A pllel index fo emiuued d Bin F. Coope Λ Dep. of Compue Siene Snfod Univeiy Snfod, CA 9435 USA oopeb@nfod.edu Nel Smple y Dep. of Compue Siene Snfod Univeiy Snfod, CA 9435 USA nmple@nfod.edu Mohe Shdmon RihOde In. 385 N. Fi S. Sn Joe, CA 95134 USA mohe@ihode.om ABSTRACT Dbe yem e ineinly bein ued o mne emiuued d, whih my no hve fixed uue o e of elionhip beween d iem. Indexe whih ue ee uue o mne emiuued d beome unblned nd diffiul o pllelize due o he omplex nue of he d. We popoe mehnim by whih n unblned veil ee i mned in blned wy by ddiionl lye of hoizonl index. Then, he veil ee n be piioned mon pllel ompuin node in blned fhion. We diu how o onu, eh nd upde uh hoizonl uue uin he exmple ofpii ie index. We lo peen imulion eul h demone he peedup offeed by uh pllelim; fo exmple, wih hee-wy pllelim, ou ehnique n povide lmo fo of hee peedup. 1. INTRODUCTION D i ely fl. Ined, dbe n onin mny elionhip beween individul d elemen, nd hee elionhip n be impon he d ielf. Ineinly, onizion mu del wih d h i emiuued: neihe he uue of d elemen no he e of elionhip beween hem i fixed in dvne. Thu, dbe mu llow ue o effiienly e d depie ieuliie in he uue. One oluion i o epeen elionhip beween d iem in hiehil mnne, uin ee uue. Thi ee n llow ue o find obje, well obje eled o hem. Ined of hvin o join oehe epe de, we n ondu op down vel of he ee. Subodine obje e oed in ubee, uh h ll he leve of he ubee epeen ll of he eled, ubodine iem. We ould piion poion of uh elionhip ee beween pllel ompuin node o h he index i di- Λ Wok done while uho w RihOde In. y Wok done while uho w RihOde In. Pemiion o mke diil o hd opie of ll o p of hi wok fo peonl o loom ue i ned wihou fee povided h opie e no mde o diibued fo pofi o ommeil dvne nd h opie be hi noie nd he full iion on he fi pe. To opy ohewie, o epublih, o po on eve o o ediibue o li, equie pio peifi pemiion nd/o fee. SAC, Mdid, Spin Copyih ACM 1-58113-445-//3 $5.. () Fiue 1: Piionin elionhip ee. ibued nd n nwe mny queie imulneouly. Fo exmple, Fiue 1() how elionhip ee, whee eh veex epeen n obje nd eh ede epeen elionhip. A wih ny ee, he uppe lye ne he oo (lbeled ff in he fiue) e likely o be mll omped o he lowe lye ne he leve (lbeled fi). Theefoe, we n dop he piionin heme hown in Fiue 1, whee he uppe lye e eplied o evey ompuin node nd he lowe lye e piioned beween node. In hi onfiuion, ue n ubmi quey o ny node i. The i node will vee he opy of he uppe lye (ff) of he index h i hold lolly unil i ehe he lowe lye (fi 1;fi :::fi n). Then, i will fowd he quey o node j h hold he lowe lye piion (fi j) neey o nwe he quey. If i = j, hen no fowdin will be neey nd i will nwe he quey diely. Thi ppoh i lled he fowdin ey. Alenively, we n ubmi he quey imulneouly o ll node (1; :::n). Eh node will vee ff o deemine if i lolly hold he oe fi j. If o, h node will nwe he quey. If no, h node will imply did he quey. Thi ppoh i lled he pllel iue ey. One wehvehieved n even piionin of he ee, we n ue diionl ehnique o mne pllelim. Fo exmple, we n uilize epliion nd voin heme o enue onieny fe upde, nd povide filove nd vilbiliy (e.. [3, 11, 7]). The benefi of piionin o beyond he peedup offeed by pllelizin ompuion. In ddiion, he piionin llow u o onu le indexe while keepin he eoue equiemen fo ny one ompuin node mll; fo exmple, we n build ebyeized index fom olleion of ommodiy p uh 5 ibye dik diibued mon off-he-helf ompue. Unfounely, wih emiuued d he elionhip ee uue n beome unblned. D elemen wih mny omplex elionhip ue poion of he ee o beome deep nd bnhy, while elemen wih imple elionhip eide in hllowe, moe line poion of he ee.
