Distributed Caching of Multi-dimensional Data in Mobile Environments

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1 Dstrut Cn o Mut-mnson Dt n Mo Envronmnts Bn Lu Wn-Cn L D Lun L Dprtmnt o Computr Sn Hon Kon Unvrst o Sn n Tnoo Crwtr B, Hon Kon {un, }@s.ust. Dprtmnt o Computr Sn n Ennrn Pnnsvn Stt Unvrst Unvrst Pr, PA 1682 w@s.psu.u ABSTRACT Cn s n n mportnt tnqu or svn ntwor tr n run rspons tm, sp n mo nvronmnts wr nwt s otn sr rsour. In ts ppr, w propos nov ppro or n mutmnson t n ustr o mo vs. In prtur, w ous on t most ommon tps o mut-mnson qurs, nm rn n -nrst nor qurs, omputn ron or vr qur, n t rsut t t nt, n nn t n n R*-tr t t ustr tw. Susqunt qurs r rst ssu to t R*-tr n on rmnr qurs or qurs tt nnot urnt t nswrs r snt to t rmot t srvr. To t st o our now, our wor s t rst to stu n rsuts rom omp mut-mnson qurs (.., NN qur) n propos to u n R*-tr on prvous t qur rsuts n ustr o mo vs. Rorous prmnts sow tt our ppro snnt rus ntwor tr n rspons tm. Ctors n Sut Dsrptors H.2.4 [Inormton Sstms]: Dts Mnmnt Sstms Gnr Trms Aortms, Eprmntton Kwors Cn, Mo Dt Mnmnt, Mut-mnson Dts 1. INTRODUCTION Mo omputn s n oursn wt t mturt o wrss n stnrs (.., IEEE82.11/), vnt rom t nrsn numr o om ppns on wrss (.., ptop, PDA, mo pon). W mo osts n ntronnt wt w-n onntons (.., IEEE82.11 provs up to 54 Mps t rt n wrss o r ntwor), t otn stuton wr tr s on nrrow-n n to t Intrnt rom t tw. For mp, mn m usrs sr on 56 MDM 5 5 A Np Cprus () 5 ACM /5/5...$5. Prmsson to m t or r ops o or prt o ts wor or prson or ssroom us s rnt wtout prov tt ops r not m or strut or prot or ommr vnt n tt ops r ts not n t u tton on t rst p. To op otrws, to rpus, to post on srvrs or to rstrut to sts, rqurs pror sp prmsson n/or. Kps pon n onnton. Morovr, n som r-to-r rs or mor sstr sts, wrss ntwors n mmt po ut t onnton to Intrnt or rmot srvrs s onstrn. Ts stuton s pt n F T prom oms mor svr s vr ptop out o tor s qupp wt ut-n wrss ss pt w Intrnt nrstrutur vops sow. In ts s, wn nts sumt qurs to Intrnt tss (.., onn r stt normton), t prormn s o nqut Intrnt onnton spt unnt ntr-ntwor nwt. In orr to sv tr rom/to t Intrnt n sp up qurn o Intrnt tss, rsr ommunt s vop smnt n sms [2, 5, 8, 6]. T s s tt mo nts mntn n tr s ot smnt srptons (smnt rons) n t rsuts o prvous qurs. Nw qurs tt n nswr wt o rsuts r not snt to t srvr, n qurs tt n prt nswr r trmm n on rmnr qur s snt. As su, mu ntwor tr to t srvr n ru. Smnt n s n sown to v sr prormn n mo nvronmnts ompr to p n or tup n [2]. Tou tr r unnt rsr rsuts n smnt n, no stu s n onut n n nvronmnt wr o onnton s mor nt n o owr ost tn onnton to t Intrnt, w s rt n mn osons. IEEE82.11 ustr Nrrow-n Ln Gtw Intrnt Dts Fur 1.1: Ntwor mo Ts ppr proposs omprnsv rmwor or n mut-mnson t n ustr o mo vs, w s sp sut or, ut not mt to, t ormnton nvronmnt. W ous on n rsuts rom t most ommon tps o mut-mnson qurs, nm rn n -nrst nor (NN) qurs, n m tr mportnt n orn ontrutons. W rst propos n nnovtv strut n mnsm w ns t t tw rons (t

