Time/Space Efficient Filtering of Streaming XML Documents Using Incrementally Constructed c

Transcription

1 九州大学学術情報リポジトリ Institutionl Repository Time/Spe Effiient Filtering of Streming XML Douments Using Inrementlly Construte Hgio, Kzuhito Mitri, Shuihi Ishino, Akir Tohoku University Tke, Msyuki 出版情報 :DOI Tehnil Report. 3, -6. Deprtment of Informtis, バージョン :epte 権利関係 :

2 Time/Spe Effiient Filtering of Streming XML Douments Using Inrementlly Construte Pth-trie Kzuhito Hgio Shuihi Mitri Msyuki Tke Akir Ishino Tohoku University Astrt In this pper, we present streming XML oument filter nme DXAXE whih is se on inrementl onstrution of pth-trie. It runs very fst, n proesses lrge numer of XPth queries effiiently. Experimentl omprison with XMLTK, well-known streming XML oument filter, shows tht DXAXE is 5 times fster n nees only 5 perent of memory. Introution Querying XML strems is reeiving muh ttention ue to its growing rnge of pplitions suh s stok n sports tikers, trffi informtion systems, eletroni personlize newsppers, n entertinment elivery. Existing pprohes to querying XML strems ssume tht user interests re written s queries using XPth [], lnguge for speifying the seletion of element noes within XML ouments. It is entrl to most XML-relte tehnologies suh s XQuery, XSLT, n XML Shem, uner the uspies of W3C. The eterministi finite-stte utomt (DFAs) n e use effetively to evlute lrge olletion of XPth expressions on streming XML t t high throughput, ompre with the noneterministi finite-stte utomt (FAs). However, most of existing XPth evlutors on XML strems suh s XFilter [], XTrie [5], YFilter [8] voie using DFAs euse their size grows exponentilly with respet to the totl size of XPth expressions. The lzy DFA tehnique [3] is goo solution to the stte explosion prolem. A lzy DFA is one whose sttes n trnsitions re ompute from the orresponing FA t runtime, not t ompile time. Thnks to this tehnique, XMLTK [4] pro- Tle. Exmples of XPth expressions DX- AXE supports. //reeiver/nme /*/orer[//sener] /orer//[ontins(nme, mikey )] /orer//ress[street or region] //ress[//region[//ountry n zipoe]] /orer[//ress]//zipoe //sener[ount(//region) > ] liner pth-pttern primitive pth-pttern sustring mth logil opertion neste preites preite in ny lotion step ggregtion esses lrge olletion of XPth expressions on streming XML t t gurntee throughput. Contriution We present new XPth filtering tehnique se on pth-trie, trie representing the set of sequenes of tgnmes on the root-to-lef pths. It inrementlly onstruts pth-trie, n using it s DFA, it evlutes lrge numer of XPth queries in prllel uring single pss through n XML t. We ll our tehnique DX- AXE (ynmi XAXE; XAXE [8] is n revition for extremely-aelerte XML filtering Egine ). Compre with the lzy DFA, our DFA is muh simpler n more time/spe effiient. Although our DFA hs often lrger numer of sttes thn the lzy DFA oes, the numer of sttes of the two DFAs re oune y the pth-trie size plus one, whih is known to e typilly very smll for XML t tht hs firly regulr struture. XPth frgment DXAXE supports A liner XPthexpression is one where (i) wilrs ( * ) re llowe in noe test, (ii) only hil n esennt xes (resp. / n // ) re llowe in lotion steps (prent, nestor n other xes re forien) n (iii) no preites re llowe in lo-