Fiue : A lyeed index ee. Thi mke i diffiul o piion he ee evenly mon pllel ompuin node o uppo pllel exeuion of queie. A eul, node ined o omplex poion of he ee beome hevily loded, while node wih imple ubee e lihly loded nd undeuilized. 1.1 Blnin n unblned index To hieve pllelim, we equie n loihm o inodue popeie of blne ino n unblned d e. We hve eed n indexin mehnim, he Index Fbi uue, h del wih he poblem of blnin n uneven uue o llow fo piionin mon pllel node. The Index Fbi uue i n inne of lyeed index: he ee i divided ino eqully ized blok, nd hen ex level of index e ued o dde hee blok. Thee ex level e hoizonl level in on wih he veil uue of he noml elionhip ee, hown in Fiue. Sehe poeed lon he hoizonl uue o lolized poion of he veil ee. The lefmo level (e.. level 1, ) indexe ove he blok in level, nd even if he numbe of level blok i le he lefmo level will be elively mll. Thu, we n eplie he lefmo level o evey ompuin node while piionin he ihmo level, muh we did wih he ff nd fi in Fiue 1. A quey n be ubmied o ny node, whih nvie he lefmo level o find he oe level piion, nd hen fowd he quey o be nweed by inle node in he pllel newok. Similly, queie n be iued o evey node, nd he node wih he oe fi j will nwe he quey. The hllene in onuin uh n index i o build blned hoizonl uue, nd hi i he iue we onfon in hi ppe. A onee exmple, we will diu how o piion Pii ie [13], omp bu poenilly unblned ee uue fo indexin in d. The Pii ie llow u o epeen elionhip beween d iem by onenin in. Fo exmple, o indie h iem 1 i eled o iem, we ine he key iem 1iem ino he ie. The eul i h ll iem iem ; iem 3:::iem n eled o iem 1 fom ubie wihin he Pii ie. Moe deil of hi epeenion n be found elewhee, in [5]. Thi elionhip uue i nul fi fo emiuued d, whih ofen onin omplex elionhip beween d iem. Queyin ph in emiuued d, uh XML, equie vel of hi elionhip uue, nd hi vel i uppoed by ou index. 1. Conibuion nd oveview We hve implemened he Index Fbi, nd hve ued i o nwe queie ove emiuued d, piully XML. The enodin nd quey poein eie e diued elewhee [9]. Hee, we fou on he blnin, piionin nd pllelizion of he index, nd peen expeimenl eul h exmine he peedup offeed by ou ehnique. Speifilly, we mke he followin onibuion: ffl We peen blnin ey fo n unblned index ove emiuued d. ffl We exmine piionin ey wheeby ome level of he blned ee e eplied o ll pllel node, nd ome e piioned mon node. ffl We peen imulion eul h illue he peedup vilble unde diffeen pllelizion eie. Fo exmple, ou ehnique n povide fo of hee peedup fo hee-wy pllel yem. Thi ppe i onized follow. In Seion we deibe how n eenilly unblned uue (uh Pii ie) n be blned uin lyeed index. Then, in Seion 3 we exmine ehin hi lyeed index uue. Seion 4 diue updin he index, nd in Seion 5 we exmine imulion eul. In Seion 6 we exmine eled wok nd Seion 7 ummize ou onluion.. BALANCING AND PARTITIONING TRIES USING LAYERED INDEXES Tie e d uue fo oin in d. A veex in he ee oepond o poiion in oed in, nd ede emnin fom he veex e ined o he poible he in h poiion in he in. Tie e ehed by ompin he ppopie he in he eh key wih he ouoin ede eh veex, nd followin he pope ede o he nex veex unil lef oninin poine o d eod e found. Pii ie e ompeed fom of ie, nd onin only he veie h hve wo o moe hilden. In hi wy, diffeene beween ineed key e epeened ined of he whole key. An exmple i hown in Fiue 3, whih ipii veion of he full ie in Fiue 3(). The numbe