Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimally cutting a surface into a disk   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.

12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph