A Fixed Parameter Algorithm for Minimum Weight Triangulation: Analysis and Experiments
Magdalene Grantson, Christian Borgelt, Christos Levcopoulos · 2005
Abstract. We discuss and compare four fixed parameter algorithms for finding the minimum weight triangulation of a simple polygon with (n − k) vertices on the perimeter and k vertices in the interior (hole vertices), that is, for a total of n vertices. All four algorithms rely on the same abstract divide-and-conquer scheme, which is made efficient by a variant of dynamic programming. They are essentially based on two simple observations about triangulations, which give rise to triangle splits and paths splits. While each of the first two algorithms uses only one of these split types, the last two algorithms combine them in order to achieve certain improvements and thus to reduce the time complexity. By discussing this sequence of four algorithms we try to bring out the core ideas as clearly as possible and thus strive to achieve a deeper understanding of these approaches as well as simplified specifications. In addition, we implemented all four algorithms in Java and report results of experiments we carried out with this implementation. 1