p) } Definiion 4: Uni_Moving_Recangle = d { ll: Uni_Moving_Poin, ur: Uni_Moving_Poin equal (ll.p, ur.p) } For modeling objec ypes such as Uni_Moving_Polygon and Uni_Moving_LineSring here is need for an inermediae objec ype called Uni_Moving_Segmen objec, which models a simple line or arc segmen ha changes is shape and size according o is saring and ending poins. As such, Uni_Moving_Segmen is formed by hree Uni_Moving_ Poin objecs and a flag indicaing he kind of inerpolaion beween he saring and ending poin of he LineSring geomery. The simples par of a LineSring geomery can be eiher a linear or an arc segmen. In oher words, his flag exemplifies he usage of he oher aribues of Uni_Moving_Segmen. This is clarified in Figure 3 where a moving segmen is mapped o a line segmen a wo differen ime insans 1 and 2. During he ime period beween 1 and 2, he saring uni moving poin mp 1 follows a simple linear rajecory, while he ending uni moving poin mp 2 follows an arc rajecory. xx' mp1 1 mp2 mp1 2 mp2 Figure 3 Linear Uni Moving Segmen Definiion 5: Uni_Moving_Segmen = d { b: Uni_Moving_Poin, e: Uni_Moving_Poin, m: Uni_Moving_Poin, kind:typeofsegmen (kind = SEG equal (b.p, e.p)) (kind = ARC equal (b.p, e.p, m.p)) }, where Π TypeOfSegmen Τ = { SEG, ARC } Consequenly, a Uni_Moving_LineSring is defined as a se of Uni_Moving_Segmen objecs, while a Uni_Moving_Polygon is a collecion of Uni_Moving_Segmen objecs, wih an addiional flag indicaing if his se of moving segmens forms he exerior ring of a polygon or an inerior (hole) ring, which a any ime does no cross or ouch he exerior boundary. In erms of se heory, Definiion 6: Uni_Moving_Linesring = d { l: se Uni_Moving_Segmen i, j ulong: i j equal (l i.b.p, l j.e.p) } Definiion 7: Uni_Moving_Polygon = d { l: se Uni_Moving_ Segmen, hole:boolean i, j ulong: i j equal (l i.b.p, l j.e.p) } Having defined he fundamenal uni moving ypes, we now inroduce he moving ypes ha play he dominan role in HERMES daa ype sysem. The process ha is followed o define he moving ypes is o inroduce a moving ype as a collecion of he corresponding uni moving ype. Having his in mind, we consruc a Moving_Poin objec ype as a collecion of Uni_Moving_Poin objecs, whose periods mus be sequenial and should no overlap. The projecion of a Moving_Poin o he spaial dimension should resul o a valid poin geomery. In oher words, Definiion 8: Moving_Poin = d { ab: se Uni_Moving_Poin i, j ulong, 1 i, j se Uni_Moving_Poin : j= i+1 before(ab i.p, ab j.p) overlaps(ab i.p, ab j.p) double: inside(, ab i.p) a_insan() Geomery(poin)} Similarly o he Moving_Poin, oher moving ypes are consruced as collecions of heir uni counerpars. Due o space limiaions, we only presen he definiion of a Moving_ Linesring. Definiion 9: Moving_LineSring = d { line: se Uni_Moving_ LineSring i, j ulong, 1 i, j se Uni_Moving_ LineSring : j= i+1 before(line i.l 1.b.p, line j.l 1.e.p) overlaps(line i.l 1.b.p, line j.l 1.e.p) double: inside(, line i.l 1.b.p) a_insan(line,) Geomery(linesring) } The definiion of Moving_Polygon is very close o ha of Moving_LineSring. Acually, he differences beween hese wo yy'

4 moving ypes arise from he differen uilizaion of heir collecions of moving segmens by he objec mehods. For example, an operaion ha maps a Moving_LineSring o a LineSring geomery checks for inequaliy on he saring and ending poins of he line and his is a prerequisie for consrucing he geomery. On he conrary, he corresponding mehod for a moving polygon checks for he opposie, in order o be able o consruc a valid polygon. Anoher discrepancy of Moving_Polygon, in conras o all he oher moving ypes, is ha in case i includes inerior moving holes, hen several Uni_Moving_Polygon objecs need o be accessed in order o ransform i o is corresponding OpenGIS-compaible spaial geomery a a specific insan. Similarly, in order o model homogeneous collecions of moving ypes, muli-moving ypes are defined as collecions of he corresponding moving ypes. Consequenly, he proposed spaioemporal model is augmened by he following objec ypes: Muli_Moving_Poin, Muli_Moving_Circle, Muli_Moving_ Recangle, Muli_Moving_LineSring and Muli_Moving_ Polygon. An ineresing issue