How Many Target Points Can Replace a Target Area?

In wireless sensor network, each sensor can monitor an area, which is a disk with center at the sensor. Considering a set of sensors and given a target area, how do we select a subset of sensors to monitor the target area?Note that a whole area is monitored (or say covered) if every point in the area is covered. We cannot check at every point. Usually, one selects a set of points in the target area, called target points, such that the target area is covered by a subset of sensors if and only if all target points are covered.The question is how many target points can replace a target area in such a way? The existing method needs O(n2) target points when n sensors are considered. In this paper, we propose a method to reduce this number. This would improve the performance of wireless sensor networks.