3 x x y π π esries metho of effiient filtering se on inrementl onstrution of pth-trie. Setion 5 reports experimentl omprison of DXAXE with XMLTK. Setion 6 mentions n extension to more omplex XPth expressions. Setion onlues this pper. Figure. An ourrene of primitive pthpttern π [π ] t lous (x, y) of XML tree is illustrte, where x is the hil of x on the x-to-y pth. tion steps. Some of existing XPth evlutors on XML strems (e.g., XFilter, YFilter, n XMLTK) fous minly on the liner frgment of XPth. XPth expressions with preites re proesse y eomposing them into set of liner XPth expressions, evluting them respetively, n then omining the results ppropritely. In ontrst, we fous on XPth expressions whih possily hve preitesin restritewy: A primitive pth-pttern is liner XPth expression π followe y single preite ontining liner XPth expression π, nmely it is of the form π [π ]. The reson why we istinguish the preiteontining XPth expressions of this type from the ones of generl type will e lrifie in Setion 6. For ny noe x of XML tree n ny esennt y of x (possily x = y), primitive pth-pttern π [π ] ours t lous (x, y) if π n π, respetively, mth the tgnme strings of the root-to-x pth n the x -to-y pth, where x is the hil of x on the x-to-y pth. Fig. shows n ourrene of primitive pth-pttern π [π ] t lous (x, y). We note tht liner XPth expression n e viewe s primitive pth-pttern π [π ] with π = ε, forwhihnox exists n x = y. DXAXE supports lrge frgment of XPth se on effiient evlution tehniques for primitive pth-ptterns presente in this pper, lthough etile isussion is outsie the sope of this pper. Some expressions elonging to the frgment re emonstrte in Tle, whih will e riefly mentione in Setion 6. It is worth to mention here tht though the exmples o not inlue ones with other xes thn hil n esennt, it is esy to el with other forwr xes suh s following, following-self, n followingsiling, n XPth expressions with kwr xes n e trnsforme into equivlent ones with forwr xes only, of size liner with their originl size, se on the tehnique y Oltenu et l. []. Pper orgniztion The present pper is orgnize s follows. Setion mentions some reltive work. Setion 3 how pth-trie n e use in pth mthing. Setion 4 then Relte work Complexity of XPth evlution Gottlo et l. [] pointe out tht existing systems onsume time exponentil with respet to query size, n showe the first polynomiltime lgorithms for the XPth. lnguge. Also they presente two frgments of XPth for whih liner-time lgorithms exist. The sme uthors showe in [] tht the omine omplexity (i.e., oth the size of the t n the query) for the full XPth. lnguge is P-hr, n then ientifie lrge n importnt frgment for whih the omine omplexity is LOGCFL-omplete. XPth. supports numer of powerful molities n it is rther expensive to proess. In prtie, mny pplitions o not nee the expressive power of the full lnguge n use only frgment of XPth. It is thus require to evelop effiient lgorithms for suh frgments of XPth lnguge. Effiient XML t strem filtering The requirement is more severe in streming XML t filtering, where lrge numer of XPth queries shoul e evlute ginst XML t strems t gurntee throughput. The prolem of evluting lrge olletions of XPth queries on streming XML t ws first introue in the work of Altinel n Frnklin []. They propose pulish-susrie system nme XFilter. Improve tehniques were isusse in XTrie y Chn et l. [5], lzy DFAs y Green et l. [3] (implemente s XMLTK [4]), n YFilter y Dio et l. [8]. Bsilly they re multi-query evlution tehniques for the liner XPth frgment, n some of them n e extene to support lrger XPth frgment. Deterministi/noneterministi finite-stte utomt ply key role in proessing XPth expressions of the liner XPth frgment. XFilter, XTrie, n YFilter expliitly voie using DFAs to gurntee their spe ouns, ut they h no gurntee on throughput. DFAs effetively proess lrge olletion of XPth expressions t gurntee throughput, ut their size grows exponentilly with respet to the totl size of XPth expressions. (See Fig..) The lzy DFA tehnique is solution to the stte explosion prolem: Sttes n trnsitions re ompute from the orresponing FA t runtime, not t ompile time. The numer of sttes in the lzy DFA ws prove in [3] to e t most the size of pth-trie plus one. XMLTK runs t By liner O( D Q ) running time is ment, where D n Q enote the size of the XML t n the queries, respetively.

