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Optimally cutting a surface into a disk

Jeff Erickson·Sariel Har-Peled
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Abstract

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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Jeff Erickson, Sariel Har-Peled. 2002-07-02. Optimally cutting a surface into a disk. https://arxiv.org/abs/cs/0207004

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