The theorem that the edge on which the distance between two set of points in the plane decides is one of the edges of the Voronoi disgrams's Delaunay triangulations is the key of this paper. On the basis of this theorem

the paper proposes how to compute the distance between two set of points in the plane by means of Voronoi dasgrams's Delaunay triangulations.Moreover

it also analyzes the complexity of the algorithm.