in he veie (he deph of he veex) indie he he poiion in he in o ompe o he lbel on he ouoin ede. Fo exmple, if we e ehin fo he in key, when we eh he veex lbeled," he he key[] hould be omped o he ouoin ede. A Pii hieve ompeion he o of no lone oin he omplee key. We n divide Pii ie ino ouhly eqully ized ubie, nd oe eh ubie in i own blok. Fo exmple, we n ke he index in Fiue 4() nd divide i. Thu, in Fiue 4, he oiinl index ill exi ( level ), bu h been pli ino wo blok. The blok boundie e indied by doed line. The veex level 1now n index ove he blok in level ; peifilly, he ie in level 1 indexe he ommon pefixe of eh ubie oed in he blok in level. The ommon pefix i he pefix of ll veie in he ubie of piul blok, nd
() Fiue 3: Tie. Level 1 Level () Fiue 4: Piionin ie. i he poion of he in epeened by he oo veex in he blok. In Fiue 4, he uppe blok h ommon pefix h i empy, while he lowe blok h ommon pefix h i ". Fo he e of hi ppe, we will efe o he lefmo hoizonl lye (e.. lye 1, ) uppe level" nd he ihmo lye (e.. he bi piioned index uue in level ) he lowe level." An uppe level index efe o he lowe level in wo diffeen wy. The fi wy i lled f link, nd i hown Fiue 4 eul ow. Thi link i he me n ede beween pen nd hild in noml ie, exep h he pen iin level i + 1 nd he hild i in level i. Thu, f link h lbel; in he fiue, he lbel i ". In on, he ohe ype of link, lled die link, h no lbel. Thi kind of link i epeened dhed ow in Fiue 4. Die link onne veie h epeen he me key pefix bu e in diffeen level. In he fiue, he pefix epeened by boh veie lbeled " i he empy pefix (lhouh ny pefix n be epeened.) Die nd f link e neey fo ehin he lyeed index ie uue deibed below. We n efe o noml" ede beween pen ndhild wihin he me blok, ne link. Ede h o blok boundie wihin he me level e lled pli link. Tie n hve moe hn wo level. In f, hi uue n be enelized o mny level needed. Eh level i onin omplee ie divided ino blok. Level i i indexed by level i + 1 uh h he ie in level i + 1 indexe he ommon pefixe of level i. In Fiue 4we illue inein level i; i + 1:::n fom ih o lef. The lefmo o hihe" level onin he oo of he hoizonl index, nd h only one blok. Thi oo blok onin omplee Pii ie nd heefoe my onin evel ie veie in ode o index evel blok he nex level. In pie, he numbe of hoizonl level in he ee emin mll, even he numbe of indexed key beome vey le. The Pii equie vey lile pe pe indexed key, levin e del of oom in blok fo poine. Conequenly, he hoizonl ee h vey hih bnhin fo nd oepondinly low heih. Fo illuion, we n mke imple umpion bou he ize of blok nd poine (e.. 8 Kb blok nd 3 bi poine) nd oe 1, poine pe blok. The oo blok (level n) n hen index 1, blok level n 1, nd eh n 1 blok n index 1, blok level n, nd o on. Thu, hee level ee n index billion iem. The uppemo level (level n > ) e vey mll omped o he lef blok (level ). In f, he uppe wo level of hee level ee oupy le hn 1 Mb of pe, nd n eily be oed in min memoy. A eul, he uppe level n be eplied ll ompuin node, nd only he blok in he lowe lye mu be piioned mon node. The numbe of blok in he lowe lye of he index i deemined by he ize of he ie nd he ined blok ize. We ould mke blok le, o h eh ompuin node i ined inle blok. Anohe poibiliy iomke blok mll, nd in muliple blok o eh node. Thi le ppoh h he benefi h ddin o emovin ompuin node o he pllel newok equie nfein few mll blok oppoed o epiionin he enie index wih diffeen blok ize.