4 high throughput se on the lzy DFA tehnique. Further reution of the numer of sttes ws resse in []. Although the lzy DFA hs smll numer of sttes, its memory usge is not very smll. The reson follows. Eh of the lzy DFA sttes is represente s list of sttes of the orresponing FA, n ll the lists re kept for lzy onstrution of DFA. Spe requirement for FA stte lists is the ominnt in totl spe requirement for the lzy DFA s reporte in [3]. Also, when uiling new trnsition from DFA stte s, the list of next sttes is ompute from the FA stte list of s n then ompre with ll the lists of existing DFA sttes in orer to etermine whether the orresponing DFA stte is lrey rete. This omprison tsk is time onsuming s pointe out in [6]. Our pproh In previous work [5], we propose metho whih uses the pth-trie expliitly. In the metho, the pth-trie is uilt y snning whole XML t, outputs re e to the pth-trie noes y running FAs for queries long the root-to-lef pths in it, n then the XML t is proesse gin using the output-e pth-trie s DFA. This might seem fr from strem proessing sine the t strem is re twie. But it is not so in setting where the pth-trie is rete only one, tthe to the XML pket, then sent long with the XML strem, n use y every onsumer. A similr setting n e foun roun SIX, the strem inex tehnique propose in [3]. In n XML messge system, messges re often inry representtions of XML, rther thn XML t in their ntive text formt (see, e.g., [9]). In [8], we propose one suh inry formt: XML t is onverte into the pthtrie n the inry one in whih every strt-tg is reple with speil symol followe y pointer to the orresponing pth-trie noe n every en-tg is reple with nother speil symol. The pointers enle us to skip performing stte-trnsitions of pth-trie s DFA: We hve only to refer the outputs tthe to the pth-trie noes. Our implementtion ws nme XAXE (extremely-aelerte XML filtering Egine). The pproh tken in this pper goes long nother line. We o not preproess XML t to proue the pth-trie: We mintin DFA se on the pth-trie eing onstrute inrementlly, n y using it, we evlute queries uring single pss through n XML t, similr to XMLTK. 3 Using pth-trie 3. Pth-tries n their size An exmple XML t, its XML tree representtion, n its pth-trie re shown in Fig. 4. Formlly, n XML tree is n orere tree suh tht the interior noes re lele with tgnmes, n the leves, lle text noes, re lele {3,} {3,6} - {,} - {,} - {} {3,5} {3} - {} - {} - {} - {} {} {,3} {3,4,5} {3,4,6} {3,4} Figure. FA n DFA for Π={P,P } re isplye on the upper n on the lower, respetively, where P = // n P = /*/*/. {} {,3} {3,4,5} {3,6} {3,} Figure 3. Lzy DFA n our DFA for the ptterns of Fig. re isplye on the upper n on the lower, respetively, where ll possile tgnme sequenes re limite to S = {,,,,}. with text. Thus pth from n internl noe u to nother internl noe v spells out string of tgnmes. Let us ll it the tgnme string of the u-to-v pth. The pth-trie of n XML tree is the trie struture tht represents ll the tgnme strings of the XML tree. We note tht pth-trie is kin of DtGuie [], whih is grph representing the tse struture, ut it is simply tree sine the unerlying t (i.e. XML t) hs tree struture. It is oserve in [4] tht most of existing XML t hve DtGuie of smll size, n therefore their pth-trie re lso smll. Generlly speking, if n XML t is highly struture, then its pth-trie eomes smll oringly. Tle gives the pth-trie sizes n other informtion out the following XML t: In this pper n ttriute noe orresponing to nme=vlue is regre s n interior noe hving unique hil (lef) lele vlue. 3

