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 %s,FModeling and Analysis of Random Walk Search Algorithms in P2P NetworksGG0LNabhendra Bisnik, Alhussein Abouzeid ECSE, Rensselaer Polytechnic Institute 2M%&H  ) Contributions# Analytical expressions for performance metrics of random walk search in decentralized P2P networks An algorithm, called equation based adaptive search (EBAS), that uses analytical results to set the parameters of random walk Feedback based mechanism for maintaining popularity estimates0$qZOutlinet Search mechanisms and trade-offs involved Analytical results EBAS Simulation results Conclusion and future workuqu t Search mechanisms and trade-offs involved Analytical results EBAS Simulation Results Conclusion and future Work<+Jq,ISearch Algorithmsg Stateless search algorithms No state information about network or links maintained e.g. Flooding, Iterative Deepening, Random Walk, k-Random Walk State-full search algorithms Improvement in performance by maintaining state information (goodness of neighbors, resource indices) Better performance but more complex e.g. Directed BFS, Local Indices, APS qxqqqx Search Algorithms (cont.){ Desired performance Low overhead Low delay High success rate Trade-offs Overhead and success rate Overhead and delayq, q/   / The k-Random Walk0    The k-Random Walk0    The k-Random Walk0    The k-Random Walk0   The k-Random Walk0  The k-Random Walk (cont.)0X Popular alternative to flooding [3] So far focus is on adaptively forwarding queries to   good  neighbors Performance depends on parameters k and T and popularity of resource (p) low k and T => high delay and low success rate high k and T => high overhead Problem: Number of nodes queried are either more or less than what is required Solution: Adaptively set parameters of random walk according to popularity of resource qZMZqZZ$ G #L G P t Search mechanisms and trade-offs involved Analytical results EBAS Simulation Results Conclusion and future Work\+q6q+5 Analytical results Random walk has statistical properties similar to sampling from uniform distribution [1] Using above we found analytical expressions of success rate, overhead and delay in terms of number of random walkers (k), TTL (T) and popularity (p)q "Verification of Analytical Results## t Search mechanisms and trade-offs involved Analytical results EBAS Simulation Results Conclusion and future Workd?q0q>/EBAS Objective: Set parameters (k,T) of random walk such that EBAS consists of two components: Popularity estimation module Parameter selection moduleF_q:^$: Popularity Estimator Module Popularity estimator is based on exponentially weighted moving average Uses the fraction of successful searches in an update interval ( ) to obtain current estimate according to Popularity estimate for next update interval is updated according to :q G Parameter selection module Uses in order to set and such that (1), (2) and (3) are satisfied Inequality (1) is satisfied if Inequalities (2) and (3) may be solved numerically in order to obtain a the range of feasible k and T The parameter selection module may be implemented by means of a parameter selection table in which feasible values of k and T corresponding to various range of popularitiesRqATG!  " An Example (r Consider a case where and Inequality (1) is satisfied if 0qqqs/ t Search mechanisms and trade-offs involved Analytical results EBAS Simulation Results Conclusion and future WorkdEqqD1Simulation Scenario Extensive simulations done for Evaluating performance of popularity estimator Comparing performance EBAS with non-adaptive random walk Network for simulation 104 nodes px104 nodes randomly chosen and marked to have resource Network grown according to [2] qhqa gR0`Simulation Results  Popularity Estimator Module11( Simulation Results - EBAS4Simulation Results - EBAS5 t Search mechanisms and trade-offs involved Analytical results EBAS Simulation Results Conclusion and future WorkDYqX3Conclusion & Future Work EBAS effectively maintains popularity estimates and performs better than random walk EBAS performs best in scenarios where same or  similar  item is searched several times Modeling problem of choosing optimal parameters as control theoretic problem Model performance of other state-full search mechanisms such as APS &CqB 7  References D[1] C. Gkantsidis, M. Mihail, and A. Saberi. Random walks in peer-to-peer networks. In Proc. of IEEE INFOCOM, Mar. 2004. [2] P. Holme and B. J. Kim. Growing Scale-free Networks with Tunable Clustering. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 65, 2002 [3] Q. Lv, P. Cao, E. Cohen, K. Li, and S. Shenker. Search and Replication in Unstructured Peer-to-Peer Networks. In Proceedings of the 2002 ACM SIGMETRICS international conference on Measurement and modeling of computer systems, pages 258 259. ACM Press, 2002. Z#ZY^Co%  W6  Thank You.  P/H9:;<=>?@AB C D E F HIJKLMNOPQRSTUVW  ` 33` Sf3f` 33g` f` www3PP` ZXdbmo` \ғ3y`Ӣ` 3f3ff` 3f3FKf` hk]wwwfܹ` ff>>\`Y{ff` R>&- {p_/̴>?" dd@,|?" dd@   " @ ` n?" dd@   @@``PR    @ ` ` p>> $(    6ܣ  `}  T Click to edit Master title style! !  0d  `  RClick to edit Master text styles Second level Third level Fourth level Fifth level!     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( 33___PPT10i.O+D=' = @B +  $$,O(  ,x , c $ `   f2 , 0"` P P f2 , 03f"`P f2 , 03f"`Pf2 , 03f"`  `f2 , 03f"`P f2 , 03f"` 0 P f2  , 03f"`P 0 f2  , 03f"`` 0 f2  , 03f"`  f2  , 03f"``  f2  , 03f"`P  f2 , 03f"`pf2 , 0"`0B , TD8c?"0@NNN?N`PPB ,@ TD8c?"0@NNN?N  B , TD8c?"0@NNN?N B ,@ TD8c?"0@NNN?N0 B ,@ TD8c?"0@NNN?Np B , TD8c?"0@NNN?N B , TD8c?"0@NNN?NP B , TD8c?"0@NNN?N 0 0 B , TD8c?"0@NNN?N 0 B , TD8c?"0@NNN?N` P B ,@ TD8c?"0@NNN?N B , TD8c?"0@NNN?N  B , TD8c?"0@NNN?N B , TD8c?"0@NNN?N @  , Z8G[H?"0`NNN?Npp : f2 , 0"`@f2  , 03f"`  !, H3f ?"6@ NNN?N  ,Nodes With the Resources ", H3f ?"6@ NNN?N` G 0Nodes Without the ResourcesE #, H 3f ?"6@ NNN?N 1Querying Node Initiates search with k = 2, T = 3 B2$B $,@ TD8c?"0@NNN?N ` H , 0޽h ?, 33___PPT10i.O+D=' = @B +  &&0Z(  0x 0 c $|  `   f2 0 0"` P P f2 0 03f"`P f2 0 03f"`Pf2 0 03f"`  `f2 0 03f"`P f2 0 03f"` 0 P f2  0 03f"`P 0 f2  0 03f"`` 0 f2  0 03f"`  f2  0 03f"``  f2  0 03f"`P  f2 0 03f"`pf2 0 0"`0B 0 TD8c?"0@NNN?N`PPB 0@ TD8c?"0@NNN?N  B 0 TD8c?"0@NNN?N B 0@ TD8c?"0@NNN?N0 B 0@ TD8c?"0@NNN?Np B 0 TD8c?"0@NNN?N B 0 TD8c?"0@NNN?NP B 0 TD8c?"0@NNN?N 0 0 B 0 TD8c?"0@NNN?N 0 B 0 TD8c?"0@NNN?N` P B 0@ TD8c?"0@NNN?N B 0 TD8c?"0@NNN?N  B 0 TD8c?"0@NNN?N B 0 TD8c?"0@NNN?N @  0 Z& G[H?"0`NNN?Npp : f2 0 0"`@f2  0 03f"`  !0 H * 3f ?"6@ NNN?N  ,Nodes With the Resources "0 H- 3f ?"6@ NNN?N` G 0Nodes Without the ResourcesE #0 H/ 3f ?"6@ NNN?N 1Querying Node Initiates search with k = 2, T = 3 B2$B $0@ TD8c?"0@NNN?N `  %0 Z8 GH?"0`NNN?Np  :  &0 H: 3f ?"6@ NNN?NP ISuccessful Termination H 0 0޽h ?