You can't get there from here: Sensor scheduling with refocusing delays

We study a problem in which a single sensor is scheduled to observe sites periodically, motivated by applications in which the goal is to maintain up-to-date readings for all the observed sites. In the existing literature, it is typically assumed that the time for a sensor switching from one site to another is negligible. This may not be the case in applications such as camera surveillance of a border, however, in which the camera takes time to pan and tilt to refocus itself to a new geographical location. We formulate a problem with refocusing delay constraints. We prove the problem to be NP-hard and then study a special case in which refocusing is proportional to some Euclidian metric. We give a lower bound on the optimal cost for the scheduling problem. Finally, we provide and experimentally evaluate several heuristic algorithms, some of them based on this computed lower bound.