Uniform sampling for directed P2P networks

Abstract

Selecting a random peer with uniform probability across a peer-to-peer (P2P) network is a fundamental function for unstructured search, data replication, and monitoring algorithms. Such uniform sampling is supported by several techniques. However, current techniques suffer from sample bias and limited applicability. In this paper, we present a sampling algorithm that achieves a desired uniformity while making essentially no assumptions about the underlying P2P network. This algorithm, called doubly stochastic converge (DSC), iteratively adjusts the probabilities of crossing each link in the network during a random walk, such that the resulting transition matrix is doubly stochastic. DSC is fully decentralized and is designed to work on both directed and undirected topologies, making it suitable for virtually any P2P network. Our simulations show that DSC converges quickly on a wide variety of topologies, and that the random walks needed for sampling are short for most topologies. In simulation studies with FreePastry, we show that DSC is resilient to high levels of churn, while incurring a minimal sample bias. © 2009 Springer.