It is also possible to formulate a version of the point set or polygon triangulation problems in which one is allowed to add Steiner points, extra vertices, in order to reduce the total edge length of the resulting triangulations. In some cases, the resulting triangulation may be shorter than the minimum weight triangulation by as much as a linear factor. It is possible to approximate the minimum weight Steiner triangulation of a point set to within a constant factor of optimal, but the constant factor in the approximation is large..