here is ha he previously menioned muli-moving ypes do no carry heir own mehods inerface. The funcionaliy for hese ypes can be invoked by he mehods of anoher objec ype, called Moving_Collecion, sanding as he superype and aggregaing he inerfaces, he objec mehods and he spaio-emporal semanics of all he muli moving ypes. Furhermore, Moving_Collecion is able o represen heerogeneous collecions of moving ypes. The mehods of Moving_Collecion rea all he muli moving ypes uniformly and hey do no have he knowledge wheher hey are dealing wih a homogeneous or heerogeneous collecion. The formal definiion of Moving_Collecion is omied as a rivial one. We also inroduce an objec ha encapsulaes all semanics and funcionaliy offered by all moving ypes. The so-called Moving_Objec objec ype is he conjuncion of all he oher moving objec ypes, which implies ha his objec can compleely subsiue any oher moving ype. Furhermore, Moving_Objec models any moving ype ha can be he resul of an operaion beween moving objecs. For example, he inersecion of a Moving_Poin wih a polygon geomery forms a second Moving_Poin ha is he resricion of he firs Moving_Poin inside he polygon. This resul can be modeled as a Moving_Objec. If he resul of an operaion is no a moving geomery hen Moving_Objec plays he role of a degeneraed moving ype. For example, le us assume an operaion ha requess he perimeer of Moving_Polygon; obviously, he resul of his mehod is a ime-varying real number (Moving_Real). Such collapsed moving ypes like moving real, sring, and boolean are also modeled using he Moving_Objec objec ype. Moving_Objec is no inended o be direcly used or consruced by HERMES user. On he conrary, i is inended o be he resul ype of operaions of he oher moving ypes (i.e., sysem generaed). For a deailed descripion of Moving_Objec ype he ineresed reader is referred o [13]. Figure 4 illusraes he UML class diagram of he above defined moving objec daa ypes [14]. 3. OPERATIONS ON MOVING OBJECTS The design of he operaions of he objec ypes inroduced by HERMES-MDC adheres o hree principles: a) design operaions as generic as possible; b) achieve consisency beween operaions on pure spaial, pure emporal and spaio-emporal ypes; c) capure he ineresing phenomena. Figure 4 HERMES-MDC Class Diagram For he firs principle we focus on properies shared by many ypes. In order o achieve consisency of operaions on spaial, emporal and moving ypes, we firs sudy operaions proposed in he lieraure for pure spaial ypes and we selec hose operaions ha we would like o associae wih emporal semanics. In a second sep, we use he funcionaliy of he emporal ypes inroduced by he emporal componen of HERMES (TAU-TLL) and we sysemaically exend he operaions defined in he firs sep o he emporal varians of he respecive ypes. The hird sep akes he previous ime-dependan operaions as is ouse and removes heir ime dimension hus no reurning pure spaial, emporal or sandard daa ypes, bu oher moving ypes (e.g. he lengh of a moving linesring independenly of a specific ime poin). Finally, o achieve closure of ineresing phenomena, our developmen is driven by sae-of-he-ar emerging applicaions such as LBS. The following secions describe he funcionaliy wih which SQL-like query languages are enhanced by he use of HERMES funcionaliy. The presenaion of he operaions hides he echnical deails ha would disorien us from expressing he power of he resuled query language. As such, we absracly describe he algorihms for only a moivaing se of operaions. Due o space limiaions we focus our discussion on mehods defined on Moving_Poin ype (as he mos challenging and LBS relevan); however operaions wih similar semanics are also defined for he res ypes. 3.1 Topological and Disance Predicaes HERMES-MDC provides objec mehods in he form of predicaes o describe relaionships beween moving ypes. There are wo ses of predicaes suppored by HERMES-MDC, namely wihin_disance and relae. Each se of predicaes consiss of eigh operaions, each of which models he relaionship of he caller moving ype wih any ime-varying (or no) geomery objec. Each operaion comes wih wo differen overloaded signaures, modeling differen semanics: he firs signaure is ime-dependen while he second is independen o he ime dimension. Below, he reader can find he pair of signaures of only one of he eigh

