Geometric three-dimensional assignment problems

We investigate two geometric special cases of the three-dimensional assignment problem: given are three sets B, R and G (blue, red and green) each containing n grid points in the Euclidean plane. We want to find a partition of B• R• G into n three-colored triangles such that (a) the total circumference of all triangles or (b) the total area of all triangles becomes minimum. Both versions of the problem are proved to be NP-hard.