Global convergence in partially fully connected networks (PFCN) with limited relays

Approximate agreement (AA) is one form of distributed agreement, in which the network nodes, by exchanging their local values, need to agree on values which are approximately equal to each other. The study on the AA problem in partially connected networks has been very limited. More specifically, no solution to the AA problem exists for such networks. This paper solves the AA problem for a specific, scalable, partially connected network with limited relays. The results show low communication costs in comparison to fully connected networks. The network can also take advantage of the results available for fully connected networks, thus finding the expressions for convergence rate and fault tolerance becomes relatively easy.