5 XML t <> <> <>...</> </> <> <>...</> </> <> <> <>...</> <> <>...</> </> </> </> </> XML tree Pth trie Figure 4. XML t n XML tree it represents re isplye on the left, where irles n squres men element n text noes, respetively. Pth-trie uilt from the XML t is isplye on the right. umers jent to the noes of XML tree n pth-trie men their IDs, n letters in the irles (noes) re their tgnmes. Tle. Pth-trie size of three XML t re shown, together with the numer of tg ourrenes n the numer of tgnmes. # tg ourrenes # tgnmes pth-trie size () 98,88,9 9 6 (),5, () 4,96, () XML t of UniProtKB/Swiss-Prot [3]..GB. () XML t of DBLP [6]. 3MB. () XML t generte rnomly y xmlgen progrm of XMrk enhmrk [3]. 6MB. For (), the XML tree hs 4, 96, 36/ =, 48, 8 noes (exluing text noes), while the pth-trie hs only 549 noes, whih is.3% of the XML tree noes. The rtios for () n () re muh lower. ext, we onsier how the pth-tries grow uring their onstrution s sequentilly proessing n XML t. Fig. 5 shows the growth of pth-trie for eh of the three XML t, where we lso isply the inreses of tg ourrenes n tgnmes. The t () hs highly regulr struture, n its pthtrie hs grown up t erly stge. Conerning the t (), the growth seems nerly stle exept the erly prt n the point roun 4MB t whih the unerlying sheme lters. For the t (), the root hs six hilren, whih orrespon to six ifferent tegories hving their own shemes, n the pth-trie size rpily inreses for every time the tegory swithes. After out 5MB point, inrese of tg ourrenes got rpi. 3. Mthing ginst pth-trie, not XML tree As seen in Setion 3, pth-tries re muh smller thn their XML trees. Hene, performing pth-mthing ginst pth-trie n then referring to the results store in its noes n e muh more effiient thn iret pth-mthing ginst XML tree. Below, we gives some illustrtive exmples. Liner pth-pttern se. Fig. 6 illustrtes ourrenes of the ptterns P = /// n P = /// within the XML t n pth-trie of Fig. 4. The pttern P ours t noe 3 n the pttern P ours t noes 4, 5, in the pth-trie. We note tht noes 3, of the XML tree orrespon to noe 3 of pth-trie, n oringly the pttern P ours t the noes of the XML tree. A similr oservtion is otine for the pttern P. Primitive pth-pttern se. Fig. illustrtes ourrenes of the pttern P = /[//] within the XML t n pth-trie of Fig. 4. The pttern P ours t loi (, 4), (, 5), (6, ), (, ) in the pth-trie, n the loi n e otine from output P, of noe 4, output P, of noe 5, n outputs P,, P, 3 of noe, respetively. From the outputs, the loi of ourrenes of P within XML 4

6 numer of tgnmes/pthtrie size numer of tg ourrenes pthtrie size numer of tgnmes numer of tg ourrenes numer of tgnmes/pthtrie size t size (MB) () UniProtKB/Swiss-Prot numer of tg ourrenes pthtrie size numer of tgnmes numer of tg ourrenes Figure 6. Ourrenes of liner pth-ptterns P = /// n P = /// in XML tree n pthtrie re isplye. For instne, the ourrene of P t noe 3 of pth-trie implies tht P ours t the orresponing noes 3 n of XML tree. tree n e otine. For instne, sine noe 5 orrespons to noe 4 of pth-trie with output P,, it hs the sme output. This implies tht P ours t lous (4, 5) of XML tree, where 4 is the prent (the st nestor) of 5. 4 Filtering with pth-trie uilt inrementlly t size (MB) () DBLP In this setion, we esrie filtering metho tht sequentilly sns n XML t strem n performs pthmthing over inrementlly onstrute pth-trie. We remrk tht the size of pth-trie oul e reue y regring tgnmes not ppering in ptterns s one tgnme. numer of tgnmes/pthtrie size pthtrie size numer of tg ourrenes t size (MB) () rnom t numer of tgnmes Figure 5. Growth of pth-tries when sequentilly snning XML t re illustrte. numer of tg ourrenes 4. Constrution of pth-trie We prse input XML t sequentilly to etet n report ourrenes of tgs s events, whih re to e input to inrementl pth-trie onstrution n to pth-mthing. We mintin trie representing the urrent set of tgnmes: If urrent tgnme is present in the set, then its ID is returne; n otherwise new ID is ssigne to it n then returne. We illustrte the lgorithm y using the XML t n the pth-trie of Fig. 4. We note tht sequentil proessing of n XML t strem gives epth-first-trversl of the orresponing XML tree. We strt with n empty pth-trie, n proee s follows. Suppose we hve proesse the noes to in the trversl of the XML tree. At this moment, the pth-trie hs noes to 4 sine the pth strings of the XML tree noes to re, respetively, 5

