James Aspnes, Zoë Diamadi, and Gauri Shah. Fault-tolerant routing in peer-to-peer systems. Twenty-First ACM Symposium on Principles of Distributed Computing, July 2002, pp. 223–232. Available as arXiv:cs.DS/0302022.
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 heuristics to efficiently maintain a network supporting efficient routing as nodes enter and leave the system. Finally, we give some experimental results that suggest promising directions for future work.
@inproceedings(AspnesDS2002,
title="Fault-tolerant routing in peer-to-peer systems",
author="James Aspnes and Zo{\"e} Diamadi and Gauri Shah",
booktitle="Twenty-First ACM Symposium on Principles of Distributed Computing",
month=jul,
year=2002,
pages={223--232}
)