AN APPROXIMATION ALGORITHM FOR LOCATING MAXIMAL DISKS WITHIN CONVEX POLYGONS
This paper considers a problem of locating the given number of disks into a container no that the area covered by the disks is maximized. In the problem, the radii of the disks can be changed arbitrarily unless they overlap outside of the container, and the disks are allowed to overlap with each other. We present an approximation algorithm for this problem assuming that the container is a convex polygon. Our algorithm achieves approximation ratio (0.78 - epsilon) for any small epsilon > 0. Since the computation tine of our algorithm depends on the number of corners of the convex polygon exponentially, we also give a heuristic to reduce the number of corners.
convex polygon disk packing disk covering