Implementations of the LMT heuristic for minimum weight triangulation

Abstract

No polynomial-time algorithm is known to compute the minimum weight triangulation (MWT) of a finite planar point set. In this paper we present efficient implementations of the LMT-skeleton heuristic, which identifies edges that must be, and cannot be, in an MWT. For uniformly distributed points, we can compute the exact MWT of tens of thousands of points in minutes. These results are obtained by improving the asymptotic time and memory usage of the LMT-skeleton heuristic and of filters that identify initial candidate edges, and also by bucketing and further tuning for evenly distributed points. Further details and an implementation as a macro for the IPE drawing program are available on the web: http://www.cs.ubc.ca/spider/snoeyink/mwt.