dde SEARCH(key x, in blok B) f while B i no poine o d do B =SEARCH BLOCK(x; B); if B = NULL hen eun NULL; if B i poine o blok no hed lolly hen Invoke SEARCH(x,B) node i holdin B; Reun mke indiin node i will nwe quey; if key(b) =x hen eun B; ele eun NULL; Fiue 5: Poedue SEARCH. dde SEARCH BLOCK(key x, blok B) f n =oo veex of B; i = deph(n); /* The deph of he veex */ B = NULL; /* Thi will be he blok in he nex level */ while B = NULL nd i < lenh(x) nd ne o f ede n! n lbeled x[i] exi f if n! n i f link hen f /* n i in he nex lowe level */ B =dde of blok poined o by ede n! n ; ele f /* n! n i ne link */ n = n ; i = deph(n); if B = NULL nd hee exi die ede n! n hen B =dde of blok poined o by die ede n! n ; /* hi poin, B my be poine o nohe blok, poine o d, o NULL */ eun B ; Fiue 6: Poedue SEARCH BLOCK. 3. SEARCHING A LAYERED INDEX The eh poedue fo he lyeed index index loely pllel he eh poe fo imple ie. Fiue 5 how poedue SEARCH, whih eun he dik dde of he d mhin he eh key, o NULL if no uh d exi. When quey i iued, he in blok umen B i e o he oo blok of he lyeed index ie (e.., he blok in he lefmo hoizonl level). Billy, he eh he op level nd poeed boh veilly (wihin he me level) nd hoizonlly (beween level). A eh level i poeed unil i i ppopie o follow f o die link o he nex level (level i 1). Then he eh eume he ie in level i 1. Fo ll level exep he lef level (i = ), poedue SEARCH ll poedue SEARCH BLOCK (Fiue 6) o eh wihin piul blok. The eul of SEARCH BLOCK i eihe poine o nohe blok, poine o d, o NULL. We n illue he eh loihm uin Fiue 4. Imine h we e ehin fo he key." Poedue SEARCH bein by findin he oo blok, whih i he blok in level 1, nd ehin hi blok wih poedue SEARCH BLOCK. The oo veex in he blok i exmined, nd h deph of." Thu, key[], o," i omped o he ouoin ede. The f link fom he oo veex h he lbel ", nd he eh hen poeed o he blok poined o by he f link. Thi blok ihe level blok in Fiue 4 oninin ie ooed veex of deph." Poedue SEARCH heefoe invoke SEARCH BLOCK in. Thi poedue bein by exminin key[], o," nd follow he ne link lbeled." Thi ke he eh o i ol, he veex whih poin diely o he d wih key." The effe i h he eh in he hih hoizonl level, nd hen poeed diely o lolized poion of he veil ie (in level ) h onin he deied d. Evey eh ee he me numbe of level; moeove, i i only neey o ene inle blok pe level. A eul, ny nodeoninin eplie of he uppe level n pefom he fi poion of he eh. Howeve, one i beome ppopie o ene he lowe lye, he quey mu be nweed by he peifi ompuin node ined o h blok. Thi ompuin node n nwe he quey ompleely, ine inle blok i needed in level. (See Seion 3.1.) Noe h beue of he ompeion hieved by he Pii ie, poedue SEARCH my eun d fo key h doe no ully exi in he index. Fo exmple, in he index in Fiue 4, he key u" doe no exi. Howeve, if u" i peified eh key o poedue SEARCH, hen he eun vlue will be he dde of he d wih key." Thi i n unvoidble onequene of he f h Pii doe no oe full key. Theefoe, he found d hould be heked o veify h he eh key mhe he d key; hi i done he boom of poedue SEARCH. Thee e ohe ompliion inodued by he ompeion h we do no dde hee due o pe limiion, ee [5]. 3.1 Sehin pllel lyeed index Thee e wo eie fo ehin lyeed index in pllel. In he fowdin ey, poedue SEARCH i exeued ny ompue node holdin hed opy of he uppe level of he lyeed index ie. Queie n be iued o node in ny eonble wy, e.. ndomly o in ound-obin ode. The node i eeivin he quey vee muh of he lyeed ie i n unil i ehe he piioned lowe lye. The i node hek o ee if he equied blok ivilble lolly. If o, he i node nwe he quey. If no, he quey i fowded o he ompue node j h doe hve he blok. The j node exeue poedue SEARCH, bu he ppopie lowe lye blok ined of he oo. The j node n hen nwe he quey. In he pllel iue ey, queie e iued o ll node imulneouly. All node vee he uppe lye of he lyeed ie unil hey eh blok B L in he lef lye. One node h been ined he piion oninin B L; hi node oninue he vel in B L unil i nwe he quey. All ohe node imply did he quey. 4. INSERTING DATA Key e ineed ino he lyeed index ie uin hee ep poe. Fi, eh i pefomed o loe he level blok h mu be upded. Nex, he key i ineed in hi blok uin he noml Pii ineion loihm.
