Resource Discovery in P2P Networks Using Evolutionary Neural Networks

Transcription

1 > PAPER IDENTIFICATION NUMBER: < Resource Dscovery n P2P Networks Usng Evolutonary Neural Networks Mkko A. VAPA, Nko P. KOTILAINEN, Annemar K. AUVINEN, Hekk M. KAINULAINEN, and Jarkko T. VUORI Abstract-- Resource dscovery s an essental problem n peerto-peer networks snce there s no centralzed ndex n whch to look for nformaton about resources. One soluton for the problem s to use a search algorthm that locates resources based on the local knowledge about the network. Tradtonally, the search algorthms have been based on few smple rules, whch often reduces the performance from optmal. In ths paper, we descrbe the results of a process where evolutonary neural networks are used for fndng an effcent search algorthm from a class of local search algorthms. The ntal test results ndcate that an evolutonary optmzaton process can produce search algorthm canddates that are competent compared to the breadth-frst search algorthm (BFS) used n Gnutella peer-topeer network. Index Terms-- resource dscovery, peer-to-peer networks, mult-layer perceptrons, genetc algorthms. I I. INTRODUCTION N the resource dscovery problem, any node can possess resources and query these resources from other nodes n the network. The problem conssts of graph wth nodes, lnks and resources. Resources are dentfed by unque IDs and nodes may contan any number of resources. One node knows only the resources t s currently hostng. Any node n the graph can start a query, whch means that some of the lnks are traversed based on a local decson n the graph. Whenever the query reaches the node wth the quered ID, the node reples. The goal s to locate a predetermned amount of resource nstances wth a gven ID usng as few query packets as possble. One possble soluton for the resource dscovery problem s the breadth-frst search algorthm (BFS) []. In BFS a node that starts a query passes the query to all ts neghbors. When the neghbors receve the query, they pass t further to all ther neghbors except the one from whch the query was receved. Nodes cache the messages that they have receved and f the query has already been receved from other neghbor then Manuscrpt receved September 2, Ths work was supported n part by the Graduate School n Electroncs, Telecommuncatons and Automaton (GETA) and Innovatons n Busness, Communcaton and Technology (InBCT) proect of Agora Center. M. A. Vapa, A. K. Auvnen, and J. T. Vuor are wth Department of Mathematcal Informaton Technology, Unversty of Jyväskylä, Fnland (emal: frstname.lastname@yu.f). N. P. Kotlanen s wth Agora Center, Unversty of Jyväskylä, Fnland (emal: nko.kotlanen@yu.f). H. M. Kanulanen s wth WTS Networks, Jyväskylä, Fnland (e-mal: hekk.kanulanen@wts.f) query s dropped. Tme-to-Lve (TTL) value s used to lmt the number of hops the query can take by reducng TTL value each tme a query s receved. When TTL decreases to zero the query s dropped. The BFS algorthm ensures that f a resource s located n the network t can be found from the network f TTL s hgh enough. The downsde of the algorthm, however, s that t uses many query packets to fnd the needed resources. Thus, we propose an alternatve algorthm that s more effcent n face of used query packets and evaluate t usng peer-to-peer scenaro wth power-law dstrbuted topology [2]. The rest of ths paper s organzed as follows. The next secton presents the references to related work done n P2P resource dscovery. Secton III descrbes the NeuroSearch algorthm as a soluton for the resource dscovery problem. Secton IV descrbes the optmzaton process and Secton V the test case used n the study. Secton VI analyzes the smulaton results and n Secton VII the paper s concluded. II. RELATED WORK Much research has been done regardng the resource dscovery problem. Adamc et al. [3] and Km et al. [4] propose a search strategy that utlzes the topologcal propertes of a power-law network. The search strategy frst proceeds towards hghest-degree node, e.g. the node that has the hghest number of neghbors, and then gradually moves to lower degree ones. The algorthm locates resources effcently f they can be found from the core of the network, but the performance decreases when the central nodes are revsted n search for lower degree nodes. Lv et al. [5] evaluate BFS, expandng rng and random walk search mechansms wth varyng topologes, ncludng random graphs [2], power-law graphs and a snapshot of the Gnutella network obtaned n October These researchers fnd that BFS s not scalable and n partcular on Gnutella and powerlaw graphs the effects of floodng are dsastrous: the number of messages ncreases drastcally when TTL s ncreased. Expandng rng, where TTL s extended gradually for BFS, s the frst ad to the problem. However, because t forwards duplcate messages to the nodes that the query has already reached, a better soluton to the problem usng random walkers s proposed by the researchers. A search ntates multple walkers and forwards them based on a random selecton of a neghbor. In addton to the TTL as a termnaton condton for the walkers, Lv et al. use checkng, where the random walkers perodcally check from the query orgnator whether the

