Performance Evaluation of Neighborhood Signature Techniques for Peer-to-Peer Search

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1 Pefomance Evaluaton of Neghbohood gnatue Technques fo Pee-to-Pee each e L Wang-Chen Lee * Anand vasubamanam Depatment of Compute cence and Engneeng Pennsylvana tate Unvesty Unvesty Pak, PA 16802, UA E-al: {mel, wlee, anand}@cse.psu.edu Receved June 13, 2007 ; Accepted June 30, 2007 Abstact. Pee-to-pee (P2P) systems have eceved a lot of attenton due to the populaty of applcatons such as ETI, Napste, Gnutella, and opheus. The P2P systems pesent temendous challenges n seachng data tems among the numeous host nodes. Whle seach has been studed n a smla but dffeent context,.e., paallel and dstbuted database systems, the lage scale and dynamc membeshp change of P2P systems eque the seach ssue to be e-examned. Exstng seach technques n unstuctued pee-to-pee ovelay netwoks ncu excessve netwok taffc. In ths pape, we nvestgate the ssues of tadng-off stoage space at pees to educe netwok ovehead n unstuctued P2P ovelay netwoks. We popose to use sgnatues fo dectng seaches, and ntoduce thee schemes, namely complete-neghbohood sgnatue (CN), patal-neghbohood supemposed sgnatue (PN-), and patal-neghbohood appended sgnatue (PN-A), to facltate effcent seachng of shaed content n P2P netwoks. Wth lttle stoage ovehead, these sgnatues mpove the pefomance of content seach and thus sgnfcantly educe the volume of netwok taffc. Extensve analyss and smulatons ae conducted to evaluate the pefomance of ou poposal wth exstng P2P content seach methods, ncludng Gnutella, andom walk, and local ndex. Results show that PN-A gves the best pefomance at a small stoage cost. Keywods: sgnatue, ndex technques, nfomaton seach, pee-to-pee systems, pefomance evaluaton 1 Intoducton The advance of facltes such as Napste [1] and Gnutella [2] has made the Intenet a popula medum fo the wdespead exchange of esouces and volumnous nfomaton between thousands of uses. In contast to tadtonal clent-seve computng models, host nodes n these Pee-to-Pee (P2P) systems can act as seves as well as clents. Despte avodng pefomance bottlenecks and sngle ponts of falue, the P2P systems pesent temendous challenges n seachng data tems among these numeous host nodes. each of nfomaton n paallel and dstbuted database systems has eceved a lot of eseach effots fom the database communty (please see [3] fo a compehensve suvey). Whle pee-to-pee systems ae smla to shaed-nothng paallel and dstbuted database systems, the challenges faced ae fundamentally dffeent. Paallel and dstbuted database systems consst of dozens o hundeds of machnes that ae desgnated to povde cetan database sevces, and thus ae athe stable. In contast, P2P systems may have nodes jon o leave fequently, and thus ae hghly dynamc. In addton, the sze of a P2P system s n the ange of thousands o even mllons of nodes, whch s much geate than the typcal szes of paallel and dstbuted database systems. Thus, P2P systems eque the seach technques to toleate membeshp changes (.e., node jon, leave, o falue), and to scale to a lage numbe of nodes, n addton to locatng data tems effcently. As a esult, the seach technques developed fo paallel and dstbuted database systems can not be smply employed to pee-to-pee systems and the seach ssue needs to be e-examned. Exstng P2P ovelays can be classfed as unstuctued P2P ovelays and stuctued P2P ovelays. The man dffeences between these two ae whethe data placement and netwok topology ae contolled. In a unstuctued P2P ovelay, lke Gnutella [2], pees fom a andom topology and stoe data tems locally. Pmay seach technques poposed fo unstuctued P2P ovelays ae floodng and andom walk [4,5]. Whle the seach costs n unstuctued P2P ovelays may not be low n tems of the total numbe of messages and/o the numbe of hops tavesed pe seach, the advantages ae n the low mantenance cost, makng them elatvely easy to handle * Coespondence autho

2 電腦學刊第十七卷第四期 (Jounal of Computes, Vol.17, No.4, Januay 2007) membeshp and data content changes. In addton, unstuctued P2P ovelays pose no estctons on the types of quees that can be suppoted effectvely. In contast, stuctued P2P ovelays tghtly contol data placement and netwok topology to pefom cetan knd of seach odeng whch can facltate seachng fo the equested data tems. CAN [6], Chod [7], Pasty [8], Tapesty [9], and W [10] ae examples of stuctued P2P ovelays. each ove these ovelays s effcent (seach path length s O(logN) whee N s the netwok sze). Howeve, they ncu hgh oveheads fo data placement and topology mantenance. ost of exstng systems deployed n pactce ae unstuctued (fo the smplcty and flexblty). In ths study, we focus on mpovng seach effcency of unstuctued P2P ovelays. In the est of ths pape, we efe unstuctued P2P ovelays as P2P ovelays fo smplcty. A P2P netwok 1 s establshed by logcal connectons among the patcpatng nodes (called pees). The pees povde dgtal nfomaton esouces, such as musc clps, mages, documents and othe foms of dgtal content, to be shaed wth othe pees. The P2P ovelay netwok topology may change dynamcally due to constant jons and leaves of the pees, namely pee jon and pee leave 2, n the netwok. In addton, the shaed nfomaton changes dynamcally snce the pees may update the dgtal content that they offe, namely pee update. Fg. 1. A patal snapshot of a P2P netwok Fg. 1 shows a patal snapshot of a P2P netwok. In ths fgue, we use a vetex to epesent a node (.e., a pee) of the P2P ovelay netwok and an edge to denote the connecton between two pees. When a pee, A, has a dect connecton wth anothe pee, B, we call these two pees neghbos. In the netwok, a pee may each anothe pee va one o a sequence of connectons, called paths. The path length can be obtaned by countng hops of connectons. The dstance between two pees s the mnmal path length between them. Each pee has a neghbohood, whch ncludes all the pees eachable wthn a gven dstance. The neghbohood adus efes to the dstance fom a pee to the edge of ts neghbohood. Fo example, as llustated n Fg. 1, thee ae two paths of length 3 and 4, espectvely, between Node 1 and Node 9. Thus, the dstance between Node 1 and Node 9 s 3. Node 1 has a neghbohood of adus 2 that conssts of Nodes 2, 3, 4, 8. Two man stateges have been exploed fo seachng n unstuctued P2P ovelays: Blnd seach: Ths stategy lets messages poll nodes, wthout havng any dea of whee the data may be held, tll the equed tems ae found. Gnutella and andom walk use such a stategy. In Gnutella, a seach message s fowaded by a pee to all ts neghbos untl the message eaches a cetan peset dstance. The down sde of ths stategy s the possble netwok oveload due to a lage numbe of geneated seach messages. To addess the ssue of excessve taffc caused by the floodng seach, andom walk chooses to fowad a seach message fom a pee to one o moe andomly selected neghbos. Howeve, ths appoach ncus a long latency to satsfy a equest. 1 We use the tems, P2P ovelays, P2P systems, P2P netwoks and P2P applcatons, whee appopate. Howeve, they ae mostly ntechangeable n the context of ths pape. 2 Pee falue can be teated smlaly as pee leave as dscussed n ecton Thus, we do not lst t sepaately. 12

