A new heuristic for minimum weight triangulation

A new heuristic for minimum weight triangulation of planar point sets is proposed. First, a polygon whose vertices are all points from the input set is constructed. Next, a minimum weight triangulation of the polygon is found by dynamic programming. The union of the polygon triangulation with the polygon yields a triangulation of the input n-point set. A nontrivial upper bound on the worst-case performance of the heuristic in terms of n and another parameter is derived. Under the assumption of uniform point distribution it is observed that the heuristic yields a solution within the factor of $O(\log n)$ from the optimum almost certainly, and the expected length of the resulting triangulation is of the same order as that of a minimum length triangulation. The heuristic runs in time $O(n^3 )$ .