Modeling and Approximating the Visit of a Set of Sites With a Fleet of UAVs

In this paper, we consider the problem of flying over an area affected by a natural disaster (e.g. an earthquake) with a fleet of self-piloting unmanned aerial vehicles with cameras or other kinds of sensors on board; the aim is to acquire knowledge of the situation before rescuers start working. We model this situation as a new graph theoretical problem; then, we study its complexity providing an approximation ratio that becomes constant in some special (though practically reasonable) cases; finally, we put in relation the approximability of this new problem and of a well-known one. To the best of our knowledge, no previous work has ever considered all together the constraints we take into account from a theoretical point of view, so this is the first very general graph theoretical model for this problem.