We challenge the idea that edge insertions are local improvement operations and show that the edge-insertion algorithm must sometimes insert an edge between vertices that are at the farthest combinatorial distance apart, and that this edge must also cross linearly many edges of the triangulation for the algorithm to escape a local optimum and return the optimal triangulation.

翻译：我们挑战了边插入是局部改进操作的传统观点，并证明边插入算法有时必须在组合距离最远的顶点之间插入一条边，且该边必须穿过三角剖分中线性数量的边，才能使算法脱离局部最优并返回最优三角剖分。