5 operaions. The ime-dependen signaure of he mehod is he one wihou he brackes, while he ime-independen version of he operaion can be obained by subsiuing he reurn ype of he operaion wih he ype in he brackes { } and by removing he Timepoin<SEC> argumen from he parameer lis. This is a common noaion in he remainder of he paper. boolean {Moving_Objec} wihin_disance (disance, Moving_Poin, olerance, Timepoin<SEC>) The ime-dependen predicae deermines wheher wo moving objecs are wihin some specified Euclidean disance from each oher a a user-defined ime poin. Afer mapping he moving objecs o physical spaial geomeries a he given insan, he funcion reurns rue for objec pairs ha are wihin he specified disance; reurns false oherwise. The disance beween wo nonpoin objecs (such as lines and polygons) is defined as he minimum disance beween hese wo objecs. Many objec mehods in HERMES-MDC accep a olerance parameer. If he disance beween wo poins is less han or equal o he olerance, he carridge considers he wo poins o be a single poin. Thus, olerance is usually a reflecion of how accurae or precise users perceive heir spaio-emporal daa o be. Also, he ime-independen wihin_disance operaion differs from he above predicae in ha he reurn value is a Moving_Objec ha represens a ime-varying boolean value. This implicily defined moving boolean objec models he sequence of he ime inervals ha he wo relaed objecs are wihin or no some specified Euclidean disance. Varchar2 {Moving_Objec} relae (mask, Moving_Polygon, olerance, Timepoin<SEC>) This generic predicae examines wo moving objecs and deermines heir opological relaionship. As previously, he relae predicae appears wih wo overloaded versions. The firs evaluaes he opological relaionship upon a specific user-defined ime poin, while he second version reurns a Moving_Objec modeling a ime-varying sring, which describes he evoluion in he opological relaionship beween he relaed objecs. The user can specify he kind of any of he well-known opological relaionships ha he/she requires o check via he mask parameer. 3.2 Ineracion wih he Temporal and Spaial Domains HERMES-MDC provides objec mehods for resricing and/or projecing moving ypes o he emporal and he spaial domain. Subsequenly, we presen he mos imporan operaions defined for Moving_Poin. Uni_Moving_Poin uni_ype (Timepoin<SEC>) The simple bu very imporan ask ha his funcion performs is ha i finds he uni moving objec whose aribue ime period conains he user-defined ime poin. In oher words, i reurns ha uni-moving ype where he ime insan represened by he argumen Timepoin<SEC> objec is inside he ime period ha characerizes he uni-moving ype. Moving_Poin add_uni (Uni_Moving_Poin) This operaion adds a new coming uni of movemen as his is described by a Uni_Moving_Poin objec. Naurally, he mehod performs special consisency operaions (e.g. he period of he argumen mus no overlap wih he lifespan of he iniial objec) o asser he soundness of he consruced objec. Union_Oupu a_insan (Timepoin<SEC>) The a_insan operaion is he operaion ha maps he moving ypes o meaningful OpenGIS-compaible spaial objecs. The reurn ype (Union_Oupu) is an objec ha represens he union of all he possible resuls of he projecion of a Moving_Objec a a user-defined ime poin. In oher words, if Moving_Objec represens a ime-varying geomery hen Union_Oupu is basically a Geomery objec. If Moving_Objec represens a moving real or sring hen Union_Oupu is a real number or a sring, respecively. In he case of Moving_Collecion, his operaion invokes he a_insan operaions of all he moving ypes of he muli moving objecs and subsequenly applies a special union operaion upon he projeced geomeries by concaenaing hem in a collecion objec and reurns he resul of he concaenaion. Moving_Poin a_period (Period<SEC>) The a_period objec mehod is an operaion ha resrics a moving objec o he emporal domain. In oher words, by using his funcion he user can delimi he ime period ha is meaningful o ask he projecion of he moving objec o he spaial domain. More