  We consider the problem of tracking $n$ targets in the plane using $2n$
cameras. We can use two cameras to estimate the location of a target. We are
then interested in forming $n$ camera pairs where each camera belongs to
exactly one pair, followed by forming a matching between the targets and camera
pairs so as to best estimate the locations of each of the targets. We consider
a special case of this problem where each of the cameras are placed along a
horizontal line $l$, and we consider two objective functions which have been
shown to give good estimates of the locations of the targets when the distances
between the targets and the cameras are sufficiently large. In the first
objective, the value of an assignment of a camera pair to a target is the
tracking angle formed by the assignment. Here, we are interested in maximizing
the sum of these tracking angles. A polynomial time 2-approximation is known
for this problem. We give a quasi-polynomial time algorithm that returns a
solution whose value is at least a $(1-\epsilon)$ factor of the value of an
optimal solution for any $\epsilon > 0$. In the second objective, the cost of
an assignment of a camera pair to a target is the ratio of the vertical
distance between the target and $l$ to the horizontal distance between the
cameras in the camera pair. In this setting, we are interested in minimizing
the sum of these ratios. A polynomial time 2-approximation is known for this
problem. We give a quasi-polynomial time algorithm that returns a solution
whose value is at most a $(1+\epsilon)$ factor of the value of an optimal
solution for any $\epsilon > 0$.
