Efficient and robust communication topologies for distributed decision making in networked systems

Distributed decision making in networked systems depends critically on the timely availability of critical fresh information. Performance of networked systems, from the perspective of achieving goals and objectives in a timely and efficient manner is constrained by their collaboration and communication structures and their interplay with the networked system´s dynamics. In most cases achieving the system objectives requires many agent to agent communications. A reasonable measure for system robustness to communication topology change is the number of spanning trees in the graph abstraction of the communication system. We address the problem of network formation with robustness and connectivity constraints. Solutions to this problem have also applications in trust and the relationship of trust to control. We show that the general combinatorial problem can be relaxed to a convex optimization problem. We solve the special case of adding a shortcut to a given structure and provide insights for derivation of heuristics for the general case. We also analyze the small world effect in the context of abrupt increases in the number of spanning trees as a result of adding a few shortcuts to a base lattice in the Watts-Strogatz framework and thereby relate efficient topologies to small world and expander graphs.