specifically, he ime period passed as argumen o he mehod is compared wih he Period<SEC> objecs ha characerize he uni moving objecs. If he parameer period does no overlap wih he compared period hen he corresponding uni ype is omied. If i overlaps, hen he ime period ha defines a uni-moving objec becomes is inersecion wih he given period. Temp_Elemen<SEC> emp_elemen () The emp_elemen operaion gives HERMES-MDC user he capabiliy o projec he ime periods ha form he uni moving objecs ha compose a moving ype on he ime line and subsequenly concaenae all hese disinc ime periods o consruc a emporal elemen. Figure 5 depics he resul of he emp_elemen operaion when applied o a Moving_Poin objec. x x ' p 1 p 2 p 3 p p 1 - > [ 1, 2 ) p 2 - > [ 2, 3 ) p 3 - > [ 4, 5 ) p 4 - > [ 5, 6 ) e m p _ e l e m e n - - > p 1 + p 2 + p 3 + p 4 Figure 5 Projecion of a Moving Poin on he ime axis Moving_Poin a_emp_elemen (Temp_Elemen<SEC>) y y ' i m e l i n e Similarly o he a_period operaion, he a_emp_elemen mehod resrics he moving objec o he emporal domain, bu he process of resricing he periods beween which he moving objec is valid is driven by a collecion of Period<SEC> objecs and no jus one Period<SEC> objec as in he previous case. Moving_Poin a_linesring (Geomery)

6 Being aware ha an objec moves on a linesring geomery during a par of is roue (e.g. a car moving along a sree), we may wish o find he porion of he Moving_Poin resriced by his 1- dimensional geomery. This is exacly he oupu of his mehod. Union_Oupu iniial () The iniial objec mehod is basically he a_insan operaion invoked a he firs insan of ime ha he moving objec is valid, meaning he firs second of he closed-open period ha idenifies he leas recen uni moving objec. Union_Oupu final () Similarly o he iniial objec mehod, he final operaion projecs he moving objec a he las valid insan of he ime period ha characerizes he mos recen uni moving objec. Geomery rajecory () This operaion reconsrucs he rajecory raveled by a Moving_Poin. More specifically, he operaion projecs he movemen of a Moving_Poin o he Caresian plane by mapping he componen Uni_Moving_Poin objecs o single linear or arc segmens, while a process of merging hese segmens follows, o form he reurned LineSring geomery. 3.3 Disance and Direcion Operaions The following mehods assis he carridge user o calculae he minimum disance or he direcional relaionship beween moving objecs. number {Moving_Objec} disance (Moving_Poin, olerance, Timepoin<Sec>) HERMES-MDC provides a disance measure ha exiss for all moving ypes, which eiher compues he disance beween wo insaniaed moving objecs (ime-dependen version) or reurns a ime-varying real number ha represens he minimum disance beween hese moving ypes a any ime (ime-independen version). The disance beween wo objecs is he disance beween he closes pair of poins or segmens of he wo objecs. number {Moving_Objec} direcion (Moving_Poin, Timepoin<Sec>) The direcion funcion reurns he angle of he line from he firs o he second moving poin (measured in degrees, 0 angle < 360 ), afer hese have been projeced o he Caresian plane a a specific ime poin. The ime-independen version of he funcion reurns a Moving_Objec modeling a moving real, which corresponds o he ime-changing angle formed by he concepual line segmen ha joins he wo moving poins and he xx axis. boolean lef (Geomery, Timepoin<Sec>, from, o) The lef operaion reurns rue if he locaion of he poin a he user defined imepoin is lef from he argumen geomery (i.e. he cenroid in case of geomeries wih exen), which is he case when i falls inside he area formed by he argumen angles from and o. Similarly, we define righ, fron, behind operaions. Furhermore, we augmen our operaor se wih a relaed se of mehods ha idenify wheher a moving poin is locaed wes, eas, norh, souh of a geomery. These mehods are differeniaed from he previous as we do no care for he heading of he moving poin. 3.4 Se Relaionships HERMES-MDC provides four objec mehods for describing serelaionships beween moving ypes. Subsequenly, we presen only one (inersecion) beween a Moving_Poin and a Geomery, while he res of hem (union, difference, xor) are omied. Geomery {Moving_Poin} inersecion (Geomery, olerance, Timepoin<Sec>) Invoking inersecion mehod for a Moving_Poin, as one would expec, he resul of his operaion is he projecion of iself on he spaial domain (poin geomery) a ime insans ha inersecs wih oher moving ypes or saic geomeries and null a ime insans where i is no on he boundary or he inerior of linesrings and polygons or i coincides wih none of he poins in a collecion of hem. The ime-independen version reurns he porion of he Moving_Poin ha inersecs wih he reference objec. Figure 6 depics he projecion of a Moving_Poin modeling is inersecion wih a polygon, a hree differen imepoins 1, 2, and 3. 1 Inersecion 2 Moving Poin 3 Polygon boundaries Figure 6 Demonsraing inersecion operaion A imepoin 1 i is obvious he resul of such an operaion is a linesring geomery. A imepoin 2 his inersecion has as resul a muli-linesring geomery due o he developmen of Moving_Poin, while a imepoin 3 he resuled geomery is a heerogeneous collecion of lines and poins. This operaion allows us o define mehods reurning he enering/leaving locaions (as well as he respecive imepoins) wherefrom a moving poin passes when raversing spaial regions (Figure 7). 3.5 Rae of Change An imporan propery of any ime-dependen value is is rae of change, i.e., is derivaive. A leas hree properies of he Moving_Poin permi he definiion of derivaive, namely he Euclidian disance, he direcion and he vecor difference (by viewing poins as wo-dimensional vecors). This leads o hree differen derivaive operaions, called speed, urn and velociy, respecively. Due o space consrains, we omi signaures and descripions of hese hree operaions. The reader ineresed in hese operaions as well as in oher operaions as he area raversed by a moving polygon, building moving buffer of specific widh around a pah, consrucing moving poins from he cenroid of moving areas, and finding he num_of_componens of collecions of moving ypes is referred o [13]. 4. HERMES LBS TOOL HERMES-MDC has been developed [14] as a sysem exension ha provides MOD funcionaliy o Oracle10g Objec-Relaional DBMS and, as such, he carridge funcionaliy exends PL/SQL ime

7 [7]. In order o demonsrae he usefulness and applicabiliy of he server-side exensions provided by HERMES we implemen a prooype applicaion on op of his funcionaliy which provides a graphical means o realize he majoriy of benchmark queries for LBS proposed in [19]. Especially, we develop an LBS applicaion scenario for ravelers enering he area of an airpor, consruc a spaial daabase modeling he ground plan of he airpor, and inpu random rajecories of ravelers moving around he area. The ool provides he abiliy o pose queries following he same classificaion as proposed in [19]. The idea is ha a user selecs one from a palee of such queries and according o his/her choice a wizard drives he user o parameerize his reques. A query builder dynamically consrucs he query using HERMES-MDC operaions, sends he query o he server and visualizes he resuls using MapViewer [12]. Indicaive suppored queries include: Queries on saionary reference objecs; o poin (e.g. does his check-in serve my fligh?), o range (e.g. are here any fellow ravelers in he area in fron of his check-in?), o disance-based (e.g. find he closes check-in), o neares-neighbor (e.g. find he closes coffee shops o my curren locaion) and o opological queries (e.g. find ravelers crossed his gae during he pas hour); Queries on moving reference objecs; o disance-based (e.g. find ravelers passed close o me his evening) and o similariy-based queries (e.g. find he hree mos similar rajecories o he one I have followed so far in he airpor); Join queries; o disance-join (find he closes check-ins o ravelers of his fligh) and o similariy-join queries (find he wo mos similar pairs of ravelers rajecories); Queries involving unary operaors, such as raveled disance or speed (e.g. find he average speed of ravelers on Saurday nighs). selec shape from gaes selec v.roue.ge_ener_leave_poins (selec gaes.shape from gaes where gaes.id=1) from visiors v where v.id=1 Figure 7 Visualizaion of ener/leave poins in an area of ineres 5. COMPARISON WITH RELATED WORK Several research