A large subgraph of the minimum weight triangulation

Abstract

We present an O(n4)-time and O(n2)-space algorithm that computes a subgraph of the minimum weight triangulation (MWT) of a general point set. The algorithm works by finding a collection of edges guaranteed to be in any locally minimal triangulation. We call this subgraph the LMT-skeleton. We also give a variant called the modified LMT-skeleton that is both a more complete subgraph of the MWT and is faster to compute requiring only O(n2) time and O(n) space in the expected case for uniform distributions. Several experimental implementations of both approaches have shown that for moderate-sized point sets (up to 350 points1 ) the skeletons are connected, enabling an efficient completion of the exact MWT. We are thus able to compute the MWT of substantially larger random point sets than have previously been computed.