1. P2P Topologies Centralized Ring Hierarchical Decentralized Hybrid

2. Two extremes when N=6 H=1 (1) M=5 (N-1) H=5 (N-1) M=2 (2) H=no. of hops M=no. of link updates when a new node joins Complete Ring

3. Consider Scale But if N=2 32 (4 billion - population of the world) Ring –M=2, H=2 32 –1 (retrieval: week with fast net) –Does not scale Complete –H=1, M= 2 32 –1 –Does not scale Key idea: place yourself in between –e.g. H=4 M=762 –e.g. H=8 M=120

4. Centralized Topology

5. Ring Topology

6. Hierarchical Topology

7. Decentralized Topology

8. Hybrid Topology Centralized + Ring

9. Hybrid Topology Centralized + Decentralized

10. Evaluating topologies Manageability –How hard is it to keep working? Information coherence –How authoritative is info? (Auditing, non-repudiation) Extensibility –How easy is it to grow? Fault tolerance –How well can it handle failures?

11. Evaluating topologies Resistance to legal or political intervention –How hard is it to shut down? (Can be good or bad) Security –How hard is it to subvert? Scalability –How big can it grow?

12. Centralized Manageable Coherent Extensible Fault Tolerant Secure Lawsuit-proof Scalable System is all in one place All information is in one place XNo one can add on to system XSingle point of failure Simply secure one host XEasy to shut down ?One machine. But in practice?

13. Ring Manageable Coherent Extensible Fault Tolerant Secure Lawsuit-proof Scalable Simple rules for relationships Easy logic for state XOnly ring owner can add Fail-over to next host As long as ring has one owner XShut down owner Just add more hosts

14. Hierarchical Manageable Coherent Extensible Fault Tolerant Secure Lawsuit-proof Scalable ½Chain of authority ½Cache consistency ½Add more leaves, rebalance ½Root is vulnerable XToo easy to spoof links XJust shut down the root Hugely scalable – DNS

15. Decentralized Manageable Coherent Extensible Fault Tolerant Secure Lawsuit-proof Scalable XVery difficult, many owners XDifficult, unreliable peers Anyone can join in! Redundancy XDifficult, open research No one to sue ?Theory – yes : Practice – no

16. Centralized + Ring Manageable Coherent Extensible Fault Tolerant Secure Lawsuit-proof Scalable Just manage the ring As coherent as ring XNo more than ring Ring is a huge win As secure as ring XStill single place to shut down Ring is a huge win Common architecture for web applications

17. Centralized + Decentralized Manageable Coherent Extensible Fault Tolerant Secure Lawsuit-proof Scalable XSame as decentralized ½Better than decentralized Anyone can still join! Plenty of redundancy XSame as decentralized Still no one to sue ?Looking very hopeful Best architecture for P2P networks?

18. Small Word Phenomenon The small world phenomenon (also known as the small world effect) –is the hypothesis that everyone in the world can be reached through a short chain of social links

19. Early conceptions of the six degrees idea The "shrinking world" of Frigyes Karinthy (Hungarian), 1929 –He believed that the modern world was shrinking due to technological advances in communications and travel –He believed that any two individuals could be connected through at most five connections –Experiment to prove that the population of the Earth is closer together now than they have ever been before select any person from the 1.5 billion inhabitants of the Earth –anyone, anywhere at all using no more than five individuals, one of whom is a personal friend, he could contact the selected individual using nothing except the network of personal friends Karinthy is often regarded as the origin of the notion of Six Degrees of Separation

20. Six Degrees of separation Stanley Milgram's small world experiments (1967) –Milgram's experiments provided evidence supporting the claim of a "small world.“ –People in the United States seemed to be connected by approximately six friendship links, on average Milgram's experiment –sent 60 letters from Omaha, Nebraska to Sharon, Massachasetts –The participants could only pass the letters (by hand) to personal they thought might be able to reach the target — whether directly or via a "friend of a friend“ –50 people responded –only three letters eventually reached their destination The expression “six degrees of separation” was born

21. The Small World Effect Stanley Milgram, 1967, Harvard University 60 letters sent to randomly chosen people in Nebraska Pass the letters to a target person in Boston using only intermediaries known to one another on a first-name basis. Each person passed the letter to a friend whom he/she thought might bring the letter closest to the target; the friend would then pass it on to another friend and so on until the letter reached the target person. 42 letters made it through via a median number of just 5.5 intermediaries.

22. Small-World Phenomena Milgram’s six degrees of separation (1967): “It’s a small world” Forwarding of letters from Nebraska to Massachusetts: Forward message to someone “closer” to the target

23. The Kevin Bacon Game “ Six Degrees of Kevin Bacon ” Invented in 1994 by two students at Albright College The goal is to link any actor to Kevin Bacon Through no more than six connections –where two actors are connected if they have appeared in a movie together

24. The Power-Law Graphs Highly clustered, short paths “short cuts”: long range edges Milgram Experiment: High-degree nodes are crucial for short paths

25. Connectivity of Gnutella (The small-world effect)