New algorithms and empirical findings on minimum weight triangulation heuristics (extended abstract)

number of edges points examined. The weight of a triangulation is the sum of the lengths of all the edges in the triangulation. A Mnimum Weight !f%iangtdation (MWT) of a point set S is a triangulation that minimizes weight over all possible triangulations. Wang and Aggarwal [19] and Baraquet and Sharir [1] use the MWT of simple polygons to reconstruct three dimensional objects from two dimensional contours (or slices). The MWT also arises in numerical analysis in a method suggested by Yoeli [20] for numerical approximation of bivariate data. Though it has been shown how to compute the MWT in time 0(n3) for the special case of n-vertex simple polygons [9], there are no known efficiently computable algorithms for the MWT of general point sets. We therefore seek efficiently computable approximations to the MWT, of which there are a number of heuristics. We report on the practical efficiency and effective nees of various of these heuristics including multiple algorithms for the greedy triangulation, other approaches to locally minimal triangulations, and some new algorithms that perform comparatively well. Our empirical findings come from a number of different tests. We report on triangulations of general points sets over random distributiona, as well as of simple polygons taken from an application to medical image proceaaingl. In addition to a comparison of run times and weights, we also analyze certain primitive operations such as the