Optimal Circle Search Despite the Presence of Faulty Robots

We consider (n, f)-search on a circle, a search problem of a hidden exit on a circle of unit radius for \(n > 1\) robots, f of which are faulty. All the robots start at the centre of the circle and can move anywhere with maximum speed 1. During the search, robots may communicate wirelessly. All messages transmitted by all robots are tagged with the robots’ unique identifiers which cannot be corrupted. The search is considered complete when the exit is found by a non-faulty robot (which must visit its location) and the remaining non-faulty robots know the correct location of the exit.