Distributed Uniform Sampling in Unstructured Peer-to-Peer Networks

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Abstract
Uniform sampling in networks is at the core of a wide variety of randomized algorithms. Random sampling can be performed by modeling the system as an undirected graph with associated transition probabilities and defining a corresponding Markov chain (MC). A random walk of prescribed minimum length, performed on this graph, yields a stationary distribution, and the corresponding random sample. This sample, however, is not uniform when network nodes have a non-uniform degree distribution. This poses a significant practical challenge since typical large scale real-world unstructured networks tend to have non-uniform degree distributions, e.g., power-law degree distribution in unstructured peer-to-peer networks. In this paper, we present a distributed algorithm that enables efficient uniform sampling in large unstructured non-uniform networks. Specifically, we prescribe necessary conditions for uniform sampling in such networks and present distributed algorithms that satisfy these requirements. We empirically evaluate the performance of our algorithm in comparison to known algorithms. The performance parameters include computational complexity, length of random walk, and uniformity of the sampling. Simulation results support our claims of performance improvements due to our algorithm.

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