7 <P, > 8 9 <P, > <P, >, <P, 3> 3 4 <P, > 5 6 <P, > <P, >, <P, 3> Figure. Ourrenes of primitive pthpttern P = //[//] in XML tree n pth-trie re isplye, where the pirs P, jent to noes y represent the ourrenes of P t (x, y) suh tht x is the -th nestor of y. For instne, P, t noe 4 of pth-trie implies tht P ours t lous (, 4) of pth-trie, n t lous (4, 5) of XML tree.,,,,,,, n these re represente y the pth-trie noes,, 3,, 4,, 3, respetively. Thus, we re now t noe of XML tree n t noe 3 of pth-trie. The next noe of XML tree is 8 n the orresponing tgnme is. Sine the pth-trie noe 3 oes not hve hil with tgnme, new noe, numere 5, is rete s hil of 3. Thus new pth from to 5 ppers. We o pthmthing tsks for this new pth for ll queries. Repeting the ove proess until the entire XML t is psse through, we inrementlly uil the pth-trie n perform pth-mthing ginst it in prllel. 4. Mthing ginst growing pth-trie This susetion esries pth-mthing lgorithms exeute when new noe is e to pth-trie. 4.. Liner pth-pttern se Suppose we re given set Π of liner pth-ptterns. Denote y Π the totl length of the ptterns in Π, nlet e the set of tgnmes ppering in ptterns of Π. Two possile implementtions re onsiere here. DXAXE-A: One implementtion woul e to uil n FA from Π in wy similr to YFilter [8]. A trie is uilt from Π regring tgnmes, *, n // s symols, n for every ege lele //, the lel is reple with ε n loop lele with * is eto its sink noeto prouen FA. The FA onstrution requires O( Π log ) time using O( Π ) spe, where the ftor log omes from use of the fmous AVL-tree for lookup/insertion ginst the set of trnsitions from n FA stte. We let pth-trie noes v hve lists of tive sttes of FA just fter reing the tgnme string of the root-to-v pth. When new pthtrie noe with tgnme is rete, we shll perform noneterministi stte-trnsitions on to rete n tivesttes list for it. We note tht eh FA stte hs t most one -trnsition for every, t most one ε-trnsition, n t most one -trnsition from it. Fining -trnsition from it requires O(log ) time. Cretion of tive-sttes list for new pth-trie noe v requires O( Π log ) time n O( Π ) spe. This implementtion is very similr to the lzy DFA in tht lists of tive sttes re kept. DXAXE-B: Another implementtion woul e to uil n FA for eh liner pth-pttern π Π, ypplying the it-prllel tehnique [9], in whih set of tive sttes of FA is store in one integer s it-vetor. The numer of ll sttes of the FA is size(π)+,where size(π) is efine to e the numer of noe tests in π. Thus, the tehnique n e use only for liner pth-ptterns of size t most the wor length (typilly 3 or 64 its) minus one. Sine onstrution of eh FA requires O( π ) time using O( ) spe n we uil Π FAs, totlly we nee O( Π ) time using O( Π ) spe. ote tht if the it-vetor of n FA onsists only of, the FA is e (never epts). Thus, eh pth-trie noe v hs list of pirs of n live FA n its it-vetor just fter hving proesse the root-to-v pth. Cretion of suh list for new pth-trie noe requires only O( Π ) time n spe. 4.. Primitive pth-pttern se Denote y L(π) the lnguge of liner pth-pttern π. Suppose we re given set Π of primitive pth-ptterns. Let π [π ] e ny of Π. Suppose sequene v,...,v k of noes is pth from the root to v k in pth-trie, n new noe v k+ is rete s hil of v k. For this newly ppering pth v,...,v k+, we hve to hek whether π π mthes it, n in se of mth, we hve to fin i suh tht π n π, respetively mth the v -to-v i pth n the v i+ -to-v k+ pth. To implement this, we onsier n FA tht reognizes the two lnguges L(π ) n L(π π ) with two istint epting sttes. Let us ll it the forwr FA for π [π ]. The forwr FA is esily onstrute y uiling two FAs with unique initil stte n unique epting stte, tht reognize L(π ) n L(π ), respetively, n then omining them with n ε-trnsition from the epting stte of FA for L(π ) to the initil stte of FA for L(π ). Fig. 8 gives n exmple. We note tht set of forwr FAs n e merge into single FA, similr to the FA isusse in DXAXE-A. We lso note tht forwr FA n e implemente y the it-prllel teh- 6

