Complexity of the bisection method
The bisection method is the consecutive bisection of a triangle by the median of the longest side. In this paper we prove a subexponential asymptotic upper bound for the number of similarity classes of triangles generated on a mesh obtained by iterative bisection, which previously was known only to be finite. The relevant parameter is / , where is the biggest and is the smallest angle of the triangle.We get this result by introducing a taxonomy of triangles that precisely captures the behaviour of the bisection method.We also prove that the number of directions on the plane given by the sides of the triangles generated is finite. Additionally, we give purely geometrical and intuitive proofs of classical results for the bisection method.
The work of the third author was partially financed by Proyecto Fondecyt 1040713. The triangulations were obtained by Carlo Calderon.
Quote ItemTHEORETICAL COMPUTER SCIENCE, v.: 382, issue: 2, p.: 131-138, AUG 31 2007