Piotr Sankowski

Consider k mobile robots inside a circular disk of unit radius. The robots are required to evacuate the disk through an unknown exit point situated on its boundary. We assume all robots having the same (unit) maximal speed and  starting at the centre of the disk. The robots may communicate in order to inform themselves about the presence (and its position) or the absence of an exit. The goal is for all the robots to evacuate
through the exit in minimum time.

We consider two  models of communication between the robots: in non-wireless (or local) communication model robots exchange information only when simultaneously located at the same point, and wireless communication in which robots can communicate one another at any time.

We study the following question what is the optimal evacuation time for k robots?