Quadratic Time Computable Instances of MaxMin and MinMax Area Triangulations of Convex Polygons

Mirzoev, Tigran, and Vassilev, Tzvetalin. "Quadratic Time Computable Instances of MaxMin and MinMax Area Triangulations of Convex Polygons." Serdica Journal of Computing 4.3 (2010): 335-348. <http://eudml.org/doc/11393>.

@article{Mirzoev2010,
abstract = {We consider the problems of finding two optimal triangulations of a convex polygon: MaxMin area and MinMax area. These are the triangulations that maximize the area of the smallest area triangle in a triangulation, and respectively minimize the area of the largest area triangle in a triangulation, over all possible triangulations. The problem was originally solved by Klincsek by dynamic programming in cubic time [2]. Later, Keil and Vassilev devised an algorithm that runs in O(n^2 log n) time [1]. In this paper we describe new geometric findings on the structure of MaxMin and MinMax Area triangulations of convex polygons in two dimensions and their algorithmic implications. We improve the algorithm’s running time to quadratic for large classes of convex polygons. We also present experimental results on MaxMin area triangulation.},
author = {Mirzoev, Tigran, Vassilev, Tzvetalin},
journal = {Serdica Journal of Computing},
keywords = {Computational Geometry; Triangulation; Convex Polygon; Dynamic Programming; computational geometry; triangulation; convex polygon; dynamic programming},
language = {eng},
number = {3},
pages = {335-348},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Quadratic Time Computable Instances of MaxMin and MinMax Area Triangulations of Convex Polygons},
url = {http://eudml.org/doc/11393},
volume = {4},
year = {2010},
}

TY - JOUR
AU - Mirzoev, Tigran
AU - Vassilev, Tzvetalin
TI - Quadratic Time Computable Instances of MaxMin and MinMax Area Triangulations of Convex Polygons
JO - Serdica Journal of Computing
PY - 2010
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 4
IS - 3
SP - 335
EP - 348
AB - We consider the problems of finding two optimal triangulations of a convex polygon: MaxMin area and MinMax area. These are the triangulations that maximize the area of the smallest area triangle in a triangulation, and respectively minimize the area of the largest area triangle in a triangulation, over all possible triangulations. The problem was originally solved by Klincsek by dynamic programming in cubic time [2]. Later, Keil and Vassilev devised an algorithm that runs in O(n^2 log n) time [1]. In this paper we describe new geometric findings on the structure of MaxMin and MinMax Area triangulations of convex polygons in two dimensions and their algorithmic implications. We improve the algorithm’s running time to quadratic for large classes of convex polygons. We also present experimental results on MaxMin area triangulation.
LA - eng
KW - Computational Geometry; Triangulation; Convex Polygon; Dynamic Programming; computational geometry; triangulation; convex polygon; dynamic programming
UR - http://eudml.org/doc/11393
ER -