Hamiltonian Quantized Gossip

The main contribution of this paper is an algorithm to solve the quantized consensus problem over networks represented by Hamiltonian graphs, i.e., graphs containing a Hamiltonian cycle. The algorithm is proved to converge almost surely to a finite set containing the optimal solution. A worst case study of the average convergence time is carried out, thus proving the efficiency of the algorithm with respect to other solutions recently presented in the literature. Moreover, the algorithm has a decentralized stop criterion once the convergence set is reached.