Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Almost Optimal Approximation Algorithm for Monotone Submodular
  Multiple Knapsack   We study the problem of maximizing a monotone submodular function subject to
a Multiple Knapsack constraint. The input is a set $I$ of items, each has a
non-negative weight, and a set of bins of arbitrary capacities. Also, we are
given a submodular, monotone and non-negative function $f$ over subsets of the
items. The objective is to find a packing of a subset of items $A \subseteq I$
in the bins such that $f(A)$ is maximized.
  Our main result is an almost optimal polynomial time
$(1-e^{-1}-\varepsilon)$-approximation algorithm for the problem, for any
$\varepsilon>0$. The algorithm relies on a structuring technique which converts
a general multiple knapsack constraint to a constraint in which the bins are
partitioned into groups of exponentially increasing cardinalities, each
consisting of bins of uniform capacity. We derive the result by combining
structuring with a refined analysis of techniques for submodular optimization
subject to knapsack constraints.

27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph