Minimum disc cover set construction in mobile ad hoc networks

The minimum disc cover set can be used to construct the dominating set on the fly for energy-efficient communications in mobile ad hoc networks. The approach used to compute the minimum disc cover set proposed in previous study has been considered too expensive. In this paper, we show that the disc cover set problem is in fact a special case of the general α-hull problem. In addition, we prove that the disc cover set problem is not any easier than the α-hull problem by linearly reducing the element uniqueness problem to the disc cover set problem. In addition to the known α-hull approach, we provide an optimal divide-and-conquer algorithm that constructs the minimum disc cover set for arbitrary cases, including the degenerate ones where the traditional α-hull algorithm incapable of handling.