Let T be a triangulation of a simple polygon. A flip in T is the operation of removing one diagonal of T and adding a different one such that the resulting graph is again a triangulation. The flip distance between two triangulations is the smallest number of flips required to transform one triangulation into the other. For the special case of convex polygons, the problem of determining the shortest flip distance between two triangulations is equivalent to determining the rotation distance between two binary trees, a central problem which is still open after over 25 years of intensive study. We show that computing the flip distance between two triangulations of a simple polygon is NP-complete. This complements a recent result that shows APX-hardness of determining the flip distance between two triangulations of a planar point set.
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机译:假设简单多边形的三角测量。 TIP IN T是移除T对角线的操作并添加不同的操作,使得所得到的图形再次成为三角剖分。两个三角形之间的翻转距离是将一个三角测量转换为另一个三角测量所需的最小次数。对于凸多边形的特殊情况,确定两个三角形之间的最短翻转距离的问题相当于确定两个二元树之间的旋转距离,在超过25年的密集研究后仍然打开的核心问题。我们表明计算简单多边形的两个三角形之间的翻转距离是NP-Complete。这补充了最近的结果,该结果显示了确定平面点的两个三角形之间的翻转距离的APX硬度。
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