3 L et al: Pefomance Evaluaton of Neghbohood gnatue Technques fo Pee-to-Pee each Dected seach: Ths stategy mantans addtonal nfomaton n the pee nodes (whch blnd seach does not eque) n ode to educe netwok taffc. Consequently, messages ae dected specfcally along paths that ae expected to be moe poductve. The addtonal nfomaton s typcally mantaned as ndexes ove the data that ae contaned ethe wthn heachcal clustes [11] o by neaby neghbos [12, 13, 14]. In addton to the hgh stoage cost ncued by stong the ndex tself and hgh mantenance ovehead ncued by ndex update, ths ndexng appoach eques detemnng what attbutes to ndex a po, thus constanng the seach that can be suppoted. Whle ndex based dected seach seems attactve n tems of seach message taffc, the dawbacks as descbed above motvate us to apply sgnatue technques to povde flexble seach ablty (.e., suppotng abtay quees) and bette seach message taffc behavo at a lowe stoage cost and mantenance ovehead than ndex-based mechansms. gnatue methods have been used extensvely fo text eteval, mage database, multmeda database, and othe conventonal database systems. A sgnatue s bascally an abstacton of the nfomaton stoed n a ecod o a fle. By examnng the sgnatue only, we can estmate whethe the ecod contans the desed nfomaton. Due to ts compactness, sgnatue ncus low stoage as well as low communcaton oveheads when beng exchanged among emote hosts. In addton, sgnatue can suppot abtay quees. All these advantages of sgnatue make t vey sutable fo flteng nfomaton stoed at nodes of P2P systems. Ths pape pesents thee novel ways of usng sgnatues, namely complete neghbohood sgnatue (CN), patal neghbohood supemposed sgnatue (PN-) and patal neghbohood appended sgnatue (PN-A), to epesent neghbohood data at netwok nodes fo optmzng seaches n P2P systems. The mets of these thee neghbohood sgnatue schemes ae exploted by analyss and smulatons. nce the sgnatue technques tade some exta stoage ovehead fo educng netwok taffc 3, we use total message volume to evaluate vaous P2P seach technques. We deve an analytc model to estmate the seach cost and the mantenance ovehead of the poposed sgnatue schemes and conduct an extensve pefomance evaluaton though both analyss and smulaton to compae the pefomance wth some epesentatve seach technques developed fo unstuctued P2P ovelays, ncludng Gnutella [2] and andom walk [5] fo blnd seach and local ndex [14] fo dected seach. We examne the pefomance of these technques unde dffeent netwok topologes (.e., unfom and powe-law netwoks) and seachng stateges (.e., floodng and sngle-path), and test the senstvty to vaous factos ncludng neghbohood adus, stoage constants, key attbute sze, numbe of data tems at a node, data dstbuton, etc. Ou expements show that the sgnatue appoaches (patculaly PN-A) ae much bette than the othe altenatves fo the most easonable stoage space avalablty assumptons on host nodes. The basc dea of the thee neghbohood sgnatue technques have been dscussed n ou pelmnay wok [15]. In ths pape, we povde a complete pesentaton of vaous opeatons usng these neghbohood sgnatues. In addton, we popose a lazy sgnatue update method that mpoves the sgnatue mantenance oveheads. oeove, we povde an analytc model and conduct an n-depth pefomance evaluaton usng both analytc and smulaton expements. The man contbutons of ths pape ae thee-fold: Thee novel neghbohood sgnatue schemes fo effcent seach n P2P netwoks ae poposed. The detals fo vaous opeatons, such as seach, pee jon, leave and update, ae pesented. An analytc model to estmate the seach cost and mantenance ovehead of the neghbohood sgnatue schemes s deved. An extensve pefomance evaluaton usng both analyss and smulaton to compae ou poposal wth othe exstng P2P seachng appoaches s conducted. To the best of ou knowledge, ths s the fst study that takes both of seach cost and mantenance ovehead nto n-depth consdeaton. Thee have been technques suggested to stoe addtonal nfomaton on ntemedate nodes, e.g., cache quey esults [16] o mantan hstoy about po opeatons [14], to educe netwok taffc. Whle the effectveness of such enhancements depends on quey pattens and the localty, they ae othogonal to ths wok and can be used n conjuncton wth ou sgnatue schemes to futhe contol netwok taffc. In addton, thee ae sevces amng at ndexng and ankng all the content avalable n a P2P netwok [17]. Ths sevce uses a technque called bloom flte, whch s smla to the sgnatue technque used n ths pape, to effcently summaze the ndexed tems. Howeve, ts focus s on povdng a seach engne athe than educng the netwok taffc. The est of the pape s oganzed as follows. In ecton 2, we pesent detals of the poposed neghbohood sgnatue schemes. In ecton 3, we povde a qualtatve compason between ou poposal and po seachng appoaches. In ecton 4, we pesent an analytc model fo vaous costs ncued by seach and mantenance of 3 gnatue technques educe seach latency as well. As we wll dscuss n ecton 3, the mpovement on seach latency can be easly obseved, and thus we focus on the mpovement on netwok taffc n the pape. 13

4 電腦學刊第十七卷第四期 (Jounal of Computes, Vol.17, No.4, Januay 2007) ou poposed schemes. ecton 5 gves the expemental setup fo the pefomance evaluaton and detaled esults fom expements unde dffeent seach stateges. Fnally, ecton 6 summazes the contbutons of ths pape and outlnes dectons fo futue wok. 2 Neghbohood gnatues In ths secton, we fst povde some backgound on the sgnatue method and then extend t fo seach n P2P netwoks. We popose thee neghbohood sgnatue schemes, CN, PN-, and PN-A, to ndex the data content offeed wthn the neghbohood of a pee, whch help to dect a seach to a subset of pobablstcally poductve neghbos. We descbe the fomaton of the sgnatues fo each scheme and then povde detals fo seach and sgnatue mantenance unde vaous scenaos (.e., pee jon, pee leave, and pee update). 2.1 Backgound gnatue technques have been wdely used n nfomaton eteval. A sgnatue of a dgtal document, called data sgnatue, s bascally a bt vecto geneated by fst hashng the attbute values and/o content of the document nto bt stngs and then pefomng a btwse-or opeaton to supempose (denoted by ) them togethe. Fg. 2 depcts the sgnatue geneaton and compason pocesses of a dgtal fle and some seaches Fg. 2. Illustaton of sgnatue geneaton and compason As llustated n the fgue, to facltate seach, a seach sgnatue s geneated n a smla way as a data sgnatue based on the seach ctea (e.g., keywods) specfed by a use. Ths seach sgnatue s matched aganst data sgnatues by pefomng a btwse-and opeaton. When the esult s not a match (.e., fo some bt set n the seach sgnatue, the coespondng bt n the data sgnatue s NOT set), the coespondng document can be gnoed. Othewse (.e., fo evey bt set n the seach sgnatue, the coespondng bt n the data sgnatue s also set), thee ae two possble cases: 1) tue match - The document s ndeed what the seach s lookng fo. 2) false postve - Even though the bts of the sgnatues may match, the document tself does not match the seach ctea. Ths occus due to cetan combnatons of bt stngs geneated fom vaous attbute values, keywods, o document content. The stoage devoted to the sgnatue can nfluence the pobablty of false postves 4. Obvously the documents wth matchng sgnatues stll need to be checked aganst the seach ctea to dstngush a tue match fom a false postve. 2.2 gnatue chemes fo P2P ystems Befoe poceedng to ntoduce the poposed sgnatue schemes, we fst assume that a local sgnatue s ceated at each pee of a P2P netwok to ndex the local content avalable at the pee. By dong ths, seach ove the local content of a pee s pocessed effcently. Futhemoe, a pee may collect and mantan auxlay nfomaton egadng dgtal content avalable wthn a specfc netwok dstance (.e., ts neghbohood). Theefoe, a pee 4 The fomula fo estmatng the pobablty of false postves s pesented n ecton 4. 14

5 L et al: Pefomance Evaluaton of Neghbohood gnatue Technques fo Pee-to-Pee each can flte unsatsfable seach equests befoe fowadng them to a neghbo. Based on ths dea, we popose thee sgnatue schemes classfed as follows: Complete Neghbohood (CN): One ntutve appoach s to ndex all the content avalable wthn the neghbohood of a pee. Thus, a complete neghbohood (CN) sgnatue s geneated by supemposng all the local sgnatues located wthn the neghbohood of a pee. Fg. 3(a) shows an example of a complete neghbohood sgnatue fo pee 1, whch ndexes all the content avalable at Pees 2, 3, 4, and 8, whose local sgnatues ae epesented by ectangles wth dffeent fllng pattens n Fg. 1. By holdng a complete neghbohood sgnatue, a pee can detemne whethe the seach should be extended n ts neghbohood o smply fowaded to some pees outsde of ts neghbohood. (a) CN (b) PN- (c) PN-A Fg. 3. Illustaton of neghbohood sgnatue geneaton Patal Neghbohood (PN): Whle the CN scheme has the advantage of jumpng out of a neghbohood when the seach sgnatue and neghbohood sgnatues do not match, t has to fowad the seach to all of ts neghbos when thee s a match between the seach sgnatue and neghbohood sgnatue. Thus, nstead of ndexng the complete neghbohood, a sgnatue can be geneated to ndex a patal neghbohood banchng fom one of the neghbos dectly connected to a pee, whch s called patal neghbohood sgnatue. The goal s to ncease the pecson of seach wthn the neghbohood of a pee. The seach wll only be extended to the neghbos whose assocated patal neghbohood sgnatues have a match wth the seach sgnatue. Thee ae two altenatves fo geneatng patal neghbohood sgnatues: upempose (PN-): In ths appoach, we use the tadtonal supemposng technque. Thus, all of the local sgnatues located wthn a neghbohood banch ae compessed nto one sgnatue, called patal neghbohood supemposed (PN-) sgnatue. Fg. 3(b) shows that pee 1 has 2 PN- sgnatues, whee PN- 2, the neghbohood sgnatue fo banch 2, ndexes all the contents avalable at Pees 2 and 4, and PN- 3, the neghbohood sgnatue fo banch 3, ndexes the contents avalable at Pees 3 and 8. Append (PN-A): The supemposng technque has been shown to be effectve n compessng a lage amount of ndex nfomaton whle suppotng effcent nfomaton flteng functon. Howeve, ths compesson comes at the cost of losng some nfomaton,.e. when the PN- sgnatue at a node matches, t does not gve a clue of whch pees should be vsted, esultng n seachng all of these pees. An altenatve that we popose, called patal neghbohood appended (PN-A) gnatue, s to append (concatenate) all of the local sgnatues wthn a banch of the neghbohood nto a patal neghbohood sgnatue 5. When a seach sgnatue matches wth some sub-sgnatues wthn a PN-A sgnatue, the seach message wll only be fowaded to these pees assocated wth the matched subsgnatues. Fg. 3(c) shows that pee 1 has 2 PN-A sgnatues, whee PN-A 2 ndexes all the contents avalable at Pees 2 and 4, and PN-A 3 ndexes the contents avalable at Pees 3 and 8. 5 An append-based CN sgnatue can be geneated by smply appendng all of the patal neghbohood sgnatues, and s thus not poposed as a sepaate method. 15

