文章基本信息

标题：The Edge-Flipping Distance of Triangulations
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作者：Sabine Hanke ; Thomas Ottmann ; Sven Schuierer 等
期刊名称：Journal of Universal Computer Science
印刷版ISSN：0948-6968
出版年度：1996
卷号：2
期号：8
页码：570-579
出版社：Graz University of Technology and Know-Center
摘要：An edge-flipping operation in a triangulation T of a set of points in the plane is a local restructuring that changes T into a triangulation that differs from T in exactly one edge. The edge-flipping distance between two triangulations of the same set of points is the minimum number of edge-flipping 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 edge-flipping 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-flipping distance between triangulations of a general finite set of points in the plane by showing that no more edge-flipping 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-flipping operations.