Fixed parameter algorithms for the minimum weight triangulation problem
Grantson Borgelt, Magdalene LU ; Borgelt, Christian and Levcopoulos, Christos LU
(2008)
In International Journal of Computational Geometry and Applications
18(3).
p.185-220
- 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... (More)
- 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. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1254955
- author
- Grantson Borgelt, Magdalene
LU
; Borgelt, Christian
and Levcopoulos, Christos
LU
- organization
- publishing date
- 2008
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- divide-and-conquer algorithm, programming, dynamic, fixed parameter algorithm, minimum weight triangulation
- in
- International Journal of Computational Geometry and Applications
- volume
- 18
- issue
- 3
- pages
- 185 - 220
- publisher
- World Scientific Publishing
- external identifiers
-
- wos:000257540600002
- scopus:45749150320
- ISSN
- 0218-1959
- DOI
- 10.1142/S0218195908002581
- project
- VR 2005-4085
- language
- English
- LU publication?
- yes
- id
- 428efced-2903-4f93-9654-a65473b04f26 (old id 1254955)
- date added to LUP
- 2016-04-01 13:26:34
- date last changed
- 2022-01-27 19:14:14
@article{428efced-2903-4f93-9654-a65473b04f26,
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 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.}},
author = {{Grantson Borgelt, Magdalene and Borgelt, Christian and Levcopoulos, Christos}},
issn = {{0218-1959}},
keywords = {{divide-and-conquer algorithm; programming; dynamic; fixed parameter algorithm; minimum weight triangulation}},
language = {{eng}},
number = {{3}},
pages = {{185--220}},
publisher = {{World Scientific Publishing}},
series = {{International Journal of Computational Geometry and Applications}},
title = {{Fixed parameter algorithms for the minimum weight triangulation problem}},
url = {{http://dx.doi.org/10.1142/S0218195908002581}},
doi = {{10.1142/S0218195908002581}},
volume = {{18}},
year = {{2008}},
}