6 電腦學刊第十七卷第四期 (Jounal of Computes, Vol.17, No.4, Januay 2007) One could wonde why we bothe consdeng PN-, afte havng descbed the benefts of PN-A. The eason s that the fome can take much less space, and allows us to fnd out whch s a bette altenatve fo a gven space ovehead at each node: (a) appendng the ndvdual sgnatues as n PN-A to fll up ths space wth each of the ndvdual sgnatues beng small (and not allowng bette flteng), o (b) allowng a much lage sgnatue fo each pee and the nfomaton loss comng only fom the supemposton. These tade-offs wll be evaluated n late expements. 2.3 each Algothms The neghbohood sgnatue schemes ae genec mechansms that can adapt to dffeent seach stateges and potocols. A use may ntate a seach of dgtal content fom any pee n the netwok, and the seach message s fowaded to all o a subset of ts neghbos to extend the seach. In ode to pevent ndefnte seach message popagaton n the P2P netwok, a stop condton needs to be specfed n the quey. The Gnutella floodng appoach uses the maxmum seach depth whle the andom walk uses the mnmum numbe of esults as the ctea fo lmtng message popagaton. In the followng, we dscuss the sgnatue based seach algothms fo the followng two stateges: floodng/maxmum-depth and sngle-path/mnmum-esult. Fo claty of ou pesentaton, we use to denote the adus of a neghbohood Floodng each In ths secton, we descbe how a pee utlzes neghbohood sgnatues to pefom seaches wth maxmum seach depth as the stop condton. nce the seach algothms fo the thee poposed sgnatue schemes ae smla, we use Algothm 1 to detal the floodng seach at a pee based on CN sgnatues and pont out the dffeences fo the PN sgnatues aftewads. Algothm 1 Floodng seach based on complete neghbohood sgnatues Incomng essage: each_sg(ttl) Local Vaables: Local_g, Neghbohood_g, each_g ystem Paametes: {the neghbohood adus} Pocedue: 1: compute each_g based on each_sg. 2: {check local content} 3: f match(each_g, Local_g) then 4: examne local content to vefy whethe ths s a tue match o not. 5: f tue match then 6: etun a ponte to the esult back to the sende. 7: end f 8: end f 9: {check whethe the maxmum seach depth s eached} 10: f TTL = 0 then 11: stop 12: end f 13: {contnue to seach the neghbohood} 14: f match(each_g, Neghbohood_g) then 15: fowad the message each_sg(ttl 1) to all the neghbos. 16: else 17: f TTL > then 18: fowad the message each_sg(ttl 1) to all the neghbos located + 1 hops away. 19: end f 20: end f Algothm 1 s nvoked when a seach message s ntated o eceved at a pee node of a P2P netwok. Ths seach message comes wth a tme-to-lve (TTL) counte whch was peset to the maxmum seach depth that ths message may be fowaded. The pee fst computes a seach sgnatue to compae wth ts local sgnatue. If thee s a match, the content at ths pee node s examned to detemne whethe ths s a tue match o a false postve. If ths s a tue match, a ponte to the esult s etuned back to the sende. Next, the pee checks the TTL to see whethe the maxmum seach depth has been eached (.e. TTL = 0), and f so, the seach message s dopped. Othewse, the seach sgnatue s compaed wth the neghbohood sgnatue. If thee s a match, the seach s extended to all of the neghbos by fowadng the message wth TTL deceased by 1. If the seach sgnatue does not match wth the neghbohood sgnatue, the pees located wthn hops (the neghbohood) 16

7 L et al: Pefomance Evaluaton of Neghbohood gnatue Technques fo Pee-to-Pee each need not be checked (as a esult, the seach message s dopped when TTL ). In ths case, the seach should be pocessed only at the pees + 1 hops away 6. The floodng seach algothms fo the two patal neghbohood (PN) sgnatue schemes ae only slghtly dffeent fom the one dscussed above (efe to Lnes 14-19). Instead of mantanng only one neghbohood sgnatue fo the whole neghbohood, a patal neghbohood sgnatue s geneated fo each of the neghbo banches n these two schemes. The PN- scheme compesses all of the local sgnatues n a neghbohood banch nto one sgnatue (by supemposng), whle the PN-A scheme enlsts (appends) all of the local sgnatues n a neghbohood banch nto one sgnatue. When a seach sgnatue matches wth a PN- sgnatue, the seach message s fowaded to the assocated neghbo. Othewse, the message s fowad to the pees + 1 hops away, located ght outsde of the patal neghbohood coespondng to the compaed neghbohood sgnatue. The compason of a seach sgnatue wth a PN-A sgnatue s pefomed by examnng all of the ncluded local sgnatues. Fo evey matched local sgnatue, a seach message s dectly fowaded to the coespondng pee node. If the seach sgnatue does not match wth a PN-A sgnatue, smla to PN-, the seach message s fowad to the pees + 1 hops away, located ght outsde of the patal neghbohood coespondng to ths neghbohood sgnatue ngle-path each In ths secton, we descbe how a pee utlzes neghbohood sgnatues to pefom sngle-path seach wth the mnmum numbe of esults as the stop condton (fo compason wth andom walk). mla to floodng, we use Algothm 2 to detal the sngle-path seach at a pee based on CN sgnatues and pont out the dffeences fo the PN sgnatues aftewads. The man dffeence between sngle-path seach and floodng seach s that f all of the neghbohood sgnatues do not match wth the seach sgnatue, one pee nstead of all pees located + 1 hops away s andomly selected to extend the seach. A system paamete TNR, ndcatng total numbe of esults found so fa, has the smla ole as TTL n floodng seach. Each tme a esult s found, the TNR s nceased by 1. The seach s stopped when TNR eaches a pe-defned value. Fo CN sgnatue, f the neghbohood sgnatue matches wth the seach sgnatue, all pees n the neghbohood ae possble canddates fo tue matches. In ode to detemne whethe the match s a tue match o not and how many esults ae thee n the neghbohood, the seach should be extended n the neghbohood fo checkng (called neghbohood checkng, efe to Lnes 15-19). Dffeent fom CN, the neghbohood checkng messages ae only fowaded to the neghbos wth matched neghbohood sgnatues n PN-, o dectly to the pees wth matched local sgnatues n PN-A. Algothm 2 ngle-path seach based on complete neghbohood sgnatues. Incomng essage: each_sg(tnr) Local Vaables: Local_g, Neghbohood_g, each_g ystem Paametes: {the neghbohood adus}, R {the mnmum numbe of esult}, T {tmeout} Pocedue: 1: compute each_g based on each sg. 2: {check local content} 3: f match(each_g, Local_g) then 4: examne local content to vefy whethe ths s a tue match o not. 5: f tue match then 6: ncease TNR by the numbe of esults satsfed at ths pee. 7: etun a ponte to the esult back to the sende. 8: end f 9: end f 10: {check whethe enough esults ae found} 11: f TNR R then 12: stop 13: end f 14: {contnue to seach the neghbohood} 15: f match(each_g, Neghbohood_g) then 16: fowad a neghbohood-checkng message Neghbohood_Check_sg(TNR, ) to all the neghbos. 17: wat fo a T peod of tme to eceve eples and fowad esult pontes back to the sende. 18: ncease TNR by the numbe of eceved esult pontes. 6 Hee we assume that a pee has the knowledge of ts pees at +1 hops away so that t may fowad the seach messages dectly. Ths knowledge can be smply obtaned though ts 1-hop-away neghbos snce the pees at hops away fom these 1-hop-away neghbos ae exactly the pees at + 1 hops away. 17