2 > PAPER IDENTIFICATION NUMBER: < 2 walker should be termnated or not. Whle random walkers ncrease the number of hops and thus latency, they decrease the total traffc because the search proceeds n a depth-frst manner. Kalogerak et al. [6] consder two search algorthms for the resource dscovery problem. The Modfed Random BFS Search behaves lke BFS, but the neghbors select only a random subset of neghbors for forwardng the query. Ths reduces traffc, but adustng the correct sze of the subset for varous networks may be dffcult. The researchers work uses a random graph n whch all the nodes have approxmately smlar degrees. Thus the performance of the algorthm n power-law graphs cannot be drectly determned from the results. In another algorthm they present, called Intellgent Search Mechansm, the nodes keep track of recent query results provded by ther neghbors. When a new query arrves, the neghbors are sorted based on the smlarty of the query to earler reples from the neghbor. Because the nodes keep track of the earler queres, the performance of the algorthm mproves as the network evolves. Yang and Garca-Molna [7] expermented wth many types of drected search strateges based on varous heurstcs. These heurstcs nclude the number of results returned, shortest average tme to satsfacton, smallest average number of hops of receved results, the hghest number of results returned, shortest message queue, shortest latency and hghest degree. Ther work suggests that, to mnmze the tme to satsfacton measure, the best strategy s to pass the query to the neghbor that has had the shortest average tme to satsfacton for last ten queres. Also, when consderng the bandwdth use, the most relable measure s the smallest average number of hops of receved results for last ten queres. The heurstcs used n the study are based on hstory data collected locally n each node. Smlar use of hstory data s found from the work by Tsoumakos and Roussopoulos [8]. In ther proposal, called Adaptve Probablstc Search algorthm, neghbors keep track of the success rates of earler queres and forward random walkers probablstcally, based on the earler success rate. The algorthm s able to adapt to dfferent query patterns and, therefore, performs better than random walkers. There are certan lmtatons n all the approaches descrbed above. Frst, each of these algorthms uses some control parameters (for example tme-to-lve, the number of walkers or the proporton of neghbors to forward the query) that can be used to tune the algorthm. For a search algorthm, the number Fg. : Processng of NeuroSearch resource query and the NeuroSearch neural network

3 > PAPER IDENTIFICATION NUMBER: < 3 of control parameters should be kept to a mnmal to allow zero confgurablty when appled to a real envronment. Second, whle some of these approaches have mechansms to adapt to the envronment, they do not utlze the entre potental of the envronment because they rely only on one strategy (for example the smlarty of the query and earler reples, shortest average tme to satsfacton for last 0 queres or the success rate of earler queres). In general, only one strategy cannot be effcent n all scenaros and therefore an effcent algorthm should be able to utlze many strateges at the same tme. To overcome these lmtatons a neural network based resource dscovery algorthm called NeuroSearch was desgned. NeuroSearch learns by tself the correct behavor n gven network condtons and uses many combnatons of strateges to locate resources. To authors' knowledge ths s the frst tme when neural networks are beng appled to resource dscovery problem. III. NEUROSEARCH RESOURCE DISCOVERY ALGORITHM The proposed algorthm, called as NeuroSearch, makes decson to whom of the node's neghbors the resource request message s forwarded based on the output neuron of threelayer perceptron neural network. The algorthm s located nsde a peer node as shown n Fg. and s the same for all peers n the network. NeuroSearch can be represented as a functon O : I {0,}, where I [ 0,] 7 s a 7-dmensonal nput vector representng the state of a resource dscovery query. The output of O defnes whether n a gven state query should be dropped O = 0 or forwarded to a peer O = and s evaluated for each neghbor peer separately. When a resource request