8 π ππ Figure 8. Forwr FA for π [π ] is isplye on the upper, where π = //// n π = //. It reognizes istintively the two lnguges L(π ) n L(π π ), n is implemente s omintion of two FAs reognizing L(π ) n L(π ), respetively. Bkwr FA is isplye on the lower, whih epts the set of reversls of strings in L(π ). nique, similrly in DXAXE-B. In oth implementtions, the sets of tive sttes re kept in pth-trie noes, n therefore we n fin i for whih π mth the v -to-v i pth. However, it shoul e emphsize tht there is no gurntee tht π mthes the v i+ -to-v k+, even though we know π π mthes the v -to-v k+ pth. To onfirm this, we use nother FA whih reognizes the lnguges of onsisting of the reverse strings of L(π ). WellsuhnFAthe kwr FA for π [π ]. The kwr FA is run long the v -to-v k+ pth kwr whenever π π mthes the pth. We n merge set of kwr FAs into single one if neessry. An exmple of the kwr FA is isplye in Fig. 8. In DXAXE-A implementtion, time n spe omplexity of onstruting forwr FA n kwr FA re the sme s those of onstruting FA for liner pthpttern se. Time omplexity of running the forwr FA n the kwr FA for new pth-trie noe to ompute its output is h-multiple of the time omplexity of running FA for liner pth-pttern se, where h is the height of XML tree. Spe omplexity is the sme s the liner pthpttern se. In DXAXE-B implementtion, time n spe omplexities of onstruting forwr FAs n kwr FAs re the sme s liner pth-pttern se. Time omplexity of running the forwr FAs n the kwr FAs for new pth-trie noe is gin h-multiple of the time omplexity for the liner pth-pttern se. Spe omplexity remins unhnge. 4.3 Totl time n spe omplexity Let D e input XML t whose XML tree hs size s n height h, n whose pth-trie hs size t. LetΠ e input set of liner/primitive pth-ptterns. When the DXAXE- A implementtion is opte, it runs in O( D +s log + t Π log ) time using O(t Π ) spe. The ftor log is roppe if the hshing tehnique sustitutes for the AVL-tree n works well s ssume in the lzy DFA [3]. For primitive pth-pttern se, the ftor t Π log in the time omplexity is multiplie y h. When the DXAXE-B implementtion is opte, it runs in O( Π + D + s log + t Π ) time using O( Π + t Π ) spe, uner the ssumption tht for eh pttern π in Π, size(π)+fits wor length. For primitive pth-pttern se, the ftor t Π in the time omplexity is multiplie y h gin. We note tht the ftor log ssumes use of the AVL-tree, n is roppe if the hshing tehnique works effetively. For the lzy DFA, the time n spe omplexity is similr to DXAXE-A, exept tht ost of serhing the FAstte lists ssoite with existing DFA sttes for newly rete list of FA sttes shoul e onsiere. Sine there oul e O(t) lists, eh hving size O( Π ), the time omplexity is O(t Π ). Totlly, the lzy DFA se metho runsino( D +s log +t Π (log +t)) time using O(t Π ) spe, where the ftor log n e roppe ssuming the hshing tehnique. 5 Computtionl Experiment We rrie out series of omputtionl experiments ginst the two XML t: XML reors of DBLP n the rnom t of XMrk enhmrk, stte in Setion 3. Sine XMLTK els only with the liner XPth frgment, we restrite ourselves to it in the experiments. We rnomly generte test sets of liner pth-ptterns y using pthgenertor 3 with DTDs of the two XML t sets. 4 We i not use the XML t of UniProtKB/Swiss-Prot in the experiments sine no DTD is provie with it. All experiments were exeute on.4 GHz Intel Pentium 4,. GB RAM, running Re Ht Linux Avne Server.. Below, we report the result of performne omprison of DXAXE with XMLTK in the three points: memory usge, proessing time n throughput. Although implementtions of XFilter, YFilter, XSQ re ville, we exlue them in the omprison sine their throughput is worse thn tht of XMLTK s reporte in [, 8]. Memory usge omprison Tle 3 ompres size of lzy DFA n reue pth-trie. The lzy DFA hs smller numer of sttes in omprison with our DFA. The totl size of FA-stte lists of lzy DFA sttes grows s FA size in- 3 relese.htm 4 We generte pttern lists of size,,...,, ut there re uplitions. The numers of istint ptterns were smller.

9 Tle3.SizeoflzyDFAnourDFAre ompre ginst the DBLP t n the rnom t. () Rnom t whose pth trie hs 549 noes. # queries lzy DFA our DFA # sttes FA stte lists # noes , 63,39 54, 54 6,49 54, 533,86,5 54 () DBLP t whose pth trie hs 66 noes. # queries lzy DFA our DFA # sttes FA stte lists # noes , 9 6,39 56, 5 8,69 56, 5 9, Tle 4. Memory usge omprison. # queries memory usge (KB) DXAXE-A DXAXE-B XMLTK 4,69 4, ,36 4,8,44 5,45 4,85,46, 8,8 5,444 5,, 4,4,68 38,8, 35,6,45 369,36 reses. The totl size of tive-stte lists store in pth-trie noes grows similrly. Tle 4 ompres the memory usge of the methos pplie to the rnom t with liner pth-ptterns of size,,...,. DXAXE-B onsumes / of memory