/ 0%0 33___PPT10i.O+D=' = @B +  ((4g(  4x 4 c $- `   f2 4 0"` P P f2 4 03f"`P f2 4 03f"`Pf2 4 03f"`  `f2 4 03f"`P f2 4 03f"` 0 P f2  4 03f"`P 0 f2  4 03f"`` 0 f2  4 03f"`  f2  4 03f"``  f2  4 03f"`P  f2 4 03f"`pf2 4 0"`0B 4 TD8c?"0@NNN?N`PPB 4@ TD8c?"0@NNN?N  B 4 TD8c?"0@NNN?N B 4@ TD8c?"0@NNN?N0 B 4@ TD8c?"0@NNN?Np B 4 TD8c?"0@NNN?N B 4 TD8c?"0@NNN?NP B 4 TD8c?"0@NNN?N 0 0 B 4 TD8c?"0@NNN?N 0 B 4 TD8c?"0@NNN?N` P B 4@ TD8c?"0@NNN?N B 4 TD8c?"0@NNN?N  B 4 TD8c?"0@NNN?N B 4 TD8c?"0@NNN?N @  4 ZT G[H?"0`NNN?Npp : f2 4 0"`@f2  4 03f"`  !4 HX 3f ?"6@ NNN?N  ,Nodes With the Resources "4 Hp\ 3f ?"6@ NNN?N` G 0Nodes Without the ResourcesE #4 H^ 3f ?"6@ NNN?N 1Querying Node Initiates search with k = 2, T = 3 B2$B $4@ TD8c?"0@NNN?N `  %4 Zf GH?"0`NNN?Np  :  &4 H, 3f ?"6@ NNN?NP ISuccessful Termination  '4 Z GH?"0`NNN?N@ :  (4 H 3f ?"6@ NNN?N@ KUnsuccessful Termination H 4 0޽h ??04%4'4 33___PPT10i.O+D=' = @B +   7/))8(  8x 8 c $P  `   f2 8 0"` P P f2 8 03f"`P f2 8 03f"`Pf2 8 03f"`  `f2 8 03f"`P f2 8 03f"` 0 P f2  8 03f"`P 0 f2  8 03f"`` 0 f2  8 03f"`  f2  8 03f"``  f2  8 03f"`P  f2 8 03f"`pf2 8 0"`0B 8 TD8c?"0@NNN?N`PPB 8@ TD8c?"0@NNN?N  B 8 TD8c?"0@NNN?N B 8@ TD8c?"0@NNN?N0 B 8@ TD8c?"0@NNN?Np B 8 TD8c?"0@NNN?N B 8 TD8c?"0@NNN?NP B 8 TD8c?"0@NNN?N 0 0 B 8 TD8c?"0@NNN?N 0 B 8 TD8c?"0@NNN?N` P B 8@ TD8c?"0@NNN?N B 8 TD8c?"0@NNN?N  B 8 TD8c?"0@NNN?N B 8 TD8c?"0@NNN?N @  8 Zl G[H?"0`NNN?Npp : f2 8 0"`@f2  8 03f"`  !8 HH 3f ?"6@ NNN?N  ,Nodes With the Resources "8 HD 3f ?"6@ NNN?N` G 0Nodes Without the ResourcesE #8 H 3f ?"6@ NNN?N 1Querying Node Initiates search with k = 2, T = 3 B2$B $8@ TD8c?"0@NNN?N `  %8 Zq GH?"0`NNN?Np  :  &8 H` 3f ?"6@ NNN?NP ISuccessful Termination  '8 Z( GH?"0`NNN?N@ :  (8 H0t 3f ?"6@ NNN?N@ KUnsuccessful Termination   )8 H ?"6@`NNN?N@  j(Search Successful Overhead = 5 Delay = 2&)H 8 0޽h ??08%8'8 33___PPT10i.O+D=' = @B +   $0(  $x $ c $P  `}   x $ c $4k  `P   H $ 0޽h ? 33___PPT10i.O+D=' = @B +    @(  @x @ c $d  `   H @ 0޽h ? 33___PPT10i.O+D=' = @B +   <(  <x < c $  `   x < c $P @ c    ` < c $A ? ?  H < 0޽h ? 33___PPT10i.O+D=' = @B +/    D(  D D `A verify_overP     D bAverify_delay   ~ D s * `    D `A verify_succ. 0   D <0P ,$D 0 OSearch Overhead vs. popularity    D <+B#style.visibility<* D%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* DD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* DD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* D%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* DD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* DD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* D%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* DD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* DD' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* D%(D' =-6B'blinds(horizontal)*<3<* D++0+ D ++0+ D ++0+ D ++0+ D +     @P(  Px P c $D `  H P 0޽h ? 33___PPT10i.O+D=' = @B +   0 Lc(  Lx L c $@ `}   ~ L s * `P  ` L c $A ? ?:` ` L c $A ? ?pI  `  L c $A ? ?     L <TR 3(1) L <p  3(2) L <  ?@  3(3)H L 0޽h ? 33___PPT10i.O+D=' = @B +  ` tB(  tx t c $ `   ~ t s *p    t0 TA ? ?P L .   t0 TA ? ?0 0   f  t s *A ? ?p   t <4   3(4)  t <p? 3(5)H t 0޽h ? 33___PPT10i.O+D=' = @B +  p x-(  xx x c $Lv `p   ~ x s *`F`   x0 TA ? ?@   x0 TA 2? ?0P  2 x x <A 0?? | 0x  x <A 3?? 3  x <0OP 3(6)H x 0޽h ? 