arrves to the algorthm t goes through all the node's neghbors (denoted as recevers) one by one wth the neural network. The nput parameters for the neural network are: Bas s the bas term and has value. Hops s the number of hops the message has travelled. NeghborsOrder ndcates n whch rank ths recever s n terms of number of neghbors compared to other neghbors. The connecton wth hghest rank has the value of 0, second rank has the value of and so on. ToNeghbors s the number of the recever's neghbors. CurrentNeghbors s the number of node's neghbors. Sent has value f the message has already been forwarded to the recever. Otherwse t has value of 0. Receved has value f the message has been receved earler, else t has value of 0. Hops and NeghborsOrder are scaled wth the functon f ( x) = and Neghbors and CurrentNeghbors wth x + f ( x) = before gvng them to the neural network. Scalng s x performed to ensure that all the nputs are between 0 and. There are two hdden layers n the network. In the frst hdden layer there are 5 nodes + bas and n the second hdden layer 3 nodes + bas. Tanh s used as an actvaton functon n the hdden layers: 2 t ( a) =, where a s the 2a + e weghted sum of nputs to a neuron. Actvaton functon n the output node s the threshold functon 0, a < 0 s ( a) =., a 0 Combnng all together, the output O of the neural network can be calculated wth the followng formula: O = s( w2 t( w3 t( + w f ( I )))), k k= = = where I s the value of nput parameter and 7 w the neural xy network weghts on layer x n poston y. Whenever the query locates a quered resource a reply message s sent back to the neghbor, whch forwarded the request to the node. When all the nodes n the query path have forwarded the reply message backward, t s fnally receved by the query ntator. IV. NEURAL NETWORK OPTIMIZATION The weghts w are unknown and therefore they need to be xy adusted to approprate values. For dong ths we use methods of evolutonary computng [9]. The decson, whch neural networks are better than the others s done by countng the query packets traversed n the test network and found resources. The ftness for the neural network s defned n two parts. Each query s scored for the neural network h and the ftness s calculated by summng up all the scores after n queres: n ftness h = score. The score s defned wth the = followng condtons:. If packets > 300 then score = 0 2. If foundresources = 0 then score = packets + 3. If foundresources < avalableresources / 2 and foundresources > 0 then score = 50 foundresources packets 4. If foundresources avalableresources / 2 then score = 50 avalableresources / 2 packets In the equatons avalableresources s the maxmum number of resource ntances that can be located n the query, foundresources s the number of resource nstances that the neural network was able to locate for the query, and packets s the number of query packets the neural network used for the query. The constant value 300 was set as crteron for determnng when the neural network s consdered to forward the query ndefntely and the query can be stopped. Another constant value, 50, was selected to be large enough to gude the tranng process towards neural networks that locate more resources than other neural networks. Now a neural network could spend 49 query packets more n a query to locate one addtonal resource compared to other neural network, whch located one resource less. The frst rule ascertans that an algorthm that eventually

4 > PAPER IDENTIFICATION NUMBER: < 4 stops s always better than algorthm that does not. The goal of fndng half of the avalable resource nstances was set to demonstrate the algorthm s ablty to balance on a predetermned qualty of servce level and not ust on locatng all resource nstances or one resource nstance. The second rule makes sure that f none of the resources are found then the neural network should ncrease the number of query packets sent to the network. The thrd rule states that f the number of found resources s not enough then the neural network develops only by locatng more resources. Fnally the last rule ensures that when half of the avalable resource nstances are found from the network the ftness grows f neural network uses fewer query packets. The optmzaton process had an ntal populaton of 30 neural networks whose weghts were randomly defned from nterval [-0.2, 0.2]. Next, every neural network was tested n the peer-to-peer smulaton envronment and ftness value calculated. When all neural networks had been tested 5 best were chosen for mutaton and used to breed the new generaton of neural networks. As a result, 30 neural networks were avalable for testng the new generaton. Mutaton was based on the Gaussan random varaton and used weghted mutaton parameter to