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Fixed parameter algorithms for the minimum weight triangulation problem

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Author

Summary, in English

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 as well as a simpler specification of these approaches. In addition, we implemented all four algorithms in Java and report results of experiments we carried out with this implementation.

Department/s

  • Computer Science

Publishing year

2008

Language

English

Pages

185-220

Publication/Series

International Journal of Computational Geometry and Applications

Volume

18

Issue

3

Document type

Journal article

Publisher

World Scientific Publishing

Topic

  • Computer Science

Keywords

  • divide-and-conquer algorithm
  • programming
  • dynamic
  • fixed parameter algorithm
  • minimum weight triangulation

Status

Published

Project

  • VR 2005-4085

ISBN/ISSN/Other

  • ISSN: 0218-1959