Minimum weight triangulation by cutting out triangles

Summary, in English

We describe a fixed parameter algorithm for computing the minimum weight triangulation (MWT) of a simple polygon with (n - k) vertices on the perimeter and k hole vertices in the interior, that is, for a total of n vertices. Our algorithm is based on cutting out empty triangles (that is, triangles not containing any holes) from the polygon and processing the parts or the rest of the polygon recursively. We show that with our algorithm a minimum weight triangulation can be found in time at most O(n(3)k! k), and thus in O(n(3)) if k is constant. We also note that k! can actually be replaced by b(k) for some constant b. We implemented our algorithm in Java and report experiments backing our analysis.

• Författare: Magdalene Grantson Borgelt; C Borgelt; Christos Levcopoulos
• Avdelning/ar: Computer Science
• Publiceringsår: 2005
• Språk: Engelska
• Sidor: 984-994
• Publikation/Tidskrift/Serie: Algorithms and computation / Lecture notes in computer science
• Volym: 3827
• Länkar: http://dx.doi.org/10.1007/11602613_98
• Dokumenttyp: Konferensbidrag
• Förlag: Springer
• Ämne: Computer Science
• Conference name: 16th International Symposium, ISAAC 2005
• Conference date: 2005-12-19 - 2005-12-21
• Conference place: Sanya, Hainan, China
• Status: Published
• Projekt: VR 2002-4049
• ISBN/ISSN/Övrigt: ISSN: 1611-3349; ISSN: 0302-9743; ISBN: 978-3-540-30935-2