Converging Quickly to Independent Uniform Random Topologies

The peer sampling service is a core building block for gossip protocols in peer-to-peer networks. Ideally, a peer sampling service continuously provides each peer with a sample of peers picked uniformly at random in the network. While empirical studies have shown that uniformity was achieved, analysis proposed so far assume strong restrictions on the topology of the overlay network it continuously generates. In this work, we analyze a Generic Random Peer Sampling Service (GRPS) that satisfies the desirable properties for any peer sampling service–small views, uniform sample, load balancing, and independence– and relieve strong degree connections in the nodes assumed in previous works. The main result we prove is: starting from any simple (without loops and parallel edges) directed graph with out-degree equal to c for all nodes, and recursively applying GRPS, eventually results in a random simple directed graph with out-degree equal to c for all nodes. We test empirically convergence time and independence time for GRPS. Finally, We use this empirical evaluation to show that GRPS performs better than previously presented peer sampling services.