by James Aspnes, Zo E Diamadi, Gauri Shah
In 21st ACM Symp. on Principles of Distributed Computing (PODC
http://www.cs.yale.edu/homes/aspnes/podc02-proceedings.ps
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Abstract:
We consider the problem of designing an overlay network and routing mechanism that permits nding resources eciently 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 identi ers, 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 [5], is close to optimal. We also give heuristics to eciently maintain a network supporting ecient routing as nodes enter and leave the system. Finally, we give some experimental results that suggest promising directions for future work. 1.
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