mprove the adaptablty of the evolutonary search. The random varaton functon was smlar to the one used by Fogel and Chellaplla n ther research [0] and s gven as: ' σ ( ) = σ ( )exp( τn (0,)), =,..., N, ' w ( ) = w ( ) + σ ( ) N (0,), =,..., N where N w = s the total number of weghts and bas terms n the neural network,, N (0,) τ = s a standard 2 N w Gaussan random varable resampled for every, σ s the selfadaptve parameter vector for defnng the step sze for fndng ' the new weght, w ( ) s the new weght value and ndex 85 denotes the number of neuron enumerated over all layers. V. SIMULATION ENVIRONMENT As a peer-to-peer smulaton envronment, we used Peer-to- Peer Realm (P2PRealm) network smulator [] that we have developed. The smulator can be used to smulate the behavor of a statc peer-to-peer network and to tran neural networks usng Gaussan random varaton. P2PRealm has been mplemented usng Java. In the test case we used power-law graphs generated usng the Barabás-Albert model [2]. A power-law network s neghbor dstrbuton follows the power-curve P( k) =, γ k where γ = 3 for Barabás-Albert graph. Therefore n powerlaw networks there exst few hubs n the network that have many neghbors as well as many nodes that have only few neghbors. A power-law graph was selected because exstng w w, P2P networks have shown to express power-law dependences [3]. The graphs tested contaned 00 nodes wth the hghest degree node havng 25 neghbors. Small network sze was selected to allow vsualsaton of query paths n the network. Dynamc changes e.g., node falures were not taken nto account to smplfy the analyss. However, the approach can be appled n dynamc scenaros also as shown n [4]. The test case data was dvded nto three dstnct data sets as descrbed n [5]: a tranng set, a generalzaton set and a valdaton set. Tranng set s used for tranng the neural network. Generalzaton set s used to measure how well the traned neural network performs wth a new data set ndcatng neural network s ablty to generalze. When performance starts to decrease n generalzaton set the tranng can be stopped, because the neural network adapts only to the tranng set f tranng process s contnued. Valdaton set s used as an obectve measure to verfy how well the algorthm performs wth arbtrarly chosen new data set and ensures that the true generalzaton ablty of the neural network s beng measured. The tranng set contaned two power-law topologes wth both beng quered n = 50 tmes per generaton for each neural network. Two topologes were used to have neural networks adapt to a wder range of stuatons than one topology would have provded. The generalzaton set conssted of two powerlaw topologes wth 50 queres. When the performance started to decrease n the generalzaton set the neural network havng hghest ftness was selected and, as a valdaton set, one topology wth 00 queres was used to produce the fnal smulaton results. For each topology, resource nstances were allocated based on the number of neghbors each node has. There were 25 dfferent resources n the test case and the number of dfferent resources n a node was the same as the number of neghbors the node had. Ths means that the largest hub had one nstance of all resources and the lower degree nodes only some of these, randomly chosen from unform dstrbuton. The queryng nodes and quered resources were selected also randomly from a unform dstrbuton for each query. As stoppng crtera for the optmzaton process, 00,000 generatons were set. Ths seemed to take approxmately two Fg. 2: Evoluton of the best neural networks n each generaton for tranng and generalzaton sets

5 > PAPER IDENTIFICATION NUMBER: < 5 weeks on our desktop PC equpped wth an AMD Athlon XP 800 processor. The evoluton of the best neural network n each generaton s shown n Fg. 2. VI. SIMULATION RESULTS To evaluate the dfference between BFS and NeuroSearch, we selected the best algorthm at the 85,736 th generaton and calculated the number of packets used and found resources for 00 dfferent queres usng valdaton set. The 85,736 th generaton was selected because between the 80,000 and 90,000 generatons the neural networks had acheved steadly good results and, n partcular, n the 85,736 th generaton, neural network had the best ftness. The results are presented n Fg. 3 and Fg. 4. The results of Fg. 3 show that the performance of NeuroSearch regardng the number of packets s nearer to BFS wth a tme-to-lve value 2 (BFS-2), rather than BFS wth a tme-to-lve value 3 (BFS-3). In average NeuroSearch consumes 47.2 packets per query whereas BFS-2 consumes 30.0 and BFS packets. The reason why there s some varaton n the number of packets for successve BFS queres s that the number of delvered packets depends on whch node s queryng. If the