IEEE P2P, Aachen, Germany, September Ad-hoc Limited Scale-Free Models for Unstructured Peer-to-Peer Networks Hasan Guclu Los Alamos National Laboratory Durgesh Kumari Murat Yuksel University of Nevada – Reno

IEEE P2P, Aachen, Germany, September Outline Motivation Topology Generation Mechanisms Barabási-Albert (Preferential Attachment) Model Our Model with Local Info, Hard Cutoffs, and Churn Search Methods Flooding Normalized Flooding Random Walk Summary and Conclusions

IEEE P2P, Aachen, Germany, September Motivation: Scale-Free Topologies Characterization is free of the system size N (i.e., scale).

IEEE P2P, Aachen, Germany, September Motivation Diameter d Exponent  Number of stubs m O(lnln N)(2,3)≥1 O(ln N/lnln N)3≥2 O(ln N)31 >3≥1 Search Efficiency vs. Exponent and Connectedness Ultra-small Small-world Characteristics of the p2p overlay topology has significant effects on the search performance.

IEEE P2P, Aachen, Germany, September Motivation Key Question: How to construct the overlay topology by using local information in p2p nets such that the search efficiency is good? Scale-freeness (i.e. power-law exponent) is related to search efficiency Key Constraints: No global knowledge No peer wants to take on the load – hard cutoff on the degree Local decisions affecting global behavior: When a new peer joins, how should it construct its list of neighbors? When a new peer leaves, how should its neighbors rewire themselves to the network?

IEEE P2P, Aachen, Germany, September Topology Generation Model: Preferential Attachment w/ Hard Cutoff How to construct a scale-free topology? Preferential Attachment (PA) Include an existing peer with probability proportional to its current degree. prefer the peers with larger degree Requires global info ? Hmmm. Which node to have as a neighbor? Degrees Prob. of Attachment We revise PA such that a node with maximum allowed degree (i.e., hard cutoff) is skipped. And the procedure is tried again..

IEEE P2P, Aachen, Germany, September Topology Generation Model: Parameters Parameters of our topology construction framework Probability of a node going down/leaving. Horizon of available state information at join. Horizon of available state information at leave. Maximum degree a node is allowed to have.

IEEE P2P, Aachen, Germany, September Topology Generation Model: Join w/  j Join() procedure: Select a node J to start with Collect J’s neighborhood topology information within  j hops Apply PA on the  j sub- topology until m links are established If m is larger than the nodes in the subtopology, repeat the procedure again until m links are established. Hmmm. Which m nodes to have as a neighbor? J

IEEE P2P, Aachen, Germany, September Topology Generation Model: Rewiring w/  l after a Leave Leave() procedure: Select a node L to delete Collect L’s neighborhood topology information within  l hops Let the  l sub-topology information be available to L’s 1-hop neighbors, r 1 and r 2 With L’s information and r 1 or r 2 being removed r 1 and r 2 apply PA on their  l sub-topology until the lost link is restored with another peer L r2r2 r1r1

IEEE P2P, Aachen, Germany, September Topology Generation Model: Growth with Joins and Leaves Topology growth process calls Join() or Leave() procedures depending on the amount of churn. At every iteration: Call Join() Call Leave() with a probability  Keep this iteration going until the target network size is reached Both the Join() and Leave() procedures assure that degrees of nodes are less than the hard cutoff Higher  means more churn. A peer is added at every iteration.

IEEE P2P, Aachen, Germany, September Degree Distributions,  =0 m=1, k c =50 m=1, no cutoff Increase in  j shifts degree distribution from Exponential to scale-free.

IEEE P2P, Aachen, Germany, September Degree Distributions,  =0 m=3, k c =50 m=3, no cutoff Lesson: Force peers to have a larger m to reduce the need for large  j. Larger m makes the shift less apparent.

IEEE P2P, Aachen, Germany, September Degree Distributions,  =0.3 m=1, k c =50 m=1, no cutoff Hard cutoff does not affect this distribution shift.. Contribution of  l in shifting the degree distribution is more significant.

IEEE P2P, Aachen, Germany, September Search Methods Flooding Source node sends a message to all its neighbors and every node which receives the message forwards it to all its neighbors except the node the message is received from until the target node receives the message Normalized flooding Similar to flooding but the nodes send the messages to at most m (minimum number of links in the network) neighbors Random walk The nodes send the messages only to one of their neighbors except the source node

IEEE P2P, Aachen, Germany, September Flooding,  =0, m=3 Cutoff is the main factor defining flooding search performance.

IEEE P2P, Aachen, Germany, September Flooding:  =0.1, 0.3; m=3  =0.3, k c =10  =0.1, k c =10 Lesson: Use churn as an opportunity to restructure the network topology by carefully rewiring the peers. Churn with larger  l helps flooding performance!!

IEEE P2P, Aachen, Germany, September Normalized Flooding: m=3  j =2,  l =1  j =2,  l =0 Again, larger  l reduces the negative effect of churn!! Again, larger  l reduces the negative effect of churn. Performance of Random Walk exhibit a similar behavior to Normalized Flooding. Lesson: State information at leave is more valuable than the one at join.

IEEE P2P, Aachen, Germany, September Design Guidelines & Principles Force all peers to have a larger m (i.e., a minimum of 3) to reduce the need for large  j. Information at the time of leave is more valuable than the information at the time of join A little responsible leave results in significantly better search performance for the leftover network Rewiring is helpful – Churn can be used as an opportunity to restructure the network

IEEE P2P, Aachen, Germany, September Summary & Future Work A generic topology growth model with churn local state info hard cutoffs rewiring Scales larger than N=10,000 Models looking at dynamic behavior are worthy of pursuing..

IEEE P2P, Aachen, Germany, September Thank you! THE END Acknowledgments This work was supported by the U.S. Department of Energy under contract DE-AC52-06NA25396 and by the US National Science Foundation under awards and