Using Mobile Relays to Strongly Connect a Minimum-Power Network between Terminals Complying with No-Transmission Zones

We present strategies for placing a swarm of mobile relays to provide a bi-directional wireless network that connects fixed (immobile) terminals. Neither terminals nor relays are permitted to transmit into disk-shaped no-transmission zones. We assume a planar environment and that each transmission area is a disk centered at the transmitter. We seek a strongly connected network between all terminals with minimal total cost, where the cost is the sum area of the transmission disks. Results for networks with increasing levels of complexity are provided. The solutions for local networks containing low numbers of relays and terminals are applied to larger networks. For more complex networks, algorithms for a minimum-spanning tree (MST) based procedure are implemented to reduce the solution cost. A procedure to characterize and determine the possible homotopies of a system of terminals and obstacles is described, and used to initialize the evolution of the network under the presented algorithms.