8 電腦學刊第十七卷第四期 (Jounal of Computes, Vol.17, No.4, Januay 2007) 19: end f 20: f TNR < R then 21: fowad each_sg(tnr) to a andomly selected pee located + 1 hops away. 22: end f 2.4 gnatue Constucton and antenance Afte descbng how the seach s pefomed wth neghbohood sgnatues, we next move on to dscuss the constucton and mantenance of these sgnatues. Bascally, neghbohood sgnatues ae constucted at a pee node when the pee newly jons a netwok. The neghbohood sgnatues of a pee wll need e-constuctons o updates when some pees jon/leave ts neghbohood o when some pees n ts neghbohood (ncludng tself) update the content. In the followng, we adopt two dffeent stateges to conduct sgnatue update. One update stategy s Eage Update whee a newly joned pee (a leavng pee, o a pee conductng content update) poactvely nfoms othe pees located wthn ts neghbohood to update the affected neghbohood sgnatues mmedately. The second update stategy s Lazy Update whee the updates on the neghbohood sgnatues ae postponed tll necessay,.e., a seach s encounteed. In the followng, we fst descbe the actons to be taken at pee jon, pee leave, and pee update fo eage update stategy. We then outlne the dffeence between eage update and lazy update stateges Eage Update on gnatues Pee jon: A new pee nfoms ts aval by sendng a jon message ncludng ts local sgnatue to the pees n the neghbohood. When a node eceves such a jon message, t fst adds (ethe supemposes o appends) the local sgnatue ncluded n the jon message to the coespondng neghbohood sgnatue, then sends back ts own local sgnatue to the new pee so that the new pee can constuct ts neghbohood sgnatues. Besdes ths, some pees that wee not n the same neghbohood eale, may be bought nto a neghbohood though the connectons of the newly joned node (when the new node jons the netwok though multple connectons and the neghbohood adus s geate than one). In ths case, these pees also need to exchange sgnatues va the newly joned node to mantan the accuacy of the neghbohood sgnatues. Pee leave: When a pee leaves the netwok, t nfoms the neghbos by sendng out a leave message. Fo PN-A, the leave message contans the node dentfe of the leavng pee. The update on neghbohood sgnatues fo PN-A only eques emovng the sgnatue of the leavng pee fom the neghbohood sgnatues. Fo CN o PN-, ths step s moe complcated. nce thee s no smple way to emove the local sgnatue of the leavng pee fom the CN and PN- sgnatues whch ae geneated by supemposng, the affected pees n the neghbohood have to e-constuct the neghbohood sgnatues fom scatch. In ode to constuct a new CN neghbohood sgnatue, the affected pee asks fo local sgnatues fom the pees n the neghbohood by sendng to these pees a pseudo jon message. The pseudo jon message functons smlaly to a eal jon message n that the eceves of both messages send back the local sgnatues, but dffes n that when a pee eceves a pseudo jon message, t does not need to update ts own neghbohood sgnatue. lghtly dffeent fom CN, fo PN-, the affected pees only need to ask fo ndvdual local sgnatues fom the pees on the affected banch. Pee update: When a pee updates ts data content, the local sgnatue s updated accodngly. The pocedue fo updatng the neghbohood sgnatues fo CN and PN- s the same as pee leave snce new neghbohood sgnatues need to be constucted. Fo PN-A, the dffeence between the updated sgnatue and the old sgnatue s ecoded n a change ecod, whch s ncluded n the update message, so that the affected pees can update the elatve sub-sgnatues n the neghbohood sgnatues accodngly Lazy Update on gnatues In lazy update, the sgnatue update s postponed tll a seach s encounteed. Howeve, a newly joned pee o a pee conductng content update needs to notfy the othe pees n the neghbohood because the affected neghbohood sgnatues have become stale. Wth ths notfcaton, a pee n the neghbohood can nvoke sgnatue update only when a seach s encounteed. Ths notfcaton s not necessay fo pee leave snce usng a stale neghbohood sgnatue whch ncludes nfomaton about data tems stoed n the leavng pee wll not esult n mssng of any data tems stoed n the system. Pee jon: To pefom the notfcaton as descbed above, a newly joned pee sends a smple message wth ts node dentfe (nstead of ts local sgnatue as n eage update) to the pees n ts neghbohood. A pee n the neghbohood ecods the eceved node dentfe n a To-Jon-Lst. If a pee wth a non-empty 18

9 L et al: Pefomance Evaluaton of Neghbohood gnatue Technques fo Pee-to-Pee each To-Jon-Lst eceves a seach message late on, t nvokes actons smla to pee jon n eage update (as descbed above). Dung ths pocess, the pees that have updated the neghbohood sgnatues affected by ths pee jon emove the elevant enty fom the To-Jon-Lsts, accodngly. Pee leave: When a pee leaves the netwok, actons on sgnatue mantenance ae not taken mmedately. Late on, dung seach pocess, when a pee detects that a neghbong pee has left the netwok, t nvokes actons smla to pee leave n eage update (as descbed above). Pee update: mla to pee jon, a pee updatng ts local content sends a message wth ts node dentfe to the pees n ts neghbohood, whch then ecod the eceved node dentfe n the To-Update-Lst. When one of these pees eceves a seach message, t nvokes actons smla to pee update n easy update (as descbed above). Dung ths pocess, the pees that have updated the neghbohood sgnatues emove the elevant enty fom the To-Update-Lst, accodngly. 3 Qualtatve Compason of Dffeent each chemes Befoe a quanttatve evaluaton, we fst povde a qualtatve compason of ou poposal wth exstng epesentatve P2P seach technques developed fo unstuctued P2P systems, such as Gnutella, andom walk, and local ndex (see Table 1). Gnutella ncus hgh seach message volume snce each seach message s flooded n the netwok. Random walk only fowads a seach message fom a pee to one o a few of ts neghbos, thus the seach message volume s educed compaed to Gnutella floodng appoach. Local ndex and sgnatue appoaches ncu low seach message volume snce the seach s only fowaded to a subset of pees n a neghbohood beng seached. In addton to the seach message volume, both local ndex and sgnatue appoaches ncu message exchanges fo ndex/sgnatue constucton and mantenance dung pee jon/leave/update, whch Gnutella and andom walk do not ncu. Ths message volume ovehead ncued by pee jon/leave/update s popotonal to the ndex/sgnatue sze. nce the ndex sze s much lage than sgnatue sze, the mantenance ovehead fo local ndex s usually lage than fo sgnatues. In addton, ths ovehead can be offset when seach s much moe fequent. The tade-off between these s nvestgated quanttatvely n the est of ths pape. Table 1. Compason between Gnutella floodng, andom walk, local ndex and sgnatue appoaches Gnutella Random Walk Local Index gnatue each cost hgh modeate low low antenance cost none none modeate lowmodeate each latency n floodng seach low - low low each latency n sngle-path seach - hgh modeate modeate toage equement none none hgh low each tems abtay abtay key attbutes abtay In Gnutella, the seach latency s popotonal to the seach adus, whch ae about 5 to 7 hops. Random walk s seach latency s nvesely popotonal to the numbe of eplcas n the netwok as descbed n [5]. When the numbe of eplcas s low n the netwok, the seach latency fo andom walk would be vey hgh compaed to Gnutella. In floodng seach, the seach latency of local ndex and sgnatue appoaches s compaable to Gnutella. In sngle-path seach, the seach latency fo local ndex and sgnatue appoaches s educed appoxmately tmes ( s the sze of the ndexed neghbohood wth adus ) compang to andom walk. nce the seach latency can be easly obseved as descbed above, we ddn t nclude plots fo seach latency n the pefomance evaluaton secton. Both local ndex and sgnatues mpove pefomance at the expense of exta stoage. Howeve, the stoage equement of sgnatue s much lowe than local ndex. oeove, the sgnatue schemes can adapt to the avalable stoage. In addton to ncung lowe total message volume at a much smalle stoage equement, the sgnatue appoach s sutable fo abtay attbute based seach, keywod based text seach, and content based seach. In ths aspect, local ndex appoach s not a good choce snce t only suppots seaches aganst some selected key attbutes. 19

10 電腦學刊第十七卷第四期 (Jounal of Computes, Vol.17, No.4, Januay 2007) 4 Analyss of gnatue Appoaches In ths secton, we develop an analytcal model fo the seach and mantenance cost of the poposed neghbohood sgnatues unde unfom netwok topology. The analyss consdes both of floodng and sngle-path seach stateges. Table 2 lsts the symbols used n ths secton fo easy efeences. nce most tems n the table ae selfexplanatoy, we only explan some of them n the followng. In P2P netwok, f a message tavelng though an edge eaches a pee that has seen the same message befoe, ths edge closes a cycle and we call ths knd of edges edundant edges. The ato of edundant edges n the netwok s denoted as β. Replcaton ato, denoted as α, epesents the numbe of eplcas pe data dvded by the total numbe of pees n the netwok. each/update ato, denoted as ϕ, ndcates the elatve popoton of seach opeatons to the othe opeatons that eque sgnatue mantenance (.e., pee jon, pee leave and pee update). Table 2. ymbols used n the analyss. ystem paametes N: numbe of nodes n the netwok B: numbe of neghbos pe node d: numbe of data tems pe node α : eplcaton ato β : ato of edundant edges ϕ : ato of seach to pee jon/leave/update top condtons T: maxmum seach depth R: mnmum numbe of esults : neghbohood adus : sze of a neghbohood wth adus Fd : false postve pobablty h : sze of message heade l : sze of leave message : sze of seach message s s: sze of esponse ecod Index/sgnatue paametes gnatue paametes essage paametes Accountng paametes P : numbe of nodes at hop dstance µ: sgnatue match ato j : sze of jon message u : sze of update message : sze of esponse message heade V seach : message volume ncued by seach fowadng V esponse : message volume ncued by seach esponse V jon : message volume ncued by pee jon V leave : message volume ncued by pee leave V update : message volume ncued by pee update V total : total message volume Q : numbe of seach messages fowaded to nodes hops away We pesent the fomulae fo message volume ncued by seach, pee jon, pee leave and content update, espectvely. The total message volume s smply a weghted summaton of the message volume ncued by vaous opeatons. V jon + Vleave + Vupdate V total = + Vseach + V ϕ esponse whee the notatons of message volumes coespondng to vaous opeatons ae self-explaned (also see Table 2). Befoe we poceed to deve fomulae fo those message volumes, we fst obtan the numbe of nodes at hop dstance (denoted as P ), the sze of a neghbohood wth adus j (denoted as j ), and sgnatue match ato (denoted as µ ), snce these vaables wll be used extensvely late on. 20

