将曲面最优切割成圆盘
Optimally cutting a surface into a disk
摘要：
我们考虑的问题，切割一组边缘的多面体流形表面，可能与边界，以获得一个单一的拓扑磁盘，最小化的切割边缘的总数或其总长度。我们表明，这个问题是NP-困难的，即使是没有边界的流形和穿孔的领域。我们还描述了一个运行时间为n^{O（g+k）}的算法，其中n是组合复杂度，g是亏格，k是输入曲面的边界分量数。最后，我们描述了一个贪心算法，输出一个O（log^2 g）-近似的最小割图在O（g^2 n log n）的时间。
英文摘要：
We consider the problem of cutting a set of edges on a polyhedral manifold surface, possibly with boundary, to obtain a single topological disk, minimizing either the total number of cut edges or their total length. We show that this problem is NP-hard, even for manifolds without boundary and for punctured spheres. We also describe an algorithm with running time n^{O(g+k)}, where n is the combinatorial complexity, g is the genus, and k is the number of boundary components of the input surface. Finally, we describe a greedy algorithm that outputs a O(log^2 g)-approximation of the minimum cut graph in O(g^2 n log n) time.
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