Nomographic Gossiping for f-Consensus

Abstract : In this paper, we present a novel class of iterative gossip algorithms called nomographic gossiping that partly allow to efficiently achieve a rapid global consensus among nodes/agents in a clustered wireless network with respect to an arbitrary function of the initial states. The algorithms are based on the surprising fact that every real-valued multivariate function has a nomographic representation, which is simply a function of a superposition of a finite number of univariate functions. Since superpositions can be effectively generated via the wireless channel by letting nodes in a cluster transmit simultaneously their pre-processed states to a cluster head, the convergence speed can be significantly increased provided that some connectivity condition between clusters is fulfilled.