Unique Coverage with Rectangular Regions

We study unique coverage problems with rectangle and half-strip regions, motivated by wireless networks in the context of coverage using directional antennae without interference. Given a set C of points (clients) and a set A of directional antennae in the plane, the goal is to assign a direction to each directional antenna in A, such that the number of clients in C that are uniquely covered by the directional antennae is maximized. A client is covered uniquely if it is covered by exactly one antenna. We consider two types of rectangular regions representing half-strip directional antennae: unbounded half-strips and half-strips bounded by a range r (i.e., 3-sided rectangular regions and rectangular regions). The directional antennae can be directed up or down. We present two polynomial time algorithms: an optimal solution for the problem with the 3-sided rectangular regions, and a constant factor approximation for the rectangular regions.