query starts from a central node (nodes 0-0), t wll produce more packets than the same query started from an edge node (nodes 90-99) because the edge query has fewer connectons where BFS can spread. In case of NeuroSearch, the performance s stable and does not depend on whch node s queryng. Fg. 4: Number of resources found by the algorthms used query packets we can determne the effcency of the algorthms. These values are shown n Table I. The results show that NeuroSearch s effcency s at the same level as BFS-2 s locatng a new resource every ffth packet. BFS-3 locates a new resource approxmately every nnth packet. Effcency s easer to keep hgh when locatng only few resources because usually those can be found from the central nodes alone. When the number of needed resources ncreases, query has to spread more to the edges to locate the addtonal resources. Therefore the effcency of BFS-3 decreases sgnfcantly. BFS-2 and NeuroSearch acheve near smlar effcency ndcatng that NeuroSearch s able to sustan a good effcency even though t needs to locate more resources than BFS-2. TABLE I EFFICIENCY OF THE ALGORITHMS Algorthm Packets Resources Effcency BFS BFS NeuroSearch For each query, NeuroSearch locates approxmately half of the resources or more, whch can be seen n Fg. 5. There are sx queres n whch NeuroSearch msses the target to locate half of the resources. Ths varaton results from the dfference Fg. 3: Number of packets used by the algorthms Fg. 4 shows how many resources the algorthms were able to locate. NeuroSearch s performance n terms of located resources s qute smlar to BFS-2 at central nodes, but better n the edge nodes. Compared to BFS-3 NeuroSearch s performance s constantly lower, reachng the same performance level only at some edge nodes. The reason why NeuroSearch s satsfed wth ths level of performance s that t has already reached the goal of fndng half of the avalable resources as defned n the ftness functon and locatng more resources s not needed. By calculatng the rato between the located resources and Fg. 5: Dfference of located resources to half of resources

6 > PAPER IDENTIFICATION NUMBER: < 6 between the tranng set and the valdaton set. Nonetheless, the results ndcate that the optmzaton process has found an algorthm that s able to locate nearly half of the resources from the network wth hgh probablty. We analyzed the behavor of the best-evolved neural network by trackng the path used by the queres. NeuroSearch seems to prefer central nodes early n the query and uses multple paths for dong ths. After reachng central nodes or one hop later the spreadng s stopped. The maxmum number of hops s 5. As verfcaton for ths the behavor of a typcal NeuroSearch query started from an edge node s llustrated n Fg. 5. In the fgure the query travels through the connectons denoted wth a black lne startng from node 99 wth queston mark (?). Nodes marked wth an exclamaton mark (!) contan the quered resource. In total the query uses 49 packets and locates resources. Sx connectons are traversed from both drectons, whch s not shown n the fgure. VII. CONCLUSION In ths paper, a new resource dscovery algorthm has been proposed. NeuroSearch algorthm takes nto account the specal characterstcs of ts envronment and can be adusted to dfferent knd of P2P networks. The algorthm s performance s also stable and compettve compared to the BFS algorthm. Whle NeuroSearch performs well compared to BFS t s by no means yet desgned to be optmal. For example, NeuroSearch does not yet nclude hstory-based nputs even though they would sgnfcantly mprove the performance. Therefore, the results obtaned n [3]-[8] wll be consdered n forthcomng research on NeuroSearch. There are also other drectons that were left out of ths research. Frst, we are studyng what mprovements to the performance would be ganed by varyng the neural network s nternal structure. Second, we are amng to fnd out what are the scalablty factors of NeuroSearch when the network sze grows, and thrd we are developng an optmal resource dscovery algorthm usng global knowledge to be able to measure the best effcency a resource dscovery algorthm can acheve. Also, we are workng on a soluton to speed up the optmzaton process by parallelzng the evolutonary algorthm usng dstrbuted computng. Ths helps us to more accurately determne the performance maxmum of NeuroSearch. ACKNOWLEDGMENT The authors would lke to thank the co-desgners of NeuroSearch Jon Töyrylä, Yevgeny Ivanchenko, Mattheu Weber and Hermann Hyytälä. Also we thank Tomm Kärkkänen for gvng useful hnts how to develop the algorthm further and Barbara Crawford for proofreadng the artcle. Fg. 5: Typcal NeuroSearch resource query

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