Sub-linear Universal Spatial Gossip Protocols

Gossip protocols are communication protocols in which, periodically, every node of a network exchanges information with some other node chosen according to some (randomized) strategy. These protocols have recently found various types of applications for the management of distributed systems. Spatial gossip protocols are gossip protocols that use the underlying spatial structure of the network, in particular for achieving the ”closest-first” property. This latter property states that the closer a node is to the source of a message the more likely it is to receive this message within a prescribed amount of time. Spatial gossip protocols find many applications, including the propagation of alarms in sensor networks, and the location of resources in P2P networks. We design a sub-linear spatial gossip protocol for arbitrary graphs metric. More specifically, we prove that, for any graph metric with maximum degree Δ, for any source s and any ball centered at s with size b, new information is spread from s to all nodes in the ball within $O( (\sqrt {b \log b}\, \log \log b + \Delta) \log b )$ rounds, with high probability. Moreover, when applied to general metrics with uniform density, the same protocol achieves a propagation time of O(log2bloglogb) rounds.