Design of communication networks for distributed computation with privacy guarantees

In this paper we address a communication network design problem for distributed computation with privacy guarantees. More precisely, given a possible communication graph between different agents in a network, the objective is to design a protocol, by proper selection of the weights in the dynamics induced by the communication graph, such that 1) weighted average consensus of the initial states of all the agents will be reached; and 2) there are privacy guarantees, where each agent is not able to retrieve the initial states of non-neighbor agents, with the exception of a small subset of agents (that will be precisely characterized). In this paper, we assume that the network is cooperative, i.e., each agent is passive in the sense that it executes the protocol correctly and does not provide incorrect information to its neighbors, but may try to retrieve the initial states of non-neighbor agents. Furthermore, we assume that each agent knows the communication protocol.