require y DXAXE-A. DXAXE-B onsumes /5 n / of memory tht XMLTK requires for, n, queries. Thus, DXAXE is muh more speeffiient thn XMLTK when lrge numer of liner pthptterns re elt with. Running time omprison Tle 5 ompres the proessing times ginst liner pth-pttern sets of size,,...,. Compre to XMLTK, DXAXE-B is pproximtely.5 to times fster n to 6 times fster Tle 5. Running time omprison. () Rnom t from XMrk # queries elpse time (se) DXAXE-A DXAXE-B XMLTK , , () DBLP # queries elpse time (se) DXAXE-A DXAXE-B XMLTK , , ginst the DBLP t n the rnom t, respetively, n the rtios eome lrger s the numer of ptterns inreses. Throughput omprison Fig. 9 ompres the throughputs for sets of n, queries ginst DBLP n the rnom t, where the X-xis is the size of t lrey proesse from the left. Results show tht DXAXE-A n -B outperforms XMLTK in throughput omprison. Low throughput of XMLTK t erly stge implies tht it is in wrm-up phse, in whih mny sttes n trnsitions of lzy DFA re rete. This orrespons to rpi inrese of pth-trie size t erly prt we hve lrey seen in Fig. 5. Compre with XMLTK, DXAXE-A n -B in their wrm-up phse hve reltively high throughput. For the rnom t (see () n ()), ll methos nnot hve stle throughput. Lower throughput fter 5MB point orrespon to rpi inrese of tg ourrenes we hve seen in Fig. 5 (). We note tht work of pthmthing is performe only when tg ourrene is foun in ll methos. For the DBLP t (see () n ()) whih hs regulr struture, the throughputs of the three metho re stle n high. In this se, DXAXE-A n -B showe pproximtely 4 times higher throughput thn XMLTK oes. 6 Complex XPth expressions So fr, we introue lss of primitive pth-ptterns, whih re regre s primitives for more omplex XPth 8

10 8 6 DXAXE-A DXAXE-B XMLTK Throughput (MB/s) Throughput (MB/s) DXAXE-A DXAXE-B XMLTK Dt size (MB) () Rnom t from XMrk, queries Dt size (MB) () Rnom t from XMrk,, queries Throughput (MB/s) 4 3 DXAXE-A DXAXE-B XMLTK Throughput (MB/s) 5 DXAXE-A DXAXE-B XMLTK Dt size (MB) () DBLP, queries Dt size (MB) () DBLP,, queries Figure 9. Throughput omprison. expressions. Although etile isussion is outsie the sope of this pper, we shll riefly sketh how this XPth frgment oul e primitives. Consier series of ssignments: Q = π [π : expr ];...; Q n = π n [πn : expr n] where Q i is logil vriles, n expr i is oolen expression over keywors or one over Q,...,Q n. Sustring mth: DXAXE oes not use ny existing XML prser suh s SAX []: It simultneously performs keywor serh n XML prsing, tht is, Aho-Corsik pttern mthing mhine (PMM for short) [] is uilt n run over XML t strem, n when the eginning of tg ( < ) is etete our own prser is invoke to etet tgnme string n proess ttriute expressions. A rstilly fst XML prsing is me possile in this wy. Sine PMM simultneously reognizes multipttern ourrenes, we n proess oolen expressions over multiple keywors. Logil opertion: Consier Q = /orer//ress [street or region]. Let Q = /orer//ress[street:true] n Q = /orer//ress[region:true]. A lous of Q n e otine s lous of Q or Q. Therefore Q n e expresse s Q 3 = /orer//ress[ε: Q Q ]. este preites: Consier Q = //ress[//region [//ountry n zipoe]]. Let Q = //ress//region[//ountry: true] n Q = //ress//region[zipoe:true]. ThenQ is represente s Q 3 = //ress[//region: Q Q ]. Preite in ny lotion steps: Consier Q = /orer[//ress]//zipoe. Let Q = /orer[//ress: true]. Q is expresse s Q = Q //zipoe[ε:true], if we llow suh expressions. This expression n e evlute y using lzy evlution tehnique. We note tht Q i is mpping tht ssigns truth-vlues to XML-tree noes. We exten this to ssign integer vlues to them, n llow expr i e n rithmeti expression, not oolen expression. For Q i = π [π : expr i ], the mpping Q i ssigns to n XML-tree noe x the summtion of the integer vlues otine y evluting t noe y the rithmeti expression expr i over ll the noes y suh tht π [π ] ours t lous (x, y). To the noes x suh tht there is no y 9

