Distributed tracking of graph parameters in anonymous networks with time-varying topology

In this paper, we propose a distributed protocol for multi-agent systems to estimate and track changes to the diameter, and radius of a network with time-varying topology, as well as the eccentricity of each agent within it. The main strengths of the proposed protocol are its finite-time convergence and robustness to re-initialization, i.e., if there are changes in the network topology or in the agents' states during the protocol execution then it does not need to be re-initialized to converge to the correct estimation at the steady-state. The expected estimation error of the protocol can be traded-off by increasing the size of locally exchanged messages. We provide a theoretical characterization of the expected steady-state error and some numerical simulations.