Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Serdica Journal of Computing, Vol. 4, No 3, (2010), 335p-348p
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.