11 L et al: Pefomance Evaluaton of Neghbohood gnatue Technques fo Pee-to-Pee each Let the numbe of neghbong pees of a pee node at one hop dstance be b. Each of these neghbong pees has 1 connectons wth 2-hop-away pees. Assumng β poton of the connectons s edundant, the numbe b of nodes at 2-hop dstance s b ( b 1)( 1 β). Thus, the numbe of nodes at hop dstance s deved as follows: ( ) 1 b 1 ( 1 ) 1 P = b β. The sze of a neghbohood wth adus j can be deved fom j = P j = 1 P as follows: atched sgnatues nclude tue matches as well as false postves, thus, µ can be expessed as tue _ match+ false _ postve = t ag et _ sze. µ (1) whee taget_sze, tue_match and false_postve ae the numbe of sgnatues to be examned, the numbe of tue matches and the numbe of false postves, espectvely. Accodng to [18], the mathematcal defnton of false postve pobablty, Fd, s Fd false _ postve t aget _ sze tue _ match =. (2) The sgnatue match ato, µ, can thus be expessed as Fd ( Fd) + 1 tue_match/taget_sze based on Equatons (1) and (2). In complete neghbohood (CN) sgnatue scheme, the value of tue_match can be appoxmated as the poduct of the numbe of esults n the seach neghbohood and, whee epesents the sze of a neghbohood wth neghbohood adus. Assumng the sze of the seach neghbohood s A, the value of tue match appoxmately equals to α. nce each pee has one CN neghbohood sgnatue, the value of taget sze n CN s the same A as the sze of the seach neghbohood A. Theefoe, tue_match/taget_sze appoxmately equals to the sgnatue match ato fo CN s µ Fd α Fd. CN = + 1 ( ) α. Thus, Fo patal neghbohood supemposed (PN-) sgnatue scheme, each pee has b neghbohood sgnatues. Theefoe, the value of taget sze n PN- s b tmes of the sze of the seach neghbohood. Thus, sgnatue match ato fo PN- s α = Fd + ( 1 Fd) µ PN. In patal neghbohood appended (PN-A) sgnatue scheme, the seach sgnatue s compaed wth each subsgnatue n a neghbohood sgnatue. Theefoe, the value of taget sze n PN-A s tmes of the sze of the seach neghbohood. The sgnatue match ato fo PN-A s Based on [18], Fd can be obtaned as PN A = Fd + α 1 b ( Fd) µ. Fd 1 e ωs = L whee w epesents the numbe of 1 s set n a bt stng, s epesents the numbe of bt stngs supemposed n a neghbohood sgnatue, and L epesents the length of a neghbohood sgnatue. Accodng to [19], the optmal false dop pobablty s acheved when The optmal false dop pobablty s appoxmately L = opt= ln2 s ω..5 ω opt 0 21

12 電腦學刊第十七卷第四期 (Jounal of Computes, Vol.17, No.4, Januay 2007) 4.1 each Next we deve the fomulae fo seach message volume n both floodng and sngle-path seach. The fomulae fo the thee sgnatue methods ae deved, espectvely. The dffeences and smlates among them ae ponted out along the way Floodng each We fst deve the numbe of seach messages fowaded to nodes that ae hops away (denoted as Q ), fo each of the thee sgnatue methods. The seach message s ethe extended wthn a neghbohood of a matched neghbohood sgnatue o fowaded to the ( + 1)-hop-away pee nodes located ght outsde an unmatched neghbohood. In the followng, we deve the numbe of seach messages fowaded due to matched sgnatues fst, then the ones due to unmatched sgnatues. Calculatng Q fo CN The numbe of seach messages fowaded to nodes one hop away due to matched sgnatues s bµ CN. The devaton fo the numbe of seach messages fowaded to nodes that ae moe than 1 hop away s moe complcated. The numbe of matched neghbohood sgnatues at hop dstance 1 s Q ( 1 β 1 ) µ CN, whee Q ( 1 β 1 ) s the numbe of vsted nodes at hop dstance 1. Fo each matched neghbohood sgnatue, the seach message s fowaded to b 1 nodes (excludng the sende) at next hop dstance to detemne whethe the match s a tue match o not. The numbe of unmatched neghbohood sgnatues at hop dstance 1 Q 1 β µ Q β s s 1 ( )( 1 CN), whee 1( 1 ) the numbe of vsted nodes at hop dstance 1. Fo each unmatched neghbohood sgnatue, + 1 seach messages ae extended to nodes + 1 hops away. Theefoe, the complete fomula fo Q s Q = { bµ Q Calculatng Q fo PN- = 1 β CN 1 CN P > 1. (3) CN 1( 1 ) µ ( b 1) + Q ( 1 β )( 1 µ ) + 1 The numbe of matched neghbohood sgnatues at hop dstance (wth > 1) s Q 1 ( 1 β)( b 1) µ PN, whee Q ( 1 β 1 ) s the numbe of vsted nodes at hop dstance 1 and b 1 s the numbe of neghbo- hood sgnatues to be compaed pe node (excludng the one assocated wth the neghbo fom whch ths pee got the seach message). Fo each matched neghbohood sgnatue, one seach message s fowaded to the assocated neghbo at next hop dstance. Theefoe the total numbe of seach messages fowaded due to matched sgnatues s the same as the numbe of matched neghbohood sgnatues. The numbe of unmatched neghbohood sgnatue at hop dstance 1 s Q 1 ( 1 β) b( 1 µ PN ). nce a seach message only needs to be fowaded to ( +1) P -hop-away pees (.e., those located ght outsde of the patal neghbohood coespondng to the unmatched neghbohood sgnatue), the numbe of seach messages fowaded to nodes + 1 hops away fo each unmatched neghbohood sgnatue s P + 1. Theefoe, Q fo PN- s Q = { b = 1 µ PN Q 1( 1 β )( b 1) µ PN + Q 1( 1 β )( 1 µ PN ) P + 1 > 1 (4) Calculatng Q fo PN-A The numbe of matched sub-sgnatues at hop dstance s P µ and fo each matched sub-sgnatue, PN A a seach message s fowaded to the node assocated to t. The numbe of unmatched sgnatues at hop dstance 1 Q 1 Q s the numbe of vsted node s 1 ( β) ( 1 µ PN A) whee 1( 1 β) at hop dstance 1 and s the numbe of sgnatues to be examned pe node. Theefoe, fo PN-A s Q 22

13 L et al: Pefomance Evaluaton of Neghbohood gnatue Technques fo Pee-to-Pee each Q = b P µ PN A 1 β Q + ( 1 β ) ( 1 ) µ PN A 1 µ PN A b P + 1 = 1 > 1 (5) Gven Q fo all thee sgnatue schemes, the seach message volume can be expessed as V seach The message volume ncued fo the esponse messages s: V esponse = T = T = 1 s Q = 1 j=. T Q ( 1 β ) + sαpj. The fst tem sums up the message volume ncued by the esponse message heade and the second tem sums up the message volume ncued by the esult ecods. nce the esponse messages fom the downsteam neghbos ae aggegated nto one esponse message dung the tavesal back to the equeste, the numbe of esults aved at one node s the total numbe of esults etuned fom ts downsteam neghbos plus ts own esults, whch denotes the meanng of = α. j ngle-path each T Pj Wthout sgnatue fles, the numbe of nodes that should pocess a seach message n sngle-path seach s R mn, N (mn denotes mnmum). Usng sgnatue fles, the numbe of nodes that should be vsted dung the α seach pocess s R mn, N R, N mn α. Takng nto consdeaton of the edundant edges, the numbe of seach messages s α. In addton, n ode to detemne whethe a sgnatue match s a tue match o not, the pee nodes ( 1 β ) wthn the neghbohood need to futhe pocess the seach message (.e., the neghbohood checkng pocess as descbed n ecton 2.3.2). Fo each matched sgnatues, the neghbohood checkng pocess ncus = 1 sq message volume whee Q s calculated accodng to the espectve fomula (.e., the fomulae (3)-(5)) of the thee sgnatue schemes fo Q n floodng seach. Thee ae total sgnatues. Theefoe, the fomula fo seach message volume s V seach = s mn mlaly, the esponse message volume s appoxmately V esponse = R mn, N α + + ( ) 1 β j= R µ mn, N α R R, N µ mn, N α α Q. R mn, N α = 1 sα R µ mn, N α + Q s ( 1 β) + = 1 j= sαpj matched The fst tem and second tem denote the message volume ncued by esponse message heade and the esult ecods n the ntal seach pocess, espectvely. The last tem s the message volume ncued by esponse messages geneated dung neghbohood checkng pocess.. 23

