Coordination Through Stochastic Channels

We consider a stochastic network model consisting of a set of n synchronous processes communicating by message passing. In each round, processes send messages directly to each other over a complete communication graph. The processes do not fail, but messages can be lost. Each message is delivered with probability p, for a given parameter p ∈ [0, 1]. We study the following optimization version of approximate agreement in this model. We assume that processes start with binary input values, execute an algorithm for a fixed number of rounds, and decide values in [0, 1] satisfying the usual validity requirement stating that if all processes start with the same input value, then they should all decide that value. We propose deterministic algorithms that minimize the expected discrepancy, namely, the expected maximum distance between the decided values. We also present lower bounds on the expected discrepancy, which demonstrate the optimality of our algorithms for two processes. Finally, we present applications of our algorithms to solve randomized consensus and randomized approximate agreement.