33___PPT10i.O+D=' = @B +     04& (  4 4 0" 7 _-Block diagram showing main components of EBAS..' F `  4   4 <"`@P  MPopularity Estimator Module 4 <@"`0 P  LParameter Selection Module 4 <"`P  = P2P Network   4 <"`` p  IDelay (Update Interval)lB  4 <DjJp0 plB  4 <DjJ pplB  4B <DjJ  ZB  4 s *DjJppZB  4 s *DjJp ZB 4 s *DjJp lB 4B <DjJ   4 <H g 5(k,T) 4 <\ 0 <  < Success Rate ZB 4B s *DjJ`P ` P ZB 4 s *DjJ``P lB 4 <DjJ`@ZB 4B s *DjJ  ` ZB 4 s *DjJ   lB 4 <DjJ  @  4 <& 6 GPopularity EstimateH 4 0޽h ? 33___PPT10i.O+D=' = @B +g  ~v (    0 x  \ E[O] and E[D] as a function of T are plotted in the figure, for kT = 300 According to the figure and is a feasible (k,T) pairq2=ARf  c >A param_select nx  c $# `   ~  s *L$   0 ZA ?AA ?0 7   0 ZA ?AA ?P`C  f  s *A ?? ?p `m ?f   s *A B? ?@ =  Bf   s *A E? ?P ` g  EH  0޽h ? 33___PPT10i.O+D=' = @B +    (  x  c $#< ` < H  0޽h ? 33___PPT10i.O+D=' = @B +  0(  x  c $ `}  < x  c $ `   H  0޽h ? 33___PPT10i.pwPع+D=' = @B +  ](    XApop_estp  x  c $0 `}     0+ sThe popularity estimate maintained by Popularity Estimator Module closely follows actual popularity of the resourcettH  0޽h ? 33___PPT10i.O+D=' = @B +  *"|(  | | ^Aover_scen10p I  ~ | s *Q `     | <`I@` _+Scenario-1 : Popularity increases with time,, | 0  }KEBAS reduces overhead by adaptively decreasing the number of random walkersLL | ^Asucc_scen10@   H | 0޽h ? 33___PPT10i.O+D=' = @B +  6.(    ^Aover_scen2  ~  s * `     <L`@` _+Scenario-2 : Popularity decreases with time,,  0@X ` WEBAS maintains required success rate by adaptively increasing number of random walkers XX  ^Asucc_scen2   H  0޽h ? 33___PPT10i.O+D=' = @B +    (  x  c $hT `  H  0޽h ? 33___PPT10i.O+D=' = @B +  6(  x  c $< `  < ~  s * 0`  H  0޽h ? 33___PPT10i.O+D=' = @B +   0(  x  c $ `}   x  c $ `  H  0޽h ? 33___PPT10i.vw1+D=' = @B +  (  r  S y `   H  0޽h ? 33___PPT10i.)~+D=' = @B + 0 ]U@(  X  C    U  S @ 0   Today I am going to talk about the modeling and analysis of random walk search mechanisms in P2P networks. I did this work with my phd advisor professor Abouzeid. In this work we derive analytical expressions for various performance metrics of random walk search in decentralized P2P networks. We use the analytical results in order to develop a search mechanism called equation based adaptive search or EBAS. Basically EBAS sets the parameters of random walk so that search maintains a certain minimum performance level. The EBAS requires knowledge of the popularity of the item being searched for. So we develop a feedback based mechanism for maintaining popularity estimates. ,H  0޽h ? 3380___PPT10. Ŏ 0  P(  X  C      S   0   The outline of this talk is as follows. First I will talk about existing search mechanism in decentralized P2P networks and the trade-offs involved. Then I will present the analytical results and how these results are utilized by EBAS. Simulation results illustrate the improvement in performance obtained by EBAS, which is followed by conclusion and discussion of future research directions. H  0޽h ? 