11 suh tht π [π ] ours t (x, y), the mpping Q i ssigns. Then, we n el with ggregtion funtions s follows. Aggregtion: Consier Q = /sener[ount(//region)>]. Let Q = /orer[//ress: ]. ThenQ is expresse s Q = /orer[ε: (Q > )]. Thus, we n el with omplex XPth expressions suh s //[//]//[//][]//e, se on effiient proessing tehnique for primitive pth-ptterns. XPth expressions with kwr xes n e elt with fter trnsforming equivlent ones without kwr xes []. Disussion Let e set of tgnmes, n let Π e set of liner XPth expressions. We note tht the elements of Π re regulr expressions over. DFAs reognizing the lnguge L(Π) oul hve exponentil numer of sttes. 5 The lzy DFA is one tht reognizes superset of L(Π) S, not L(Π), wheres is the set of tgnme strings of the pths from the root. The output-e pth-trie of DXAXE n e regre s DFA, whih reognizes extly the lnguge L(Π) S. The grph struture of the DFA epens only on XML t, not on XPth queries (unless the reution tehnique mentione in Setion 4 is pplie to), n the FA reognizing L(Π) is use to outputs to the DFA sttes. In ontrst, the lzy DFA is uilt from FA tht reognizes L(Π),silly with the stnr suset onstrution. For this reson, the DFA onstrution time of our metho is muh smller thn tht of the lzy DFA. The size of lzy DFA is upperoune y the size of pth-trie representing S. Using the lzy DFA, we hve to py reltively high ost in omputing stte n trnsition runtime, lthough the ost is reovere when the stte n the trnsition re reuse. The ost is minly evote to erese the DFA size. It, however, pprohes the pth-trie size s the numer of queries grows. DXAXE requires lower ost to ompute stte n trnsition. Referenes [] A. V. Aho n M. Corsik. Effiient string mthing: An i to iliogrphi serh. Comm. ACM, 8(6):333 34, 95. [] M. Altinel n M. Frnklin. Effiient filtering of XML ouments for seletive issemintion of informtion. In VLDB, pges 53 64,. [3] R. Apweiler, A. Biroh, C. H. Wu, W. C. Brker, B. Boekmnn, S. Ferro, E. Gsteiger, H. Hung, R. Lopez, M. Mgrne, M. J. Mrtin, D. A. tle, C. O Donovn, 5 More preisely, DFAs hve to not only reognize the lnguge ut lso report whih ptterns in Π re foun. Hene they shoul e Mely mhines.. Reshi, n L.-S. L. Yeh. UniProt: the universl protein knowlegese. 3:D5 D9, 4. [4] I. Avil-Cmpillo, T. J. Green, A. Gupt, M. Onizuk, D. Rven, n D. Suiu. XMLTK: An XML toolkit for slle XML proessing. In PLAX,. [5] C.-Y. Chn, P. Feler, M. Groflkis, n R. Rstogi. Effiient filtering of XML ouments with XPth expressions. VLDB Journl, (4):354 39,. [6] D. Chen n R. K. Wong. Optimizing the lzy DFA pproh for XML strem proessing. In Pro. 5th Austrlsin Dtse Conferene (ADC4), 4. [] J. Clrk n S. DeRose. XML Pth Lnguge (XPth) Version.. W3C Reommention 6 ov [8] Y. Dio, M. Altinel, M. Frnklin, H. Zhng, n P. Fisher. Pth shring n preite evlution for high-performne XML filtering. ACM TODS, 8(4):46 56, 3. [9] D. Floresu, C. Hillery, D. Kossmnn, P. Lus, F. Riri, T. Westmnn, M. J. Crey, n A. Sunrrjn. The BEA streming XQuery proessor. The VLDB Journl, 3(3):94 35, 4. [] R. Golmn n J. Wiom. DtGuies: Enling query formultion n optimiztion in semistruture tses. In VLDB 9, pges , 99. [] G. Gottlo, C. Koh, n R. Pihler. Effiient lgorithms for proessing XPth queries. In VLDB, pges 95 6,. [] G. Gottlo, C. Koh, n R. Pihler. The omplexity of XPth query evlution. In PODS 3, 3. [3] T. J. Green, A. Gupt, G. Miklu, M. Onizuk, n D. Suiu. Proessing XML strems with eterministi utomt n strem inexes. ACM TODS, 9(4):5 88, 4. [4] L. H. n S. D. XMill: n effient ompressor for XML t. In SIGMOD, pges 53 64,. [5] A. Ishino n M. Tke. A proposl for XQuery proessor with eterministi utomton n pth pruning. DBSJ Letters, 4(4), 6. (in Jpnese). [6] M. Ley. DBLP omputer siene iliogrphy. [] D. Megginson. SAX.: Simple API for XML. [8] S. Mitri, A. Ishino, n M. Tke. Light-weight elertion for streming XML oument filtering. In SWOD,. [9] G. vrro n M. Rffinot. Flexile pttern mthing in strings: Prtil on-line serh lgorithms for texts n iologil sequenes. Cmrige University Press,. [] D. Oltenu, H. Meuss, T. Furhe, n F. Bry. Xpth: looking forwr. In XMLDM, volume 49, pges 9,. [] M. Onizuk. Light-weight XPth proessing of XML strem with eterministi utomt. In CIKM 3, pges , 3. [] F. Peng n S. S. Chwthe. XSQ: streming XPth engine. ACM TODS, 3():5 63, June 5. [3] A. Shmit, F. Ws, M. L. Kersten, M. J. Crey, I. Mnolesu, n R. Busse. XMrk: A enhmrk for XML t mngement. In VLDB, pges ,.