2 rons n t smnt sp tt w n otn ompt now rom prvous qur rsuts). T tu t, owvr, r or pro (spn) t t nts tt ssu t qurs. Son, w propos to u CR-tr, sp R*-tr, t t tw to n rons totr wt tr spn. W so suss n t t onstruton n mntnn o CR-tr. Our tr ontruton s qur prossn ortms or rn n NN qurs tt t vnt o t o s strut n t ustr o mo vs n snnt sv tr rom t rmot ts. T tvnss o our ontrutons s vt rorous prmnts wt r tsts. T rst o t ppr s ornz s oows. Ston 2 survs rt wor on smnt n n R*-tr, u to tr mmt rvn to our tnqus. Ston 3 provs n ovrvw o t sstm, n Ston 4 susss mnmnt ssus. Ston 5 srs qur prossn ortms o rn n NN qur, n Ston 6 prmnt vts t n o propos tnqus. Ston 7 onus t ppr wt utur wor. 2. RELATED WORK Smnt n sm ws nt propos Dr t. [2] or nt-srvr nvronmnts. In ts sm, t nt mntns smnt srpton (.., Sr >5 A 3) o t n ts, n mn t ss normton n prorm rpmnt t t unt o smnt rons. B n smnt onstrns, t nt n wtr ston qur n o nswr or prt nswr. T t n rom t srvr r sp s rmnr qur. Smnt n sm n mnn oton-pnnt normton n mo omputn s stu n [5, 8]. Rn t [6] torou stu prossn o ston qurs, sp on ormn rmnr qurs. 3. SYSTEM OVERVIEW Ts ston provs n ovrvw o t propos n strutur, or w pro wt ts n susqunt stons. As sown n F.1.1, our wor trts on rst nvronmnt wr () omputrs (mo nts) wtn ustr ntronnt v w-n onnton (.., IEEE82.11/) n () nts n ustr onnt to t Intrnt trou nrrow-n n rom t tw. Ts mo s sp rst wt t popurt o wrss ntworn (most nw notoo omputrs r qupp wt wrss LAN r). As t R*-tr s t omnnt n or mut-mnson t (mpmnt n PostrSQL, Or, IBM Inorm n DB2, t), w ssum tt nt ns ts t usn n R*-tr. In ts ntwor, nts ssu mut-mnson qurs to n Intrnt ts srvr, w stors mut-mnson t (.., onn r stt normton). In orr to sv tr twn t Intrnt n t ustr, nts prvous t qur rsuts ns t ustr n sn to t ts on t prt o t qur tt nnot sts o. Towrs ts, t tw ts s o ornzr or mntnn normton n o qur prossn. Not tt, n our mo t tw s not rspons or storn prvous rsuts or n, sn t mt v mt rsours. Inst, nts wo ssu qurs r t to stor t rsuts or pro, sn t s tt t n tos rsuts n s w. For rn n NN qurs, t tw mntns rors on prvous t qur rsuts nn rons (ort n ston 4.1) n n R*-tr vrnt, C R-tr (rvt s CR-tr), w ns rons n t tm t r mtt to. T n tn us to pross qurs. For mp, upon rvn rn qur, t tw rst s wtr t qur n o sts wt rsuts. In prtur, t tw ssus t sm qur to ts CR-tr n s wtr t qur wnow ntrsts n prvous rons. Tr r tr poss outoms: () t qur wnow s u ontn n n tror t qur s nswr o; () qur wnow prt ntrsts rons, n t qur s ompos nto prts tt n/nnot o nswr; () qur wnow os not ntrst wt rons. In t ttr two ss, t prt o qur wnow tt nnot o nswr s snt to t srvr s rmnr qur n rsuts r wn rturn. For t prt o t qur tt n o nswr, rsuts r t t tw rom orrsponn nts tt ost t t. Atrwrs, t omn rsuts r snt to qur ssur. An trntv sm tt rus t woro o t tw s to sn t qur ssur t rss o nts tt ontn poss rsuts. Sn ts t os not t our n n, w oos t prvous sm. B n qur rsuts o n ustr, mn qurs n nswr ompt or prt wt o t wt p ommunton ost. As su, mu ommunton to t rmot srvr n vo. T ov srpton srvs s -v ptur o our rmwor, omttn two omponnts: mnmnt n qur prossn ortms, w w suss n t n susqunt stons. 