3380___PPT10.m 0 KC`(  X  C    C  S l 0   The search algorithms in decentralized P2P networks may be categorized into stateless and state-full algorithms. In stateless algorithms no extra state information is maintained at the nodes. The example of such stateless search mechanisms are flooding, iterative deepening, Random walk and k-random walk, which is just an extension of random. In contrast the state-full search mechanisms strive for better performance by maintaining some sort of state at each active node. The state may in terms of information gathered regarding which neighbors are more likely to reply to a search query that is gathered from past searches. Other kind of state information that may be maintained is the list resources stored by the neighbors. Here are some of the examples of state-full search algorithms. Directed diffusion and APS store information about goodness of neighbors while In local indices each node maintains the list of resources available by all nodes within two hops.H  0޽h ? 3380___PPT10.9q 0 p#(  X  C      S  0   %It is desired that a search algorithm yields low overhead, in terms of number of messages transmitted, low delay and at the same time achieve high success rates. Unfortunately it might not be possible to achieve all these objectives simultaneously since there are various tradeoffs involved. For example the flooding achieves very high success rate but it also incurs high overhead. On the other hand random walk search may have a very low overhead compared to flooding but the delay of random walk search is considerably higher.H  0޽h ? 3380___PPT10. Mpf 0 v(  X  C      S 84 0   xBSomewhere in middle of this spectrum lies k-random walk algorithms. We will present a brief example of k-random walk in order to make terminology clear. The node that is interested in discovering a resource is refered to as querying node. The querying node issues k random walkers with TTL T. In this example k = 2, T =3. jH  0޽h ? 3380___PPT10.)[  0  k(   X   C       S   0   mYThe intermediate nodes randomly choose a neighbor in order to forward the random walkers.H   0޽h ? 3380___PPT10.Pް  0 (  X  C      S C  0   A random walker is terminated if its discovers a node with the resource. Such a termination is referred as successful terminationH  0޽h ? 3380___PPT10.О  0 (  X  C      S H  0   On the other hand a random walker that is not able to discover the resource but its TTL expires is referred to have undergone unsuccessful termination. H  0޽h ? 3380___PPT10.  0 IA(  X  C    A  S \  0   Overhead of a search is the number of messages transmitted during the search. Delay is the time elapsed before the first node with resource is discovered. For this example overhead = 5 and delay = 2.H  0޽h ? 3380___PPT10.࣭) 0 {(  X  C    {  S  0   It has been discovered that k-random walk is very attractive alternative to flooding. There has been lot of work that focuses on development on adaptive k-random walk. However the focus of such works is on adaptively forwarding the query to good neighbors. The performance of such k-random walk also depends largely on the value of parameters k, T. Low k and T leads to high delay and low success rate while high k and T leads to high overhead. Not much research has been done on how choose the parameters k and T. The problem of k-random walk is that depending on k and T the number of nodes queried is either less or more than what is required. Our goal is to adaptively set the parameters of k-random walk according to the popularity of resource being searched for. H  0޽h ? 3380___PPT10.̩{  0 C; (   X   C    ;   S  0   The analytical results of our work are based on work by Gkantsidis et al in INFOCOM 04, that states that a random walk on P2P network like graphs has statistically properties similar to sampling from uniform sampling. Using the above result we derived analytical expressions for the performance metrics such as overhead, delay and success rate in terms of number of random walkers, TTL and popularity of the item. 8 ^H   0޽h ? 3380___PPT10.@v 0 4,$(  $X $ C    , $ S  0   In order to verify the analytical model we simulate k-random walk search on P2P network and compare the simulation results with analytical results. First graph shows the plot of the search delay vs. popularity of the resource, second graph shows plot of search overhead vs. popularity and last graph shows the plot of success rate vs. popularity. These plots show that the analytical results agree closely with the simulation results.H $ 0޽h ? 3380___PPT10.0  0 ((  (X ( C     ( S  0    H ( 0޽h ? 3380___PPT10. < 0 ,(  ,X , C     , S H 0    The objective of the equation based adaptive search is to set the parameters of k-random walk so as to provide some probabilistic performance guarantee. More precisely EBAS sets k, T such that the success rate is more that 1-\e for \e very small and overhead is less than alpha and delay is greater than delta. (k, T) pair is feasible if (1), (2) and (3) satisfied. Note that \e, alpha and delta are functions of popularity of the item being searched for. For high p feasible (k, T) may exist for low \e, alpha and delta while for low popularity resources a feasible (k, T) pair may not exist for similar \e, alpha and delta. The EBAS consists of two components: the popularity estimation module and the parameter selection module. Both these modules use the analytical results. H , 0޽h ? 3380___PPT10.yf! 0 rj@8(  8^ 8 S    <d 8 c $  0  < This figure shows the main components of EBAS. The PEM maintains the pop estimate that is utilized by the PSM to choose a feasible (k, T). The feedback from search results are then utilized by the PEM to update the pop estimate.H 8 0޽h ? 3380___PPT10.Џ9| 0 P<(  <X < C     < S C 0   XWe use the exponentially weighted moving average in order maintain popularity estimation module that filters out the high frequency component. The popularity estimate is updated after an ``update interval . The fraction of successful searches in an, denoted by r(j), is used to obtain the current estimate of popularity estimate according to this equation. The overall popularity estimate is adjusted according to the equation.H < 0޽h ? 3380___PPT10. 0  `@(  @X @ C    < @ S  0  < eThe parameter selection module uses the estimate of popularity maintained by popularity estimation module in order to choose the parameters of random walk. The parameters are updated after each update interval immediately after the popularity estimate update. The performance constraint (1) is satisfied if k.T satisfy this inequality. Unfortunately the constraints (2) and (3) cannot be reduced to simple relation as (6). Therefore (2) and (3) may be solved numerically in order to obtain the feasible range of k, T pairs. One practical way to implement the parameter selection module is to generate offline a parameter selection table, that lists the value of parameters for various popularities, such that the performance criterion is satisfied. The module then simply looks up the parameter selection table for choosing parameters for a given popularity estimates. 30H @ 0޽h ? 