Spatial gossip and resource location protocols

The dynamic behavior of a network in which information is changing continuously over time requires robust and efficient mechanisms for keeping nodes updated about new information. Gossip protocols are mechanisms for this task in which nodes communicate with one another according to some underlying deterministic or randomized algorithm, exchanging information in each communication step. In a variety of contexts, the use of randomization to propagate information has been found to provide better reliability and scalability than more regimented deterministic approaches. In many settings --- consider a network of sensors, or a cluster of distributed computing hosts --- new information is generated at individual nodes, and is most “interesting” to nodes that are nearby. Thus, we propose distance-based propagation bounds as a performance measure for gossip algorithms: a node at distance d from the origin of a new piece of information should be able to learn about this information with a delay that grows slowly with d, and is independent of the size of the network. For nodes arranged with uniform density in Euclidean space, we present natural gossip algorithms that satisfy such a guarantee: new information is spread to nodes at distance \DIST, with high probability, in O(\log^{1 + \ve} \DIST) time steps. Such a bound combines the desirable qualitative features of uniform gossip, in which information is spread with a delay that is logarithmic in the full network size, and deterministic flooding, in which information is spread with a delay that is linear in the distance and independent of the network size. Our algorithms and their analysis resolve a conjecture of Demers et al. We show an application of our gossip algorithms to a basic resource location problem, in which nodes seek to rapidly