The Edge- ipping Distance of Triangulations

An edgeipping operation in a triangulation T of a set of points in the plane is a local restructuring that changes T into a triangulation that di ers from T in exactly one edge. The edgeipping distance between two triangulations of the same set of points is the minimum number of edgeipping operations needed to convert one into the other. In the context of computing the rotation distance of binary trees Sleator, Tarjan, and Thurston show an upper bound of 2n 10 on the maximum edgeipping distance between triangulations of convex polygons with n nodes, n > 12. Using volumetric arguments in hyperbolic 3-space they prove that the bound is tight. In this paper we establish an upper bound on the edgeipping distance between triangulations of a general nite set of points in the plane by showing that no more edgeipping operations than the number of intersections between the edges of two triangulations are needed to transform these triangulations into another, and we present an algorithm that computes such a sequence of edgeipping operations.