The Focus of Attention Problem Revisited

The Focus of Attention (FOA) Problem is, given a set of targets and a set of sensors in the plane, to track the targets with ‘maximum possible accuracy’. The accuracy is measured in terms of the angle subtended by the sensor pairs at the assigned targets. In this paper, we consider a scenario in which we are given n targets on a line l and 2n sensors on a line m such that l || m and the objective is to assign sensor-pairs to the targets such that the minimum angle subtended at the targets is maximized. We give a polynomial time algorithm for a restricted version of this problem and also study some properties of the optimal solution. To our knowledge, no deterministic and exact polynomial time algorithm is known for any non-trivial version of the FOA problem when the accuracy is measured in terms of the angles subtended by the sensor pairs.