Before revision:  We present a deterministic O(n \log n)-time algorithm for the case that the centers of the two optimal disks are close together , that is, the overlap of the two optimal disks is a constant fraction of the disk area.
After revision:  We present a deterministic O(n \log n)-time algorithm for the case that the centers of the two optimal disks are close to each other , that is, the overlap of the two optimal disks is a constant fraction of the disk area.