We study approximation algorithms for the following geometric version of the maximum coverage problem: Let P be a set of n weighted points in the plane. Let D represent a planar object, such as a rectangle, or a disk. We want to place m copies of D such that the sum of the weights of the points in P covered by these copies is maximized. For any fixed ε > 0, we present efficient approximation schemes that can find a (1 − ε)-approximation to the optimal solution. In particular, for m = 1 and for the special case where D is a rectangle, our algorithm runs in time O(n log(
The problem to place m rectangles such that the sum of the weights of the points in P covered by these rectangles is maximized is considered in REF .
Linear Time Approximation Schemes for Geometric Maximum Coverage
Computer Science