Random walks in peer-to-peer networks: Algorithms and evaluation

We quantify the effectiveness of random walks for searching and construction of unstructured peer-to-peer (P2P) networks. We have identified two cases where the use of random walks for searching achieves better results than flooding: (a) when the overlay topology is clustered, and (b) when a client re-issues the same query while its horizon does not change much. Related to the simulation of random walks is also the distributed computation of aggregates, such as averaging. For construction, we argue that an expander can be maintained dynamically with constant operations per addition. The key technical ingredient of our approach is a deep result of stochastic processes indicating that samples taken from consecutive steps of a random walk on an expander graph can achieve statistical properties similar to independent sampling. This property has been previously used in complexity theory for construction of pseudorandom number generators. We reveal another facet of this theory and translate savings in random bits to savings in processing overhead.