Optimal Arrangements for Assembling a Network in an Emergency

In many situations, especially those surrounding emergencies, the fast assembly of a set of actors is an important prerequisite for planning and subsequent action. For example, a search team, human or robotic, first needs to convene. What shape is optimal if the goal is the establishment of full communication as soon as possible? We consider spirals, concentric circles and tree-like structures and show analytically how a spiral shape minimizes the maximum distance to be traveled. We also discuss how other shapes can provide a higher degree of communication redundancy. These results, which have parallels in biological systems, suggest new ways that sensor networks might be envisioned.