 
Summary: Greedy Routing in PeertoPeer Systems
James Aspnes
Zoše Diamadi
Gauri Shah§
June 22, 2006
Abstract
We consider the problem of designing an overlay network and routing mechanism that per
mits finding resources efficiently in a peertopeer system. We argue that many existing ap
proaches 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 peertopeer system where nodes are embedded at grid points in a simple
metric space: a onedimensional 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 powerlaw distributions in routing, as suggested by Kleinberg [10],
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.
1 Introduction