3380___PPT10.p:7 0  pD(  DX D C     D S P8 0   /This is a simple example to illustrate EBAS. Suppose one needs to search a resource with popularity p = 0.01 and corresponding \e = 0.05, alpha = 175 and delta = 50. The constraint on success rate is satisfied if product of k.T is greater than 298. SO suppose we fix k.T=300 and try to fing a (k, T) pair such that constraint on overhead an delay are satisfied. For k.T = 300, this figure shown delay and overhead as a function of T. The values of T between green and light blue lines satisfy both the constraints. Thus we may choose k=2, T=150 as an example.P(LH D 0޽h ? 3380___PPT10.`ãE 0 HU(  HX H C     H S   0   WCSo we perform simulations in order to evaluate the performance of the popularity estimator module and to compare the performance of EBAS with k-random walk. The simulation scenario included a network with 10^4 nodes that is grown according to [2] such that we have a scale free network with tunable clustering coefficient. H H 0޽h ? 3380___PPT10.  0 IAL(  LX L C    A L S (Q 0   In this plot we have actual popularity of an item plotted in blue while the popularity estimate maintained by a PEM is shown in red. This shows that PEM effectively maintains the popularity estimate.H L 0޽h ? 3380___PPT10.8˰@ 0 PP(  PX P C     P S  0   R>In order to evaluate performance of EBAS we consider two scenarios. In scenario 1 the popularity of a resource of interest increases with time. These plots indicate that the EBAS is able two maintain desired success rate while incurring less overhead. This because it adaptively decrease the aggressiveness of search. H P 0޽h ? 3380___PPT10.P 0 T'(  TX T C     T S xD 0   )In scenario-2 the popularity of resource decreases with time. It is shown that EBAS maintains the desired success rate even when the popularity of the resource decreases. This because EBAS adaptively becomes more and more aggressive and as a result it incurs a higher overhead.H T 0޽h ? 3380___PPT10.n  0 X(  XX X C     X S l< 0    H X 0޽h ? 3380___PPT10. !H  0 \(  \X \ C     \ S  ' 0    H \ 0޽h ? 3380___PPT10. !H  0 `(  `X ` C     ` S   0    H ` 0޽h ? 3380___PPT10. 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WOh+'0L `h   $<Modeling and Analysis of Random Walk Search in P2P Networks NabhendrandAAh69hMicrosoft PowerPoint of@v`%@!@` c Gg  @  -- @ !--'@Arial-. -2 Modeling and Analysis of s7%%%%%%%%-%%!"!%."System4-@Arial-. $2 Random Walk Search 0%%%%9A%"-%%"%.-@Arial-. .2 _gAlgorithms in P2P Networks-%%$8"%-$-0%/%"".-@Arial-. 332  Nabhendra .-@Arial-. 332 uBisnik  .-@Arial-. 33 2 , .-@Arial-. 332  Alhussein .-@Arial-. 332 Abouzeid.-@Arial-. @2 ^&ECSE, Rensselaer Polytechnic Institute        .-՜.+,0    ;On-screen Show RPIbA #Arial WingdingsMonotype CorsivaDefault DesignMathType 5.0 EquationGModeling and Analysis of Random Walk Search Algorithms in P2P NetworksContributionsOutlineSlide 4Search AlgorithmsSearch Algorithms (cont.)The k-Random WalkThe k-Random WalkThe k-Random WalkThe k-Random WalkThe k-Random WalkThe k-Random Walk (cont.) Slide 13Analytical results#Verification of Analytical Results Slide 16EBASPopularity Estimator ModuleParameter selection module Slide 20 An Example Slide 22Simulation Scenario1Simulation Results Popularity Estimator ModuleSimulation Results - EBASSimulation Results - EBAS Slide 27Conclusion & Future Work References Slide 30  Fonts UsedDesign TemplateEmbedded OLE Servers Slide Titles_)AAAA  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~Root EntrydO)PicturesCurrent UserSummaryInformation(PowerPoint Document(MDocumentSummaryInformation8