Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Nearly-linear Time Algorithm for Submodular Maximization with a
  Knapsack Constraint   We consider the problem of maximizing a monotone submodular function subject
to a knapsack constraint. Our main contribution is an algorithm that achieves a
nearly-optimal, $1 - 1/e - \epsilon$ approximation, using
$(1/\epsilon)^{O(1/\epsilon^4)} n \log^2{n}$ function evaluations and
arithmetic operations. Our algorithm is impractical but theoretically
interesting, since it overcomes a fundamental running time bottleneck of the
multilinear extension relaxation framework. This is the main approach for
obtaining nearly-optimal approximation guarantees for important classes of
constraints but it leads to $\Omega(n^2)$ running times, since evaluating the
multilinear extension is expensive. Our algorithm maintains a fractional
solution with only a constant number of entries that are strictly fractional,
which allows us to overcome this obstacle.

15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics