Scale-Free Overlay Topologies with Hard Cutoffs for Unstructured Peer-to-Peer Networks

1. Scale-Free Overlay Topologies with Hard Cutoffs for Unstructured Peer-to-Peer Networks Murat Yuksel University of Nevada – Reno yuksem@cse.unr.edu Hasan Guclu Los Alamos National Laboratory guclu@lanl.gov

2. Outline • Motivation and Problem Statement • Topology Generation Mechanisms • Barabási-Albert (Preferential Attachment) Model • Configuration Model • Hop-and-Attempt Preferential Attachment • Discover-and-Attempt Preferential Attachment • Search Methods • Flooding • Normalized Flooding • Random Walk • Summary and Conclusions

3. Motivation • Characteristics of the p2p overlay topology has significant effects on the search performance. Search Efficiency vs. Exponent and Connectedness Ultra-small Small-world

4. 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 • When a new peer joins, how should it construct its list of neighbors? • A local decision affecting global behavior (emergence).

5. Scale-Free Topologies • Fat-tailed power-law degree distribution: • No typical scale • Two well-known topology generation algorithms: • Preferential Attachment (PA) by Barabasi and Albert. • Dynamic model (fixed exponent) • Configuration Model (CM) • Static model • Pre-defined degree distribution with a parameterized exponent

6. Natural and Hard Cutoff • Definition of natural cutoff: • For scale-free networks with power-law degree distribution (m: minimum degree) • Natural cutoff • Natural cutoff for PA model ( ) • Hard cutoff is the value of the maximum degree imposed on nodes.

7. Network Generation Mechanisms • Preferential attachment (Barabási-Albert, PA) model (PA) • Configuration model (CM) • Hop-and-attempt PA model (HAPA) • Discover-and-attempt PA model (DAPA)

8. Preferential Attachment (PA) • Connect to an existing peer with probability proportional to its current degree. • prefer the peers with larger degree • simply skip the existing peers already saturated their hard cutoffs • Requires global info

9. PA with Hard Cutoff Probability to connect to the nodes with degree k Total rate: At steady state:

10. PA with Hard Cutoff

11. PA with Hard Cutoff

12. Configuration Model (CM) • Given a target hard cutoff and a power-law exponent, generate the perfect scale-free degree distribution… • allows multiple links and self loops • may have disconnected components • not practical, but does generate the best possible scale-freeness within the hard cutoff constraint – i.e., good for studying

13. Hop-and-attempt PA Model (HAPA) • At every time step a new node is added to the network • This new node attempts to connect to a randomly chosen existing node A by using the preferential attachment rule • Then it attempts to connect to a randomly chosen node B which is a neighbor of A • The node repeats this procedure until it fills all its stubs (or the number of links it has reaches m)

14. Discover-and-attempt PA Model (DAPA) • First, a substrate network with a specific topology and a large number of nodes (we use geometric random network) is generated • A finite number of nodes are selected randomly and put into p2p network which is empty at the beginning • A node is randomly selected from the substrate network and let it send a broadcasting message to its neighbors reachable in sub steps • The selected node finds all the nodes in its horizon belonging to the peers network and attempts to connect by using the preferential attachment rule until having m links if possible • If it is connected to at least one peer it is added to the peers network • This process is repeated until the number of peers reaches to the number desired

15. Discover-and-attempt PA Model (DAPA)

16. Global versus Local Information

17. 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 • Similar to flooding but the nodes send the messages only to one of their neighbors except the source node

18. Flooding PA is better due to nodes at the edge

19. Flooding HAPA rocks, DAPA not bad

20. Normalized Flooding PA likes cutoff, CM does not.

21. Normalized Flooding The lower the cutoff the better the performance

22. 22 Normalized Flooding Cutoff is goooood. Not so short-sighted network gives good results.

23. Random Walk (The same number of messages in NF and RW) PA likes cutoff, CM does not.

24. Random Walk The lower the cutoff the better the performance

25. 25 Random Walk The lower the cutoff the better the performance.

26. Conclusions • In flooding the lower the hard cutoff the lower the number of hits. HAPA without cutoff does especially good in flooding due to the star-like topology. Increasing the minimum degree eliminates the negative effect of the hard cutoff. • There exists an interplay between connectedness (m) and the degree distribution exponent if there is a hard cutoff, except CM. • Harder cutoffs may improve search efficiency in normalized flooding and random walk except CM. • Extended version of the paper in http://arxiv.org/abs/cs/0611128 Acknowledgments • DOE (DE-AC52-06NA25396), NSF (0627039) and Sid Redner (Boston University).

27. THE END Thank you!