Optimally cutting a surface into a disk

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 <i>n</i> <sup>O(<i>g</i>+<i>k</i>)</sup>, where <i>n</i> is the combinatorial complexity, <i>g</i> is the genus, and <i>k</i> is the number of boundary components of the input surface. Finally, we describe a greedy algorithm that outputs a <i>O</i>(log<sup>2</sup> g)-approximation of the minimum cut graph in <i>O</i>(<i>g</i> <sup>2</sup> <i>n</i> log <i>n</i>) time.

DOI: 10.1145/513400.513430
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@article{Erickson2002OptimallyCA, title={Optimally cutting a surface into a disk}, author={Jeff Erickson and Sariel Har-Peled}, journal={Discrete & Computational Geometry}, year={2002}, volume={31}, pages={37-59} }