Gossip-Based Computation of Aggregation Information. David Kempe Alin Dobra Johannes Gehrke Presented by Hao Zhou. Content. Introduction Gossip-based Algorithm Analyze Gossip-based Algorithm. Introduction. Peer to peer network Unstructured network Gnutella, Napster Structured network
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
Presented by Hao Zhou
Analyze Gossip-based Algorithm
Peer to peer network
such as Pastry, Chord, Tepastry, CAN
Advantages of DHT-based systems
Fast: O (log n)
Can exactly find a publishing object in a gigantic network space
Define a variance error= | Xeavg-Xavg |
Our objective is to make the variance close to 0
Calculate the converge speed of this variance
In every round, the variance drops to less than half its previous value
var(t+1) = ( ) var(t)
Gossip-based algorithm is an approximation method
We can control the accuracy
Xeavg never = Xavg, but Xeavg can be very close to Xavg
When variance error=| Xeavg – Xavg| <= ε, we can say Xeavg is Xavg.
Roughly say, after O(logn+log(1/ ε)) rounds, can we say variance error <= ε in every node
Maybe there are broken network connections
We have to control the percentage of nodes who obtain err<=ε
We say with probability at least 1-δ,
after O(logn+log(1/ε)+log(1/δ)) rounds,
The err=|Xeavg – Xavg| <= ε
The diffusion speed of uniform gossip is O(logn+log(1/ε)+log(1/δ)) , with probability at least 1- δ, and variance error <= ε
Algorithm is very simple
Converge speed is very fast
Can automatically adjust itself
Nodes join the network
Nodes leave the network
From their theory, we know after O(logn+log(1/ε)+ log(1/δ)) rounds,
the estimation average value in a local node can be see as a global average value.
But in practice, If we do not know the size of the network, how do we know how many rounds a estimation average value is close enough to the real average value.