1. Search in Power-Law Networks Presented by Hakim Weatherspoon CS294-4: Peer-to-Peer Systems Slides also borrowed from the following paper Path Finding Strategies in Scale-Free Networks by Beom Jun Kim, Chang No Yoon, Seung Kee Han, and Hawoong Jeon By Lada A. Adamic, Amit R. Puniyani*, Rajan M. Lukose, and Bernardo A. Huberman HP Labs and Stanford University* P P PP P P SS SS Q R D P P PP P P Q R P Q Q NapsterGnutella

2. P2P Systems 2003©2003 Hakim Weatherspoon/UC BerkeleySearch in Power-Law Networks:2 Review of Existing File Location Mechanisms Various design objectives –Gnutella: works well for short-lived nodes, highly dynamic environments Haystack –Freenet: provides “anonymity” –CAN, Chord, Pastry, Tapestry: Low, scalable response latency No false negatives Needles Independent of usage behavior –Applied to music sharing communities –What about others? Scientific collaborations Others?

3. P2P Systems 2003©2003 Hakim Weatherspoon/UC BerkeleySearch in Power-Law Networks:3 Questions Do networks/collaboration/file sharing/etc exhibit any particular network patterns (small-world?Scale- Free?Power-Law?Poisson?)?

4. P2P Systems 2003©2003 Hakim Weatherspoon/UC BerkeleySearch in Power-Law Networks:4 High-Energy Physics Collaboration Fermi National Accelerator Laboratory’s D0 experiment: 1000s physicists (not all actively accessing data at any moment), 18 countries, 70+ institutions Small world!

5. P2P Systems 2003©2003 Hakim Weatherspoon/UC BerkeleySearch in Power-Law Networks:5 Exploit Small-World Behavior Kleinberg’s algorithm: –Search in (structured) small-world network –Greedy search: O(log 2 N) –However, works only for particular type of small world Assumes global knowledge

6. P2P Systems 2003©2003 Hakim Weatherspoon/UC BerkeleySearch in Power-Law Networks:6 Search in Dynamic P2P Networks Not possible to know target host –Due to dynamic nature Node storing file not known until a real-time search is performed. No global information about position of target –Not possible to determine forward progress Solution –Central index (e.g. Napster) –Distributed Queries (e.g. Gnutella) –Distributed Directories+Queries (e.g. this paper)

7. P2P Systems 2003©2003 Hakim Weatherspoon/UC BerkeleySearch in Power-Law Networks:7 Power-Law Many communication and social networks have power-law link distributions Containing a few nodes which have a very high degree and many with low degree. The high connectivity nodes play the important role of hubs in communication and networking

8. P2P Systems 2003©2003 Hakim Weatherspoon/UC BerkeleySearch in Power-Law Networks:8 Power-Law Dynamic Generation Starting with a small number (m 0 ) of nodes Add node with m edges at each time step –probability  i of being connected to the existing vertex i is proportional to the connectivity k i of that vertex –k i is the number of directly connected vertices to i. –k i = (k i + 1)/  j (k j + 1) with the summation over the whole network at a given instant. –Constructs scale-free network Ideas based on growth and preferential attachment Shows the power-law behavior in the connectivity distribution. Need path connecting two nodes in the network.

9. P2P Systems 2003©2003 Hakim Weatherspoon/UC BerkeleySearch in Power-Law Networks:9 Search in Power-Law High connectivity can be exploited when designing efficient search algorithms. As shown by AT&T –the out-link degree distribution for a massive graph of telephone calls between individuals has a clean power- law form with an exponent of approximately 2.1. –Reflects the presence of central individuals who interact with many others on a daily basis and play a key role in relaying information.

10. P2P Systems 2003©2003 Hakim Weatherspoon/UC BerkeleySearch in Power-Law Networks:10 Goals Propose local search strategies –Utilize high degree nodes in power-law graphs –Search costs scale sub-linearly with the size of the graph. –Better than random Demonstrate strategies on the Gnutella P2P network.

11. P2P Systems 2003©2003 Hakim Weatherspoon/UC BerkeleySearch in Power-Law Networks:11 Search Algorithms Random –Choose a random neighbor to forward msg. Max –Choose neighbor with highest degree –Requires that local node knows neighbors degree –Effect Short initial climb Continue down degree sequence

12. P2P Systems 2003©2003 Hakim Weatherspoon/UC BerkeleySearch in Power-Law Networks:12 Results I –Scaling of the average search time vs graph size –Max performs better than Random But not as good as analytical mode. Nodes revisted

13. P2P Systems 2003©2003 Hakim Weatherspoon/UC BerkeleySearch in Power-Law Networks:13 Results II –Max finds 50% of nodes in 10 steps It takes 10+2=12 hops to reach 50% of graphs –Average number of hops 217! Large number of 1- or 2- degree nodes

14. P2P Systems 2003©2003 Hakim Weatherspoon/UC BerkeleySearch in Power-Law Networks:14 Power-Law compared to Poisson Poisson graph –All links are randomly distributed (I.e. have same degree) Revisits more likely in power-law graphs. Power-Law Poisson

15. P2P Systems 2003©2003 Hakim Weatherspoon/UC BerkeleySearch in Power-Law Networks:15 Summary of Power-Law Search Start at a random node Follow degree sequence –That is, node with richest links –Followed by node with second richest Scan the maximum number of nodes –Minimum number of steps

16. P2P Systems 2003©2003 Hakim Weatherspoon/UC BerkeleySearch in Power-Law Networks:16 Gnutella Modifications Use Max instead of broadcast –Store index for neighbor files. Results in efficient search for 50% of files. Need rich nodes in CPU,Bandwidth,Storage capacity –The “rich get richer”

17. P2P Systems 2003©2003 Hakim Weatherspoon/UC BerkeleySearch in Power-Law Networks:17 Notes about Power-Law Algorithm created local directories valid within a two hop radius. Network is resilient to random failures More resistant than central server Power-Law in general –More resistant to random failure than poisson –Less resilient to attack on high degree nodes.

18. P2P Systems 2003©2003 Hakim Weatherspoon/UC BerkeleySearch in Power-Law Networks:18 Closing Questions How is file-sharing different than maintaining personal storage?