Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximate Decomposable Submodular Function Minimization for
  Cardinality-Based Components   Minimizing a sum of simple submodular functions of limited support is a
special case of general submodular function minimization that has seen numerous
applications in machine learning. We develop fast techniques for instances
where components in the sum are cardinality-based, meaning they depend only on
the size of the input set. This variant is one of the most widely applied in
practice, encompassing, e.g., common energy functions arising in image
segmentation and recent generalized hypergraph cut functions. We develop the
first approximation algorithms for this problem, where the approximations can
be quickly computed via reduction to a sparse graph cut problem, with graph
sparsity controlled by the desired approximation factor. Our method relies on a
new connection between sparse graph reduction techniques and piecewise linear
approximations to concave functions. Our sparse reduction technique leads to
significant improvements in theoretical runtimes, as well as substantial
practical gains in problems ranging from benchmark image segmentation tasks to
hypergraph clustering problems.

37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph