The Edge--ipping Distance of Triangulations Institut F Ur Informatik | Report 76 *

An edge-ipping operation in a triangulation T of a set of points in the plane is a local restructuring that changes T into a triangulation that diiers from T in exactly one edge. The edge-ipping distance between two triangulations of the same set of points is the minimum number of edge-ipping operations needed to convert one into the other. In the context of computing the rotation distance of binary trees Sleator, Tarjan, and Thurston 7] show an upper bound of 2n ? 10 on the maximum edge-ipping 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 edge-ipping distance between triangulations of a general set of points in the plane by showing that not more edge-ipping 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 edge-ipping operations. Furthermore in the case of triangulations of convex polygons we present a combinatorical proof of a weaker lower bound of 3 2 n ? 5 with the aid of two triangulations.