f Level 1 Level f f h f () f h f f Fiue 7: Spliin blok. Thi my involve ein one o moe veie in n exiin blok. Thid, if fe ein new veie hee e now oo mny veie o fi in he blok, he blok mu be pli. Mo ineion will no equie pli nd n be wholly hndled by he ompuin node ined o he ffeed blok. I i only when pli ou e he uppe level ffeed nd ll node mu be noified. Evey blok in he index onin onneed ubie. The pliin opeion mu peeve hi popey. Theefoe, in ode o pli we mu ele pli ede, uh h pliin he blok' ubie on hi ede podue wo onneed ubie. One ubie emin in he exiin blok, while he new ubie mu be pled in newly eed blok. Boh ubie eulin fom he pli hould be of ppoximely equl ize o minin ood pe uilizion of he dik blok. I i ofen impoible o ele pli ede h podue wo ubie of exly equl ize. In hi e, pli hould be eleed whih i loe o hi idel. Fiue 7 illue he pliin poe. Fiue 7() how ie, wih he pli ede mked. Afe he pli, hi ie oupie wo blok, hown in Fiue 7. Afe he pli i ompleed, poine o he new blok mu be dded o he level 1 ie. We ke he pli veex, whih i he pen veex on he pli ede, nd opy io he level 1 ie. Thi veex ein i deph. The opy of he pli veex in level 1 i iven f poine, wih he me lbel he pli ede, poinin o he new blok. The opy of he pli veex i lo iven die (unlbeled) poine efein o he old blok. The eul i hown in Fiue 7, whee he hded veex, lbeled," h been opied o level 1. Finlly, he newly opied pli veex mu be onneed o ny exiin veie in he level 1 blok o peeve he popey h eh blok h onneed ubie. Thi my involve onvein f link o ne link nd opyin ddiionl node fom level o level 1. The omplee poe i deibed in [5]. If opyin he veie o level 1 ue level 1 blok o oveflow, h blok mu be pli well. Thi i done in he me wy he pli level, nd hi poe n onine hihe level in he index. Evenully, imybe neey o pli he blok he oo level (level n). If o, hen new level (level n +1) i eed. Thi i how he lyeed index ow hoizonlly. 5. PERFORMANCE RESULTS We hve exmined he pefomne of ou piioned index by unnin imulion expeimen. We ook blok e fom n implemened, inle-node veion of he Index Fbi, nd fed he e o imuled pllelized veion of he index. In hi wy, we n exmine he effe of piionin nd pllelizion on el woklod. 5.1 Expeimenl eup The Index Fbi w ued o index XML doumen fom he DBLP, he popul ompue iene bibliophy [1]. Eh XML doumen oepond o inle publiion. The dbe onined ove 18, doumen, olin 7 Mb of d, ouped ino eih le (jounl ile, book, e.) The doumen wee oed in popul ommeil elionl dbe yem, nd he Index Fbi w ued ined of he dbe yem' nive quey poeo. We n eie of 1, queie ove hi dbe; eh quey equied one index key lookup. The deil of he indexin ey, well pefomne numbe in he non-pllel e, n be found in [9]. Hee, i i uffiien o noe h he Index Fbi povided up o n ode of mniude peedup veu he dbe yem' nive quey poeo. Fom hee expeimen, we olleed blok e whih indied he ode of index blok eque, nd whehe hoe blok oeponded o lefmo level (e.. ff in Fiue ) o he ihmo level (e.. fi in he me fiue). Thi blok e w fed o imulo. The imulo onued enio whee he index w piioned mon muliple node, nd epoed eul bou he numbe of queie h ould be nweed by eh node h w iued quey. The piionin w pefomed by ndomly inin blok o node. In hi wy, we ould ompe he benefi of he fowdin (wih queie iued in oundobin fhion) nd pllel iue pllelizion eie (ee Seion 1). We omped in he be e of no pllelizion (e.., one node). We umed he followin pmee in ou imulion: ffl The ime o poe he ff lye (in memoy) fo quey i 1 uni. ffl The newok o o fowd quey o nohe node i 4 uni. ffl The ime o ed fi blok fom dik o nwe he quey w 1 uni. ffl If he fi blok w in he, hen i ould be poeed in memoy wihou dik ed, nd hu he o w 1 uni. Thee o efle ndd umpion bou lenie, e.. newok lenie e bou 4 ime memoy leny, nd dik e bou n ode of mniude lowe hn memoy.
Fiue 8: Pefomne fo pllel index wih no he, 3 node. 5. Reul The fi expeimen we n exmined he imp due o piionin he index mon pllel node. In hi expeimen, he ize wee e o zeo o elimine he effe. We omped he fowdin nd pllel iue eie in he be e of no pllelim. In he fowdin ey, node mu be hoen o eeive eh quey; we iued queie o node in ound-obin fhion. The eul e hown in Fiue 8 fo he e of 3 node. Thi fiue illue wo mei. Speedup i he io of he ime o nwe queie fo he pllel index veu he ime fo he non-pllel index. Effo i he io of he ol uni of wok done by he pllel index o he ol uni of wok done by he non-pllel index. Speedup hu epeen he inee in he houhpu due o pllelim, while effo efle yle wed." In he fowdin ey, yle e wed by he fowdin of queie, nd in he pllel iue ey, yle e wed by node h e iued quey bu did i beue hey do no hold he oe fi j. An effo vlue of 1 indie he pllel index did muh wok he non-pllel index, while ny vlue ove 1 indie he popoion of wed wok. Fiue 8 illue h boh eie offe moe hn peedup. Howeve, i i le h he pllel iue ey offe he be houhpu. The effo wed" by node h exmine quey bu doe no nwe i i le hn he effo wed" by fowdin queie. Thi mke ene, iven h he o of fowd i 4 uni, bu he o fo wo node o exmine hei lol ff opy i only wo uni. Nex, we exmined he peedup nd effo he numbe of pllel node hned. Fiue 9 how he eul, wih he numbe of node lon he hoizonl xi. Thi fiue how he peedup nd effo fo boh he fowdin nd pllel iue ey. A he numbe of node inee, he peedup unde he fowdin ey inee linely, while he peedup unde he pllel iue ey inee le quikly. In f, when hee e fou node, boh eie e eqully f, bu beyond fou node, he fowdin ey i be. Rell h in ou o model, he o o fowd quey i 4 uni, while he o o poe n ff lye in memoy i 1 uni. Unde fowdin, he only wed effo" i wok done o fowd quey, while unde pllel iue, he wed effo i done when node Fiue 9: Pefomne fo pllel index wih no he veu numbe of pllel node. Fiue 1: Pefomne fo pllel index wih hin, 3 node. poe he ff lye bu hen did he quey. Thu, fou node, boh eie e doin ouhly equl moun of wed" wok, while moe hn fou node, fowdin doe le wed wok hn pllel iue. The eul i bee ue of ompuin eoue unde he fowdin ey, nd hu moe peedup veu pllel iue, when hee e moe hn fou node. Thi eul depend on he io R of he o o fowd quey veu he o o poe n ff lye. Howeve, he enel eul emin he me: fowdin povide moe peedup when hee e le R node. Anohe benefi of pllelim i he biliy o onu yem h hve le moun of eoue fom mlle, hepe omponen. In hi onex we n onu yem h h le moun of ee he fom omponen h hemelve hve mll he. To exmine hi effe, we n nohe expeimen, whee we umed h n individul node ould devoe enouh memoy o he one peen of he ol index ize. The eul fo hee node e hown in Fiue 1. Thi fiue demone h he biliy o build le ee he fom muliple individul mll he impove pefomne inifinly. Boh eie hve le :5 peedup; in f, he pllel iue ey ppohe 3 peedup, he heoeil mximum fo hee-wy pllelim. (The ul peedup i
:99.) Thi i beue he o of ein he dik domine he o o poe queie, nd hin n edue hi dominn o. By piionin he index mon hee node, we hve effeively ipled he ee he ize. In f, ou expeimen indie h he vee hi e in eh node' he i he me (39 peen) if hee w inle-node index wih hee ime muh he. Even houh eh node h mll individul he (only one peen of he index ize), he ee effe i h of le lobl he, beue eh node need only he blok fom i lol piion of he fi lye. The inee in effeive hin edue numbe of dik ed, nd hi benefi ompene fo he wed" yle needed o ondu queie in pllel. The end eul i h he yem n ppoh 3 peedup. We n nohe expeimen whee we vied he numbe of node in iuion whee node hd he, nd meued he