4. CACHE MANAGEMENT C mnmnt nvovs omputn rons rom qurs n nn o tos rons n t CR-tr. W w so suss t onstruton n mntnn o t CR-tr. 4.1 C Amsson Contro Cnts sumt vrous tps o mut-mnson qurs (.., rn qurs, -nrst nor qurs) trou t tw to t ts srvr. From t qur rsuts snt t srvr, w n otn ompt now out rtn ron ( ron) n t smnt sp o rmot t. T ron n nsrt nto t, n t tu rsuts r stor t nt tt ssus t qur. To ustrt, onsr mps n F. 4.1 (rn qur) n F. 4.2 (NN qur) Rn Qur Atr t tw sns rn qur wt qur wnow q (s rtn n Fur 4.1) to t ts srvr (on ts nt s ) n rtrvs rsuts, t ompt now o ron q t t srvr s v to t tw. Nm, t ots n ron q t rmot srvr v n rtrv. Tror, q n n t tw s tm. T tu rsuts (ot n ) orm smr MBR, n t r stor

3 t nt w ssus t qur. For n-mnson t (n 3), t ron s so t qur wnow. Smnt sp o t nt ostn t tu t n t msson tm nto t. Ts tm w pr tr tm T n s to pun. I t s u, t tw s to vtmz som stn tms. Qur rn q Rsut MBR Fur 4.1: C ron o rn qur NN Qur T nswr to NN qur n n sn w n s w rsp t ompt now out rtn ron n n t ts. Fur 4.2 ustrts 3-NN qur n 2D sp wt qur pont q n rsuts,, n. From t qur rsuts, w now tt tr s no otr ot n t rur ron ntr t q wt rus q, wr q s t stn rom qur pont to t -t nor (or t rtst nor mon rsuts). Tou w v ompt now out t rur ron, t s nonvnnt to n su ron n n R*-tr. In 2D sp, w n us Consrvtv Bounn Rtn (CBR), w s t rst squr oun t rtnur ron (sown s s squr). NN n n-mnson sp (n 3) s smr, s monstrt n mpr NN qur n 3D sp (F. 4.2). Dnot t rtst nrst nor mon rsuts s NN. W r urnt no otr ot n t spr ntr t q wt rus, wr s stn rom q to NN. W v Consrvtv Bounn Bo (CBB), w s t rst u nos t spr. T CBB s nsrt nto t sn w v ompt now out t t ovrs. T s nt o t u s 2/sqrt(3), n t s strtorwr to tn to n- mnson s wr s nt o t CBB s 2/sqrt(n). Smnt sp q Rsut MBR () 2D NN qur () 3D NN qur Fur 4.2: C ron o NN qur z q t -t NN Wt ormnton mtos, tw n t ron poss to. I t sp s not u, t ron n mtt to t totr wt normton out t nt tt tu s t t. Howvr, sn stor sp s usu mt n mo vs, nts on srv tr t or on pro. W nm ts pro spn, n not t s T. T spn n nott twn nt n t tw wn t rst onnt, ut w ssum t sm spn or tms (or smpt). T n so st s t pt tm ntrv tr w rmot t r upt n orr to utomt pun osot ntrs. As su, t tw nsrts t ron totr wt t rss NN 4.2 C Ornzton W propos to us t R*-tr, t omnnt spt n, s our strutur. As w mntn mor normton tn trton R-tr n t nos r strut n nts, w nm our R-tr vrnt C R-tr (CR-tr). W w suss onstruton n mntnn o CR-tr Construton o CR-tr Wnvr qur rsuts r rtrv rom t srvr, t tw omputs t ron usn mtos n ston 4.1. I t s not u, t ron, totr wt t rss o t nt ostn t tu t n t urrnt tmstmp, s nsrt nto t CR-tr. In orr to tt rpmnt, w so mntn ss ount or ntr tr t s ss. As su, ntr n t no o t CR-tr nt s t oown normton: () MBR, () rss o t nt n t n t MBR, () nsrton tm, n (v) ss ount (nt zro). An ntrn no, owvr, ps tmstmp s t nsrton tm o ts nwst snnt. Ts wou n t tw to sovr wtr nos n su-tr v pr, t t pr o mntnn tr normton (tmstmp) t ntrn nos. Bn to sovr su-tr prton s two vnts: () qur prossn n stop snn t su-tr rr (mor orton n ston 5), n () w n s pun su-tr t prs. As su, mu I/O ost s sv t sm ost n sp (mntnn tmstmp normton os not nur tr I/O). T