effors have ried o model spaio-emporal daabases using he concep of ADTs for moving objecs. Such ypes for moving poins and moving regions have been inroduced by Güing and colleagues in [8], ogeher wih a se of operaions on such eniies. This model was he firs aemp o deal wih coninuous moion, while in [6] he definiion of he discree represenaion of he above-discussed ADTs was presened. The nex sep in his developmen was he sudy of algorihms for he raher large se of operaions defined in [8]. Whereas [6] jus provides a brief look ino his issue, in [11] he auhors presen a comprehensive, sysemaic sudy of algorihms for a subse of he operaions inroduced in [8]. This paper also proposed a blueprin for implemening such a moving objecs exension package for suiable exensible daabase archiecures. Anoher model using moving objecs is proposed by Wolfson and colleagues in [17], [22] and [21]. The auhors propose he socalled Moving Objecs Spaio-Temporal (MOST) daa model for daabases wih dynamic aribues, i.e. aribues ha change coninuously as a funcion of ime, wihou being explicily updaed. The auhors also offer a query language (Fuure Temporal Logic - FTL) based on emporal logic o formulae quesions abou he near fuure movemen. The approach is resriced o moving poins and does no address more complex ime-varying geomeries such as moving regions. As an exension o he absrac model in [8], he concep of spaio-emporal predicaes is inroduced in [5]. The goal is o invesigae emporal changes of opological relaionships induced by emporal changes of spaial objecs. Furher work on modeling includes [18] where he auhors focus on moving poin objecs and he inclusion of conceps of differenial geomery (speed, acceleraion) in a calculus based query language. In conras o he previous approaches, which offer limied emporal funcionaliy, HERMES provides a full operaive framework for he managemen of any emporal relaed ype of daa, as moving objecs are. This is realized hrough he implemenaion of TLL [9] as a daa carridge [13]. TAU-TLL provides clear semanics for he ime line including he ime boundaries, ime order, ime reference, muliple emporal granulariies, and he suppored calendar. In addiion, i provides an exensive se of objec ypes and mehods (superse of he corresponding ODMG [2]) for hese emporal ypes. In HERMES, he spaial funcionaliy is provided by an OpenGIScompaible ORDBMS as a separae daa carridge. The models proposed in he lieraure, provide separae objecs for consrucing differen spaial geomeries (e.g. poins, lines, regions). In our case, we have a uniform represenaion of all kinds of geomeries under he same spaial objec, which increases he flexibiliy and he ineroperabiliy beween moving ypes and pure spaial objecs. HERMES-MDC inroduces a rich ype sysem of ime-varying geomeries ha change locaion or shape in discree seps and/or coninuously. An exensive se of objec mehods is developed ha expresses all he ineresing spaio-emporal phenomena and processes. This se of operaions is a superse of he operaions inroduced in [8]. HERMES Type Sysem inroduces new objecs like Moving_Circle, Moving_Recangular, Moving_Collecion, Moving_Objec. The Moving_Collecion objec suppors no only

8 a homogeneous collecion of moving ypes bu also heerogeneous. The Moving_Objec can subsiue any of he oher moving ypes, as well as moving geomeries ha resul as operaions on oher moving geomeries and, moreover, i can model ime-varying objecs like he ime-changing perimeer of a moving region. In [8], such degeneraed moving ypes (e.g. moving real) are consruced as separae objecs, leading o a unnecessary proliferaion of objec ypes. Wha is more, he flexibiliy of HERMES-MDC can be demonsraed in various ways. For example, moving linesrings ha inersec hemselves during heir developmen are adoped by HERMES, while hey are forbidden in [8]. Apar from linear inerpolaions of spaial and moving ypes uilized in [6], HERMES also uilizes arc inerpolaions. The expressiveness of he query language was esablished in Secion CONCLUSIONS AND FUTURE WORK In his paper, a daa carridge for moving objecs, called HERMES- MDC, was inroduced. This daa carridge is a sysem exension ha provides spaio-emporal funcionaliy o OpenGIScompaible ORDBMS and suppors modeling and querying of moving objecs changing locaion eiher in discree seps or coninuously. To evaluae HERMES server-side MOD exensions we implemened a prooype applicaion whose purpose is o provide a flexible means o apply benchmark queries proposed for he evaluaion of sysems providing locaion based services. Fuure work includes considering query opimizaion as well as indexing exensibiliy inerfaces of curren ORDBMS in order o enhance he performance of HERMES-MDC daa carridge, as well as knowledge discovery from MODs using daa mining echniques. 