peedup nd effo. The eul (no hown) e imil o hoe of Fiue 9. Speifilly, fowdin povide bee peedup (up o 8.3 ime peedup fo en node) hn pllel iue when hee e moe hn fou node. The be peedup obeved fo pllel iue w 5.9 ime peedup fo en node. 6. RELATED WORK Mny inveio hve exmined he poblem of diibuin nd epliin dbe o povide lod blnin while poein dbe onieny [7, 14]. Tdiionlly, he poblem i onfined o mnin uued d h n be eily piioned. Semiuued d h eeived muh enion eenly [6, 1, ], lhouh he uho know ofnowok foued on pllelizin nd diibuin emiuued indexe. The mo ommon indexin ehnoloy i he B-ee nd i vin [4]. The ize of B-ee i eniive o he lenh of key well he numbe of key ineed. A eul, B-ee end o hve mny level, eduin he eh effiieny. Anohe ype of index i he hh ble, whih ompue hh funion ove key o ple key in epe buke [13]. Alhouh he hh ble n be uppo effiien queyin, i equie ome knowlede bou he nue of he indexed d o h n ppopie hh funion n be eleed. Boh B-ee nd hh ble index homoeneou e of key. The Index Fbi opee he me wy edle of he nue of he d. Moeove, hh ble doe no uppo ne queie, while he Index Fbi n. Ohe eehe hve exmined moe flexible ee indexe (e.. enelized eh ee [1]) nd fuhe wok need o be done o ee if ou ehnique n be pplied o uh indexe. Ohe eehe hve inveied piionin unblned ee. Fo exmple, Diwn e l [8] exmine wy o lue veie of ee ino blok o minimize exenl e ime. The Index Fbi i imil o hee peviou effo in he emp o hieve blne houh ee piionin. Howeve, ou ppoh i moe diely foued on piionin he ee fo ue wih he pllel mehnim hown in Fiue 1. uue llow quey poeo o poeed diely o he elevn poion of he ee, llowin he quey o be nweed independen of ohe node. Thi uue llow u o exploi pllel ompuin o nwe muliple queie nd o build le indexe by diibuin hem ove ommodiy hdwe. The biliy o build nd pllelize uh ee uue ive u he biliy o epeen nd eh emiuued d elionhip effeively. We hve implemened piionble, lyeed index, nd ondued expeimen h meued he peedup offeed by pllelim. Fo exmple, ou eul indie h hee pllel node n hieve fo of.5 peedup imply by piionin he index, nd lmo fo of 3 peedup if eh node h even mll lol he. Clely, he Index Fbi i nul uue fo pllel exeuion of queie ove emiuued d. 8. REFERENCES [1] DBLP ompue iene bibliophy. hp://www.infomik.uni-ie.de/~ley/db/. [] See Abieboul. Queyin emi-uued d. In Po. ICDT, 1997. [3] Bb T. Bluein nd Chle W. Kufmn. Updin eplied d duin ommuniion filue. In Po. VLDB, pe 49 58, 1985. [4] D. Come. The ubiquiou b-ee. Compuin Suvey, 11():11 137, 1979. [5] Bin Coope nd Mohe Shdmon. The Index Fbi: A mehnim fo indexin nd queyin he me d in mny diffeen wy,. RihOde Inopoed Tehnil Repo. [6] Alin Deuh, My Fenndez, nd Dn Suiu. Soin emiuued d wih STORED. In Po. SIGMOD, 1999. [7] Dvid J. DeWi nd Jim Gy. Pllel dbe yem: The fuue of hih pefomne dbe yem. CACM, 35(6):85 98, 199. [8] A. A. Diwn, Snjeev Rne, S. Sehdi, nd S. Sudhn. Cluein ehnique fo minimizin exenl ph lenh. In Po. VLDB, pe 34 353, 1996. [9] Bin Coope e l. A f index fo emiuued d. In Po. VLDB, Sepembe 1. [1] Jon MHuh e l. Loe: A dbe mnemen yem fo emiuued d. SIGMOD Reod, 6(3):54 66, Sepembe 1997. [11] D. Giffod. Weihed voin fo eplied d. In Po. SOSP, pe 49 58, 1979. [1] Joeph M. Helleein, Jeffey F. Nuhon, nd Avi Pfeffe. Genelized eh ee fo dbe yem. In Po. VLDB, pe 56 573, Sepembe 1995. [13] Donld Knuh. The A of Compue Pommin, Vol. III, Soin nd Sehin, Thid Ediion. Addion Weley, Redin, MA, 1998. [14] M. Tme Ozu nd Pik Vlduiez. Piniple of Diibued Dbe Syem (Seond Ediion). Penie Hll, Uppe Sddle Rive, New Jeey, 1999. 7. CONCLUSION We hve deibed how o nfom n unblned ee ino blned, piionble uue. The lyeed index