14 電腦學刊第十七卷第四期 (Jounal of Computes, Vol.17, No.4, Januay 2007) 4.2 Pee Jon The jon pocess fo all thee appoaches s the same. When a node jons the netwoks, t fst sends jon messages to nodes n ts neghbohood wth adus, ncung messages. Upon ecevng jon messages, the 1 β pee nodes n the neghbohood send the own local sgnatues to the newly joned node, ncung addtonal messages. As explaned n ecton 2, when s geate than 1 and the new pee jons the netwok though multple connectons, some pee nodes (wthn 1hops) that wee fa away fom each othe befoe the jon ae bought nto the same neghbohood va the newly joned node. In ths case, addtonal taffc s equed to update the neghbohood sgnatues of othe pee nodes wthn 1 hops. Thus, the jon message volume can be appoxmated as follow: V jon = j j β β j β The fomulae fo jon message volume of the thee sgnatue methods ae the same as above. Howeve, the szes of jon messages fo CN, PN- and PN-A ae dffeent. As can be obseved fom Fgue3, n ode fo CN, PN- and PN-A to have the same szed neghbohood sgnatues, the sze of the sub-sgnatues that fom PN-A neghbohood sgnatues s smalle than the sze of sub-sgnatues fo CN and PN-, whle the sze of subsgnatues fo PN- s smalle than the sze of sub-sgnatues fo CN. Theefoe, gven the same stoage sze fo all thee sgnatue schemes, the sze of jon messages fo PN-A s smalle than the sze fo PN-, whch s smalle than the sze fo CN. = 1 o only one new connecton > 1 and multple new connecton 4.3 Pee Leave When a node leaves the netwok, t fst sends a leave message to nodes n ts neghbohood wth adus, ncung 1 β leave messages. Fo CN, a node ecevng the leave message sends a pseudo jon messages to ts neghbohood, whch ncus send back the local sgnatue, ncung messages wth sze as 1 β messages wth sze as j. Theefoe, the message volume ncued by each node to constuct a new neghbohood sgnatue n CN s fo pee leave n CN s: V CN leave l 2 h β 1 β = j h. On ecevng pseudo-jon messages, pee nodes h + 1 β j the message volume. (6) Dffeent fom CN, when a pee leaves the netwok, only the pees on the affected banch need to constuct a new neghbohood sgnatue. Theefoe, the message volume fo pee leave n PN- s: V PN leave 2 l h = β b 1 β j. (7) In PN-A, when a node leaves, the affected nodes only need to delete the sgnatue of the leavng node fom ts neghbohood sgnatues. Theefoe, the message volume fo pee leave n PN-A s PN A l V leave =. (8) 1 β 24

15 L et al: Pefomance Evaluaton of Neghbohood gnatue Technques fo Pee-to-Pee each 4.4 Pee Update The fomulae fo the update message volume of the thee sgnatue schemes ae smla to the fomulae (6)-(8) fo the leave message volume except that the s eplaced by. l u 5 Pefomance Evaluaton In ths secton, we pesent the pefomance evaluaton conducted to compae ou poposal wth some epesentatve appoaches fo seachng unstuctued P2P netwoks. Total message volume s used as the pmay pefomance metc n ou smulaton. We fst evaluate the pefomance of the poposed sgnatue technques analytcally. In addton to analytcal esults, we also pefom smulaton based expements. Whle the analytc esults ae obtaned based on unfom netwok topology and unfom data dstbuton, the smulaton expements ae conducted unde both of unfom and powe-law netwok topologes wth both of unfom and non-unfom data dstbutons. Though these expements, we examne the pefomance of neghbohood sgnatue schemes, Gnutella, andom walk, and local ndex 7 based on both of floodng and sngle-path seachng stateges. The stop condtons fo the floodng and sngle-path seach ae maxmum seach depth and mnmum numbe of esults, espectvely. In the floodng expements, we compae ou sgnatue mechansms wth Gnutella and local ndex, whle n the sngle-path seach we compae wth andom walk and local ndex. In addton, though these expements we tested the senstvty of the evaluated P2P seachng appoaches to vaous factos ncludng neghbohood adus, stoage constants, sze of key attbute, numbe of data tems at a node, seach/update ato, eplcaton ato, numbe of neghbos pe pee fo unfom netwok topology, and powe-law netwok coeffcent fo powe-law netwok topology. In the followng, we fst descbe the paamete settng fo analytc expements and smulaton expements. We then pesent the detaled expement esults. 5.1 Expement etup As mentoned above, the analytc expements ae based on unfom netwok topology and unfom data dstbuton, n the smulaton, we consde powe-law netwok topology and nonunfom data dstbuton n addton to unfom netwok topology and unfom data dstbuton. nce the setups fo analytc expements and smulaton expements wth unfom netwok topology and unfom data dstbuton ae the same, we pesent them togethe and pont out the settngs that ae unque to the smulatons wth powe-law netwok topology and nonunfom data dstbuton when necessay n the followng. The smulatons ae ntalzed by geneatng sgnatues fo pe-exstng pees n the tested netwoks. A lage numbe of opeatons consst of a andomzed mx of seach, pee jon, pee leave, and pee update ae njected nto the P2P netwok n each expement. The smulaton expements ae un unde both unfom and powe-law netwok topologes. Fo the unfom netwok topology, the default aveage numbe of neghbos s set to 4, whch s consstent wth the aveage node degee n Gnutella [20]. We conduct expements wth aveage numbe of neghbos set to 8 as well. Fo the powe-law netwok topology, based on measuement of Gnutella netwok [20], we set the powe-law topology usng a default coeffcent of 1.4 f not specfed othewse. In one set of expements, we also vay the powe-law netwok coeffcent to study the effect on the pefomance of vaous schemes. Fo both netwok topologes, we consde two dffeent data dstbutons: unfom and nonunfom. Unde the unfom data dstbuton, each node holds the same numbe of data tems. We use the ule to compose a nonunfom data dstbuton. That s, 80% of data tems ae dstbuted among 20% of the nodes, called popula pees, and the emanng 20% of data tems ae dstbuted among the emanng 80% nodes, called unpopula pees. Unfom data dstbuton s the default settng f not specfed othewse. Table 3 lsts the paametes and the default values used n the analytc expements as well as smulaton expements. The justfcaton fo these choces s as follows: ystem paamete settngs: The aveage numbe of shaed fles pe pee has been obseved to be aound 340 n [14]. Theefoe we set the default numbe of data tems pe pee to 400. Key attbutes, whch contan the key value(s) of data tems n vaous foms, e.g., bnay musc clp, keywods, nteges, etc, ae used fo evaluaton of seach ctea. nce the sze of data tems tself s not a sgnfcant facto n dffe- 7 The mplementaton of local ndex follows the descpton n [19]. 25

16 電腦學刊第十七卷第四期 (Jounal of Computes, Vol.17, No.4, Januay 2007) entatng the schemes unde nvestgaton, we use sze of key attbute as an mpotant paamete to chaacteze data tems. In most of ou expements, we use 4 bytes as a default fo the sze of key attbute (.e., we assume a sngle value attbute unless specfed). We also an expements by vayng the numbe of data tems pe pee and nceasng the sze of key attbute (.e., to epesent a mult-key composte attbute o a complex attbute wth bnay data such as musc clp) n ode to obseve the mpacts on dffeent seach appoaches. To smulate a genec data set n P2P systems, we use syntheszed key attbutes whch ae andom nteges (o composton of seveal andom nteges fo the stuatons when the sze of key attbutes s lage than 4). The ato of edundant edges s set to 30% accodng to [21] n the analytc expements 8. The default eplcaton ato and default seach/update ato ae set at 0.5% and 10, espectvely, whle we also vay these two paametes n the expements n ode to study the effect on the pefomance of vaous schemes. Table 3. Default paamete settngs fo the expements ystem paametes N = b = 4 d = 400 k = 4 bytes α = 0.5% β = 30% φ = 10 top condtons T = 7 (unfom), 5 (powe-law) R = 1 h = 80 = 80 + length of seach pedcate = 84 (ndex/pn-a), 80 (CN/PN-) l essage paametes (bytes) = 80 + ndex/sgnatue sze j = 88 + s numbe of esults u = 92 (ndex), 80 (CN/PN-) 84 + sze of change ecod(pn-a) top condton settngs: The maxmum seach depth s set to 7 fo unfom netwok topology. We an some pelmnay expements and found out that n ode to acheve the same seach coveage n both unfom netwok topology and powe-law netwok topology, the maxmum seach depth should be set to 5 n powe law netwok. Whle we vay the eplcaton ato n one of the expements to obseve ts mpact on the sngle-path seach, the mnmum numbe of esults s set to 1. essage paametes settngs: The message heade ncludes both the Gnutella message heade and the TCP/IP heade, whch s 80 bytes [2]. The sze of a seach message s the sze of message heade plus the sze of the seach pedcate (n a netwok envonment wth system settngs as above, we can smply assume that a seach pedcate only nvolves the key attbute, whch has a sze of 4 bytes by default). The seach esponse message conssts of the message heade, the node dentfe of the equestng pee, a counte ndcatng the total numbe of etuned esult pontes (a 4-byte ntege) and a lst of the esult pontes. In addton to seach messages and esponse messages, some othe messages ae equed fo mantanng ndces and sgnatues. The sze of jon messages s the sze of message heade (80 bytes) plus the sze of local ndex/sgnatues. Fo local ndex and PN-A, the sze of leave messages s 84 bytes wth 4 bytes of pee dentfe and 80 bytes of message heade; fo CN and PN-, the sze of leave messages s 80 bytes snce t s an empty message as explaned n ecton 2.4. mlaly, the sze of update messages fo CN and PN- s also 80 bytes. Fo PN-A, the sze of update message s the sze of the message heade plus the sze of change ecod (also mentoned n ecton 2.4). To estmate the sze of change ecod n analytc expements, we make a consevatve assumpton that all the postons (epesented by 4-byte nteges) of the bts set n both old and new sgnatues ae ecoded n the change ecod. Thus, the sze of the change ecod s estmated as 8W opt, whee W opt epesents the optmal numbe of bts set n a sgnatue fle as explaned n ecton 4. Fo local ndex, the sze of update messages s 92 bytes wth 80 bytes of message heade, 4 bytes fo node dentfe of the pee pefomng update, 2 bytes fo the dentfe of the data tem to be updated, 2 bytes to ndcate the poston of the updated data attbute n the data tem, and 4 bytes fo the new key attbute value. 8 Ths paamete s dependent on the specfc netwok topology,.e., the netwok sze and numbe of neghbos pe node, n the smulaton. Thus, t s not peset sepaately. 26

