An optimal algorithm for the minimum disc cover problem

Abstract

The minimum disc cover can be used to construct a dominating set on the fly for energy-efficient communications in mobile ad hoc networks, but the approach used to compute the minimum disc cover proposed in previous studies is computationally relatively expensive. In this paper, we show that the disc cover problem is in fact a special case of the general alpha-hull problem. In spite of being a special case, the disc cover problem is not easier than the general alpha-hull problem. In addition to applying the existing alpha-hull algorithm to solve the disc cover problem, we present a simple, yet optimal divide-and-conquer algorithm that constructs the minimum disc cover for arbitrary cases, including those degenerate cases where the alpha-hull approach would fail.