nsrton n ton ortms o t CR-tr r ssnt t sm s n [1] wt som mnor rn. Estn ntrs n no m pun rr (or tr spn pr) t v mu ovrp wt n nomn ntr n tr spn w soon pr. T rton n ts s to sv sp n n r st tus ntrs ovrn rs rons n ommot tr. Howvr, ts strt m ovro nts srvn ot t sn t rpton s ru. In orr to rm ts, w t nto ount t ss ount o n ntr. I n ntr s n rqunt ss, t w not pun rr vn tr s n nomn ntr ovrn t sm ron sn t ovr ot ron. W w ustrt usn n mp. F. 4.3 sows rons rom nts C2, C3, C4, n C5, n R*-tr nos t orm n 2D sp (ssumn no pt o 2 ntrs), w F. 4.4 sows t orrsponn CR-tr mntn t t tw. For smpt, w v omtt t ss ount normton n ntrs. To ustrt rom srt, ssum tt t nt s mpt n nt C2 ssus qur (rn qur or KNN qur). A ron s orm n t MBR ouns rsut ots n. An ntr, E7, w ontns t MBR, rss o C2, nsrton tm (), n ss ount (), s nsrt nto t mpt R*-tr t t tw. Smr, notr ntr E9 s rt t tmstmp 1 wn nt C4 ts ots n. Intrn nos (.., E3) t t tst tmstmp mon ts snnts (.., 2 or E3). In ts son, w n u up t CR-tr. Not tt t v o t CR-tr ontns no

4 tu t rom t ts srvr. Inst, t ontns t rsss o nts w tu t orrsponn MBRs n t ots (.., ntr E7 stors rss o C2). Dts on mntnn o CR-tr s v n t u vrson [4]. C 2 C 3 ontnt omtt 2 Fur 4.3: C rons Root,3,5 Lv 1,2 E 4,3,5,2 E 7, C 2, E 8, C 3, 2, C 4, 1, C 3, 3, C 4, 3 2, C 5, 5 omtt Fur 4.4: Corrsponn CR-tr 5. QUERY PROCESSING Upon rvn mut-mnson qur to t ts srvr rom nt, t tw s t CR-tr or rsuts n sns rmnr qurs to t srvr nssr. In ts ston, w w suss prossn ortms or t two tps o qurs o most mportn, rn n NN qurs. 5.1 Rn Qur Prossn Gvn qur wnow q t tmstmp t, t tw qurs ts CR-tr or ntrs ntrstn q. T prossn ortm s ssnt t sm s n Ston 2.1 pt tt w so tmstmp o no urn trvrs. I no s tmstmp smr tn rn twn t n spn, t s not urtr por sn t s pr. Wn n ntr wt MBR ntrstn q s oun, t ntrston ron s snt to t nt tt tu osts t t (not ts nt s C). Cnt C s ts o or qu rsuts n t ron n rturns tm to t tw. T ron tt ns no ntrston n t CR-tr s ompos to rmnr qurs n snt to t ts. T omposton ortm s n torou stu Rn t [6] n tror omtt r. F. 5.1 sows n mpr rn qur t tmstmp 4 wt qur rn sown n r. Assum spn 1 or ntrs, ntr E8 n E11 ntrst t qur ron. Ts stuton s mn n F Ron R1 n R2 r ts n ontn potnt rsuts, n tror t r snt to nt C3 n C4, rsptv. T rmnr n t qur wnow s ompos nto tr rons, R3, R4, n R5, n t r snt to t ts srvr. Wn rsuts to t qur r r, C 4 C 5 t r omn n snt to t qur ssur, n t qur wnow s nsrt to t CR-tr s nt tm. C 2 C 3 ontnt omtt 2 () () Fur 5.1: Rn qur n ts rmnr qurs 5.2 NN Qur Prossn For NN qurs, sn t tw os not v t ompt now o t n t ts, t s poss tt o nt nrst nors r tu s ts. Ts stuton s ustrt n F 5.2, wr 2-NN qur s ssu n t qur pont s q. Wt on o t, ot n r oun to nt nrst nors. Howvr, tr s n ot m n MBR B (s MBR n t owr rt ornr) n t ts, n t s osr to q tn. Ts stuton s vt s mor rons r. In prtur, t rur ron ntr t t qur pont wt rus D s ompt n rons, w r urnt o t nswr, wr D s t stn rom q to t rtst NN mon rsuts. Ts s t nssr n sunt onton or t tw to urnt vt o o nt rsuts. As su, w prov st-ort qur prossn or NN qurs. I no t nswrs r v, t qur s orwr to t ts srvr. ontnt omtt C 4 C 5 2 qur q Fur 5.2: Empr NN qur 6. EXPERIMENTAL EVALUATION In ts ston, w monstrt t tvnss o propos tnqus wt tnsv prmnts. 6.1 Smuton Sttns Eprmnts r prorm on PC wt Pntum 4 2.4G CPU n 1GB RAM. W ssum ustr o mo nts o sz C m B E 8 R 1 R 3 R 5 R 4 R 2