17 L et al: Pefomance Evaluaton of Neghbohood gnatue Technques fo Pee-to-Pee each 5.2 Result We conduct both analytc expements and smulaton expements to examne the pefomance of poposed sgnatue schemes. We found that the smulaton esults ae consstent wth the analytc esults. In the followng, we fst befly explan the analytc esults and pesent one set of analytc esults and smulaton esults sde by sde to demonstate the consstency between them. Then fo pesentaton claty, we pesent detaled smulaton esults only Compason Between Analytc Results and mulaton Results We have the followng obsevatons based on the analytc model deved n pevous secton: Wth neghbohood adus nceasng, the mantenance ovehead ncued by neghbohood sgnatues nceases whle the seach message volume ethe deceases o nceases dependng on the stoage sze. Wth stoage sze nceasng, the seach message volume ncued by neghbohood sgnatues mpoves whle the sgnatue mantenance ovehead nceases. The mantenance ovehead ncued by PN-A s much smalle compaed to the oveheads ncued by PN- and CN, whch makes PN-A the best among the thee poposed neghbohood sgnatues. All of these obsevatons ae vefed by smulaton expements as we wll pesent late. We fnd that ou smulaton esults ae consstent wth the analytc esults, whch vefes the coectness of ou smulaton. In the followng, we pesent one set of the analytc esults and smulaton esults unde both unfom and powe-law netwok topologes when the stoage sze s set to 6.4KB and the neghbohood adus s vaed fom 1 to 5 n Fg. 4. We focus on the smlaty between these esults hee whle leavng the ntepetaton of these fgues to next secton. Fom ths fgue, we can see that the smulaton esults ae vey close to the analytc esults. In addton, the smulaton esults unde unfom netwok topology and powe-law netwok topology ae smla to each othe. Fg. 4. Compason of analytc esults and smulaton esults unde unfom and powe law Netwok topologes. The y axs s on logathmc scale fo eadablty In the followng, the smulaton esults fo floodng and sngle-path seach ae pesented, espectvely. Fo each of these two seach stateges, we have conducted vaous smulaton expements unde unfom and powe law netwok topologes n combnaton of both unfom data dstbuton and nonunfom data dstbuton. The geneal tend obseved fom the esults obtaned unde unfom topology s vey smla to the one obseved unde powe-law topology. Thus, we only pesent the esults unde powe-law topology fo pesentaton claty Floodng each In the followng, we fst vay the neghbohood adus and stoage sze to compae the pefomance of the poposed sgnatue schemes (Gnutella as a baselne) and to detemne the best settngs of those two paametes fo those schemes. Then, we show the mpacts of othe paametes on the pefomance of Gnutella, local ndex, and ou sgnatue schemes. In the expements, unless explctly specfed, the total message volume ncludes all message volume ncued by pee jon, pee leave, pee update and seach. We fst pesent the esults unde unfom data dstbuton and then compae wth the esults unde nonunfom data dstbuton. 27

18 電腦學刊第十七卷第四期 (Jounal of Computes, Vol.17, No.4, Januay 2007) Neghbohood Radus: In ode to detemne the best neghbohood adus fo sgnatue schemes unde ou expement settngs, we vay neghbohood adus fom 1 to 5 and show the total message volume of CN, PN- and PN-A wth stoage sze 6.4KB n Fg. 5. We dsplay the message volume fo pee jon, pee leave, pee update and seach opeatons ndvdually n Fg. 5 so that we can obseve the effects of neghbohood adus on the seach cost and sgnatue mantenance cost. The y-axs s on a logathmc scale fo eadablty. The seach message volumes ncued wth neghbohood adus as 1 n sgnatue schemes CN, PN-, PN-A ae 93%, 37%and 37% of the Gnutella taffc. When the neghbohood adus nceases to 2, the seach message volumes ncued by PN- and PN-A decease to 18% and 14%. Ths s due to the desable (ntended) flteng effect acheved by neghbohood sgnatues. When the neghbohood adus s nceased futhe, moe neghbohood nfomaton s foced to be compessed wthn the same stoage space (ethe by supemposng moe sgnatues n CN and PN-, o appendng moe sgnatues wth smalle sze n PN-A), whch nceases the false postve pobablty. The end esults s that the seach message volume nceases, though we stll fnd that the seach messages volume s not hghe than Gnutella even at adus of 5. Of the thee sgnatue schemes, the patal sgnatues ae povdng bette focused seaches at smalle neghbohood adus values. Fg. 5. Floodng: effect of neghbohood adus on sgnatue schemes. The y axs s on logathmc scale fo eadablty At the same tme, when the adus s nceased, the oveheads of pee leave and pee update become much moe sgnfcant, and even ovewhelm the seach messages fo the supemposng stateges (CN and PN-). As was mentoned eale, these schemes eque sgnatues to be geneated fom scatch dung pee leave/update. Between these two appoaches, the message volume fo CN s lage than fo PN-, because only pees along one banch n PN- ae nvolved fo geneatng new sgnatues whle all neghbos ae nvolved fo CN. In contast to CN and PN-, the affected sgnatues can be updated easly n PN-A. Theefoe, ts leave and update message volume s substantally lowe compaed to CN and PN-. toage ze: Fg. 6 shows the total message volume as we allow vaous stoage capabltes at each pee fo the sgnatues. Fom ths fgue, we can see that when stoage sze nceases, the total message volume deceases fst, then nceases agan. The ntal decease s due to the bette flteng effect of sgnatues wth lage sze. Howeve, when the stoage sze keeps nceasng, the mantenance ovehead ncued by pee jon/leave/update s ovewhelmng, esultng n nceased total message volume. The mnmum total message volume ncued by CN, PN- and PN-A s 94%, 20% and 6% of Gnutella taffc when stoage sze s 1.6KB, 6.4KB, and 25.6KB, espectvely. The values shown n Fg. 6 use a neghbohood adus that gves the lowest message volume fo the gven stoage sze (and these adus values, efeed to as optmal adus, fo each stoage sze ae gven n Table 4). Fo CN, the optmal adus s 1 fo all consdeed stoage szes as shown n Table 4. The eason s that when the sgnatue sze s small, jon/leave/update cost s small and quey cost domnates the total message volume as shown n Fg. 6(a). A small neghbohood adus foces less nfomaton supemposed togethe and esults n low false postve pobablty, theeby ncung lowe total message volume. When the stoage sze nceases, the cost of jon/leave/update domnates the total cost and a smalle neghbohood adus esults n lowe jon/leave/update message volume, povdng the best esults agan. The latte effect (ovehead of jon/leave/update) s less sgnfcant fo PN- and PN-A, makng a lage neghbohood adus moe pefeable n these two schemes when stoage sze s lage, as shown n Table 4. 28

19 L et al: Pefomance Evaluaton of Neghbohood gnatue Technques fo Pee-to-Pee each Fg. 6. Floodng: effect of stoage sze on sgnatue schemes Table 4. Floodng: optmal neghbohood adus fo dffeent stoage szes toage sze(kb) CN PN PN-A essage Volume and toage Tadeoff: Fg. 7 compaes the pefomance of the thee sgnatue schemes wth the local ndex, along wth the Gnutella shown as a sold hozontal lne, by nceasng stoage sze. Fom ths fgue, we can obseve that wth stoage sze as small as 400 bytes, the patal neghbohood sgnatue schemes (PN- and PN-A) educe message taffc by ove 35% compaed to the Gnutella floodng appoach. Wth a hghe stoage capablty, PN- and PN-A poduce even futhe savngs. On the othe hand, the local ndex appoach stats outpefomng Gnutella only wth stoage not less than 6.4KB. Wth a stoage sze of 6.4KB, the message volume of PN-A s only 40% of local ndex s taffc. As the stoage space gets lage, ndex/sgnatue constucton and updates become moe expensve (due to jon/leave/update opeatons), causng the message volume to ncease agan. Even when the stoage sze keeps nceasng, the pefomance of PN-A s smla to local ndex. These esults demonstate that the sgnatue appoaches (patculaly PN-A) can have bette pefomance than the local ndex wth a much smalle stoage space equement. Fg. 7. Floodng: total message volume compason among Gnutella floodng, local ndex, CN, PN and PNA ze of Key Attbute: Fg. 8 shows the total message volume wth dffeent szes of key attbute. The y-axs s on a logathmc scale fo eadablty. In ths smulaton, we use nceased attbute szes to epesent the stuatons whee the (logcal) key attbute conssts of multple keys o contans bnay data (e.g., musc clp). The values shown hee uses a gven stoage sze (.e., 6.4KB) and a fxed numbe of data tems pe node (.e., 400). Thus, by nceasng the sze of key attbute at a data tem fom 4 bytes to 1.6KB, the stoage/total-attbute-sze 29