7. ACKNOWLEDGMENTS Research parially suppored by he FP IST/FET Projec GeoPKDD (Geographic Privacy-aware Knowledge Discovery and Delivery) funded by he European Union and he Pyhagoras EPEAEK II Programme of he Greek Minisry of Naional Educaion and Religious Affairs, co-funded by he European Union. 8. REFERENCES [1] T. Abraham, J.F. Roddick. Survey of Spaio-Temporal Daabases. GeoInformaica, 3:61-99, [2] R.G.G. Cael, D.K. Barry (eds.). The Objec Daabase Sandard: ODMG 2.0. Morgan Kaufmann, May [3] S. Dieker and R. H. Guing, Plug and Play wih Query Algebras: Secondo. A Generic DBMS Developmen Environmen, Proc. In l Daabase Engineering and Applicaions Symposium (IDEAS), [4] M. Erwig, R.H. Güing, M. Schneider, and M. Vazirgiannis. Spaio-Temporal Daa Types: An Approach o Modeling and Querying Moving Objecs in Daabases. GeoInformaica, 3(3): , [5] M. Erwig and M. Schneider. Spaio-Temporal Predicaes. IEEE Transacions on Knowledge and Daa Engineering, 14(4): , [6] L. Forlizzi, R. H. Güing, E. Nardelli, M. Schneider. A Daa Model and Daa Srucures for Moving Objecs Daabases. Proc. ACM SIGMOD In l Conf. on Managemen of Daa, Dallas, Texas, USA, [7] S. Feuersein and B. Pribyl. Oracle PL/SQL Programming. O Reilly & Associaes, [8] R.H. Güing, M. H. Bohlen, M. Erwig, C. S. Jensen, N. A. Lorenzos, M. Schneider, and M. Vazirgiannis. A Foundaion for Represening and Querying Moving Objecs. ACM Transacions on Daabase Sysems, 25(1): 1-42, [9] I. Kakoudakis. The TAU Temporal Objec Model. MPhil Thesis, UMIST, Deparmen of Compuaion, [10] M. Koubarakis, T. Sellis e al. (eds.). Spaio-emporal Daabases: The Chorochronos Approach. Springer, [11] J. A. C. Lema, L. Forlizzi, R. H. Güing, E. Nardelli, M. Schneider. Algorihms for Moving Objecs Daabases. The Compuer Journal 46(6): , [12] Oracle Corp. Oracle Daabase Documenaion Library, 10g Release 1 (10.1), URL: hp://on.oracle.com/pls/db10g/. (accessed on 10 April 2006). [13] N. Pelekis. STAU: A Spaio-Temporal Exension o ORACLE DBMS. PhD Thesis, UMIST, Deparmen of Compuaion, [14] N. Pelekis, Y. Theodoridis, S. Vosinakis, T. Panayioopoulos. Hermes - A Framework for Locaion-Based Daa Managemen. Proc. 10h In l Conference on Exending Daabase Technology (EDBT), LNCS 3896, Munich, Germany, [15] N. Pelekis, B. Theodoulidis, I. Kopanakis, Y. Theodoridis. Lieraure Review of Spaio-Temporal Daabase Models. The Knowledge Engineering Review journal, 19(3), , June [16] D. Peuque. Making Space for Time: Issues in Spase-Time Daa Represenaion. GeoInformaica, 5: 11-32, [17] P. Sisla, O. Wolfson, S. Chamberlain, S.Dao. Modeling and Querying Moving Objecs. Proc. 13h In l Conf. on Daa Engineering (ICDE13), Birmingham, UK, [18] J. Su, H. Xu and O. Ibarra. Moving Objecs: Logical Relaionships and Queries. Proc. 7h In l Symp. on Spaial and Temporal Daabases (SSTD), Redondo Beach, California, USA, [19] Y. Theodoridis. Ten Benchmark Daabase Queries for Locaion-based Services, The Compuer Journal, 46(6): , [20] D. Pfoser, C. S. Jensen, and Y. Theodoridis, Novel Approaches o he Indexing of Moving Objec Trajecories, Proc. 26h In l Conf. on Very Large Daa Bases, Cairo, Egyp, [21] O. Wolfson, A. P. Sisla, S. Chamberlain and Y. Yesha. Updaing and Querying Daabases ha Track Mobile Unis. Disribued and Parallel Daabases, 7 (3): , [22] O. Wolfson, B. Xu, S. Chamberlain, L. Jiang. Moving Objecs Daabases: Issues and Soluions. Proc. 10h In l Conf. on Scienific and Saisical Daabase Managemen, Capri, Ialy, [23] P. Zhang. The Spaial Movemen Exensions of STAU. MPhil Thesis, UMIST, Deparmen of Compuaion, 2003.