5 (vr). Mo nts ssu rn n NN qurs v tw to n Intrnt ts, w ns r tst ontnn 1314 orp otons (X, Y oornts) n Corn, Los Ans [7]. T vus r normz to rn [, 1]. T tst s n n R*-tr [1] wt no (s p) sz o 1 ts, n t pt (.., t mmum numr o ntrs pr no) s 5. Sn nts r mor ntrst n ps wt mor t, w nrt rn n NN qurs strut orn to t struton. Rn qurs r squr rons o s nt q L, w vrs rom to 1. At t tw, prvous qur rons r n n wt CR-tr o no sz 1 ts n pt o 5. Gtw to Intrnt ts ommunton nn s mo s FIFO quu wt mpmntton rom [3]. Cpt o t n twn t tw n ts s 56 ps. Qurs t t srvr r ut not ropp t n s ovro. Intrnt onnton ovr (.., pt r, t) s not mo, sn our n tnqu os not n t tot numr o msss twn t ustr n ts n tror t ovr s t sm. 6.2 Cn vs. No Cn W smut 6 mnuts o qurn to t ts wt n vn mtur o rn n 1-NN qurs n vr t numr o nts n ustr. Fur 6.1 n 6.1 sow t ntwor tr rom t ts n rspons tm pr qur, rsptv. Wt n, ot ntwor tr n rspons tm r ru. Wn t ustr sz nrss, mor qurs r sumtt pr unt tm, n t ntrou rr mount o Intrnt tr n st nrs rspons tm. tot tr (MB) Wtout n Wt n num. o nts rspons tm (ms) num. o nts () Ntwor tr () Rspons tm Fur 6.1: Etvnss o n 6.3 Impt o Qur Stvt W msur prormn wt vrous s nts o rn qurs, n vrous vus or o NN qurs. Lrr s nt or vu or mns rr stvt, n n nrs numr o ots n qur rsuts. W smut 6 mnuts o qurn wt tp o qur. F. 6.2 n F. 6.3 sow t mpt o q L n, rsptv. W ot Intrnt tr n rspons tm nrs wt q L n, n tnqus ws prov mu ttr prormn tn wtout n. Mor prmnts r prorm to vut t mpt o qur stvt, v sp, n spn. W so msur t mntnn ost o CR-tr t t tw. Dts o ts prmnts r v n t u vrson [4]. A prmnts sow tt our sstm s roust n nt n vrous stutons tot tr (MB) Wtout n Wt n qur s nt rspons tm (ms) qur s nt () Ntwor tr () Rspons tm Fur 6.2: Impt o s nt o rn qurs tot tr (MB) Wtout n Wt n num o NNs rspons tm (ms) Num. o NNs () Ntwor tr () Rspons tm Fur 6.3: Impt o 7. CONCLUSION AND FUTURE WORK In ts ppr, w propos nov n rmwor or ustrs o mo vs n m tr mportnt n orn ontrutons. W rst propos n nnovtv strut n mnsm tt n snnt ru Intrnt tr t sm osts o CPU n stor sp. Son, w propos to u t CR-tr, sp R*-tr, to n prvous t qur rsuts. Our tr ontruton s qur prossn ortms or rn n NN qurs tt t vnt o o s strut n t ustr o mo vs. T tvnss o our ontrutons s vt prmnts wt r tsts. W r urrnt vopn nt mos or our rmwor, w w tt t optmzton o t sstm. REFERENCES [1] Bmnn, N., Kr, H. P., Snr, R., Sr, B. T R*-tr: An Ent n Roust Ass Mto or Ponts n Rtns. SIGMOD, 199. [2] Dr, S. t. Smnt Dt Cn n Rpmnt. VLDB, [3] Lw, A., Kton D. Smuton Mon n Anss. MGrw-H,. [4] Lu, B., L, W., L, D. Dstrut Cn o Mutmnson Dt n Mo Envronmnts. (v t ttp://om.ust./~un). [5] Rn, Q., Dunm, M. Usn Smnt Cn to Mn Loton Dpnnt Dt n Mo Computn. Moom,. [6] Rn, Q., Dunm, M., Kumr, V. Smnt Cn n Qur Prossn. IEEE TKDE, 15(1), 3. [7] ttp:// [8] Zn, B., L, D. Smnt Cn n Loton- Dpnnt Qur Prossn. SSTD, 1.