Today I read a paper titled “Fault-tolerant routing in peer-to-peer systems”
The abstract is:
We consider the problem of designing an overlay network and routing mechanism that permits finding resources efficiently in a peer-to-peer system.
We argue that many existing approaches to this problem can be modeled as the construction of a random graph embedded in a metric space whose points represent resource identifiers, where the probability of a connection between two nodes depends only on the distance between them in the metric space.
We study the performance of a peer-to-peer system where nodes are embedded at grid points in a simple metric space: a one-dimensional real line.
We prove upper and lower bounds on the message complexity of locating particular resources in such a system, under a variety of assumptions about failures of either nodes or the connections between them.
Our lower bounds in particular show that the use of inverse power-law distributions in routing, as suggested by Kleinberg (1999), is close to optimal.
We also give efficient heuristics to dynamically maintain such a system as new nodes arrive and old nodes depart.
Finally, we give experimental results that suggest promising directions for future work.