Fixed Parameter Algorithms for the Minimum Weight Triangulation Problem

Published as Technical Report LU-CS-TR:2005-238 on February 13, 2006, ISSN 1650-1276 Report 158, Lund University, Sweden 2006 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 tract 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...

• Type: Journal
• Year: 2008
• Where: IJCGA
• Authors: Magdalene G. Borgelt, Christian Borgelt, Christos Levcopoulos
• Keywords: Algorithms, IJCGA 2008, Issn 1650-1276 Report, Minimum Weight Triangulation