On exclusion regions for optimal triangulations

An exclusion region for a triangulation is a region that can be placed around each edge of the triangulation such that the region can not contain points from the set on both sides of the edge. We survey known exclusion regions for several classes of triangulations, including Delaunay, Greedy, and Minimum Weight triangulations. We then show an exclusion region of larger area than was previously known for the Minimum Weight triangulation, which signiicantly speeds up an algorithm of Beirouti and Snoeyink. We also show that no exclusion region exists for the general class of Locally Optimal Triangulations, in which every triangulation edge optimally triangulates the region determined by its two incident triangles.