20 電腦學刊第十七卷第四期 (Jounal of Computes, Vol.17, No.4, Januay 2007) atos at a pee fo the chosen ponts n the fgue ae deceased fom 400%, 100%, 50%, 10%, 5%, down to 1% 9. It can be obseved fom the fgue that the sgnatue appoaches outpefom Gnutella and local ndex sgnfcantly as the attbute sze becomes lage (.e., the stoage/total-attbute-sze ato becomes small). Fo nstance, when the attbute sze fo each data tem s 1.6KB (.e., stoage/total-attbute-sze ato s 1%), the total message volume fo PN-A s meely 18% compaed to Gnutella and local ndex. The total message volume fo Gnutella nceases as the sze of key attbute nceases, because the seach message contans the key attbute value(s). Local ndex pefoms well when the stoage/total-attbute-sze ato s lage. Howeve, as the attbute sze nceases, the gven stoage sze s not suffcent to ndex all data tems 10. Theefoe, local ndex s pefomance s the same as Gnutella appoach fo lage attbute sze. Fg. 8. Floodng: effect of key attbute sze on Gnutella floodng, local ndex and sgnatue appoaches. The y axs s on logathmc scale fo eadablty Numbe of Data Items: Fg. 9 shows the total message volume as we allow the numbe of data tems pe pee to ncease fom 100 to Wth a fxed stoage of 6.4KB at each pee, the stoage/total-attbute-sze atos fo the chosen data ponts n Fg. 9 ae 1600%, 400%, 100%, 50%, 10%, 5%, 1%, espectvely. As shown n the fgue, local ndex outpefoms PN-A only when each pee has meely 100 data tems (.e., the stoage/total attbute-sze ato s 1600%). On the othe hand, the patal neghbohood sgnatues pefom extemely well as the numbe of data tems pe pee nceases apdly. Howeve, when the numbe of data tems s ovewhelmed, (e.g., 16000), exta stoage sze should be allocated fo sgnatues to educe the false postve pobablty and the total message volume. Dffeent fom the pevous fgue, the total message volume fo Gnutella emans as a constant snce the attbute sze fo each data tem s fxed. Fg. 9. Floodng: effect of numbe of data tems pe pee on Gnutella floodng, local ndex and sgnatue appoaches 9 The stoage/total-attbute-sze ato can be ntepeted as the stoage ovehead nomalzed accodng to the total sze of the key attbutes of data tems stoed pe pee. 10 The mnmum stoage ovehead fo local ndex s 6.4KB, 25.6KB, 51.2KB, 256KB, 512KB and 2560KB, espectvely, fo each of the ponts n Fg

21 L et al: Pefomance Evaluaton of Neghbohood gnatue Technques fo Pee-to-Pee each Obseved fom the above two fgues, t s obvous that the patal neghbohood sgnatues ae much moe stoage effcent and flexble than local ndex. Wth vey lttle stoage ovehead, the patal neghbohood sgnatues can facltate focused seach effectvely whle local ndex has some mnmal stoage equement. each/update Rato: Fg. 10 shows the optmal total message volume of CN, PN- and PN-A unde dffeent seach/update atos usng two dffeent update stateges (.e., eage update and lazy update) as dscussed n ecton 2.4. The y axs s on logathmc scale fo eadablty. We can see fom Fg. 10 (a) that when the eage update stategy s adopted, the total message volume deceases wth nceasng seach/update ato. Ths s due to the educed sgnatue mantenance ovehead ncued by deceasng numbe of pee jon/leave/update opeatons. The smla tend s obseved when lazy update stategy s adopted as shown n Fg. 10(b). Howeve, when the seach/update ato s smalle than 1 (.e., thee ae moe pee jon/leave/update opeatons than seach opeatons), the total message volume usng lazy update stategy s much smalle than the one usng eage update stategy, whch demonstates the benefts of lazy update n educng the sgnatue mantenance oveheads when the pee jon/leave/update opeatons ae ovewhelmng. Fg. 10. Floodng: effect of seach/update ato on sgnatue schemes. The y axs s on logathmc scale fo eadablty Netwok Topology: Fg. 11(a) and Fg. 11(b) show the total message volumes of dffeent appoaches wth stoage sze 6.4KB when the numbe of neghbos pe pee s 4 and 8, espectvely. Fom these two fgues, we can see that the total message volume nceases when the numbe of neghbos pe pee nceases fom 4 to 8. In addton, wth the numbe of neghbos pe pee as 4, the optmal values fo neghbohood adus n CN, PN- and PN-A ae 1, 2, and 2, whle the optmal neghbohood adus fo all neghbohood sgnatues becomes 1 wth the numbe of neghbos pe pee as 8. Ths s because wth lage numbe of neghbos pe pee, moe nfomaton s compessed nto the sgnatues wth the same stoage space, esultng n hghe false postve pobablty, thus wose flteng effect. Fg. 11. Floodng: effect of numbe of neghbos pe pee unde unfom netwok topology on Gnutella floodng, local ndex and sgnatue appoaches 31

22 電腦學刊第十七卷第四期 (Jounal of Computes, Vol.17, No.4, Januay 2007) Fg. 12. Floodng: effect of powe law netwok coeffcent unde powe law netwok topology on Gnutella floodng, local ndex and sgnatue appoaches Fg. 12 shows the effect of powe-law netwok coeffcent on the total message volume. Fom ths fgue, we can see that the total message volume deceases wth the powe-law netwok coeffcent. The eason s that as powelaw netwok coeffcent nceases, a few nodes have lage numbe of neghbos, whle majoty of the nodes have a vey small numbe of neghbos. Theefoe, false postve pobablty of neghbohood sgnatues fo majoty of the nodes deceases, ncung educed total message volume. Data Dstbuton: Fg. 13 compaes the pefomance of Gnutella floodng, local ndex and thee sgnatue schemes unde unfom and nonunfom data dstbutons (as specfed n ecton 5.1). In ths compason, stoage sze fo local ndex and sgnatues ae set to be 6.4KB. Fo both Gnutella floodng and local ndex appoach, thee s no pefomance dffeence unde these two dffeent data dstbutons. Fo the sgnatue schemas, the total message volume unde nonunfom data dstbuton nceases a lttle bt. Ths can be explaned by the nceased false postve pobablty of the neghbohood sgnatues whch ae contbuted by popula pees. One mpotant obsevaton fom Fg. 13 s that the pefomance of PN-A s bette than local ndex unde both unfom and nonunfom data dstbutons. Fg. 13. Floodng: effect of data dstbutons on Gnutella floodng, local ndex and sgnatue appoaches ngle-path each In addton to the seven paametes (neghbohood adus, stoage sze, key attbute sze, numbe of data tems, seach/update ato, numbe of neghbos pe pee, and powe-law netwok coeffcent) nvestgated n floodng seach, we nclude one moe paamete, eplcaton ato, n sngle-path seach snce the pefomance of seach wth mnmum numbe of esults as seach stop condton can ely heavly on the numbe of eplcas n the system. We compae the pefomance of the poposed sgnatue schemes wth andom walk and local ndex. The geneal tend obseved fom the esults s smla to that obseved fo floodng. Fo pesentaton claty, we only pesent the compason among andom walk, local ndex and sgnatue schemas when stoage sze and eplcaton ato ncease, espectvely. 32

23 L et al: Pefomance Evaluaton of Neghbohood gnatue Technques fo Pee-to-Pee each essage Volume and toage Tadeoff: Fg. 14 shows the total message volume compason among andom walk, local ndex, CN, PN- and PN-A. Once agan, we fnd that the sgnatue schemes (PN-A n patcula) ae able to ncu lowe message taffc n etevng the equed numbe of data tems at a much lowe stoage cost than local ndex. Fg. 14. ngle path: total message volume compason among andom walk, local ndex, CN, PN and PNA. The y axs s on logathmc scale fo eadablty Replcaton Rato: Fg. 15 compaes andom walk, local ndex and PN-A fo dffeent degees of eplcaton of data tems n the netwok. The y-axs s on a logathmc scale fo eadablty. In these expements, both local ndex and PN-A ae un wth a stoage sze of 6.4KB (local ndex only stats to povde easonable pefomance wth stoage sze 6.4KB). At hgh degees of eplcaton, as expected, andom walk can pefom athe well, snce thee s a hghe lkelhood of fndng the equested data tems even when andomly tavesng the netwok (wthout ncung any jon/leave/update oveheads). Howeve, at lowe degees of eplcaton t does much wose than the sgnatue o local ndex appoaches whch can dect seaches n a moe poductve manne. Of these two appoaches, we fnd that PN-A s moe effectve at educng taffc even at vey small degees of eplcaton. PN- A ncus an ode of magntude lowe message taffc wth espect to andom walk unde a eplcaton ato of 0.1% and only 17% of andom walk taffc unde a eplcaton ato of 0.5%. Compaed to local ndex, PN-A ncus 29% of local ndex taffc unde a eplcaton ato 0.1% and 43% of local ndex taffc unde a eplcaton ato 0.5%. Fg. 15. ngle path: effect of eplcaton ato on andom walk, local ndex and sgnatue appoaches. The y axs s on logathmc scale fo eadablty 6 Concludng Remaks and Futue Wok Pee-to-Pee (P2P) applcatons such as Napste and Gnutella have made the Intenet a popula medum fo esouce and nfomaton exchange between thousands of patcpatng uses. A pmay consdeaton n the desgn of such applcatons s the hgh netwok taffc that they geneate when seachng fo esouces/nfomaton. One can ague that wth nfnte stoage capacty t s possble to mantan complete auxlay nfomaton fo all the 33