Computing the Line-Constrained k-center in the Plane for Small k.

In this paper, we study the line-constrained k-center problem in the Euclidean plane. Given a set of demand points and a line L, the problem asks for k points, called center facilities, on L, such that the maximum of the distances from the demand points to their closest center facilities is minimized. For any fixed k, we propose an algorithm with running time linear to the number of demand points.