P2P Topologies CentralizedCentralized RingRing HierarchicalHierarchical DecentralizedDecentralized HybridHybrid

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

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

Centralized Topology

Ring Topology

Hierarchical Topology

Decentralized Topology

Hybrid Topology Centralized + Ring

Hybrid Topology Centralized + Decentralized

Evaluating topologies ManageabilityManageability –How hard is it to keep working? Information coherenceInformation coherence –How authoritative is info? (Auditing, non- repudiation) ExtensibilityExtensibility –How easy is it to grow? Fault toleranceFault tolerance –How well can it handle failures?

Evaluating topologies Resistance to legal interventionResistance to legal intervention –How hard is it to shut down? (Can be good or bad) SecuritySecurity –How hard is it to subvert? ScalabilityScalability –How big can it grow?

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?

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

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

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 Theoretically yes

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

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 Usually Best architecture for P2P networks

Small Word Phenomenon The small world phenomenonThe small world phenomenon (also known as the small world effect) (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

Early conceptions of the six degrees idea The "shrinking world" of Frigyes Karinthy (Hungarian), 1929The "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 Earthselect 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 friendsusing 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

Six Degrees of Separation Stanley Milgram was an American researcher in experimental social psychology at Harvard University in Boston, USAStanley Milgram was an American researcher in experimental social psychology at Harvard University in Boston, USA Stanley Milgram's small world experiments (1967)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 did not use the term „six degrees of separatio n Milgram's experimentMilgram'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 bornThe expression “six degrees of separation” was born

The Small World Effect Pass the letters to a target person in Boston using only intermediaries known to one another on a first-name basisPass 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 personEach 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 intermediaries42 letters made it through via a median number of just 5.5 intermediaries Milgram’s six degrees of separation: “It’s a small world”Milgram’s six degrees of separation: “It’s a small world”

One possible path of a message in the Small World experiment

The Power-Law Graphs Highly clustered, short pathsHighly clustered, short paths “short cuts”: long range edges“short cuts”: long range edges High-degree nodes are crucial for short pathsHigh-degree nodes are crucial for short paths

Connectivity of Gnutella (The small-world effect)