Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Randomized Bicriteria Approximation Algorithm for Minimum Submodular
  Cost Partial Multi-Cover Problem   This paper studies randomized approximation algorithm for a variant of the
set cover problem called minimum submodular cost partial multi-cover (SCPMC),
in which each element $e$ has a covering requirement $r_e$ and a profit $p_e$,
and the cost function on sub-collection of sets is submodular, the goal is to
find a minimum cost sub-collection of sets which fully covers at least
$q$-percentage of total profit, where an element $e$ is fully covered by
sub-collection $S'$ if and only if it belongs to at least $r_e$ sets of
$\mathcal S'$. Previous work shows that such a combination enormously increases
the difficulty of studies, even when the cost function is linear.
  In this paper, assuming that the maximum covering requirement
$r_{\max}=\max_e r_e$ is a constant and the cost function is nonnegative,
monotone nondecreasing, and submodular, we give the first randomized bicriteria
algorithm for SCPMC the output of which fully covers at least
$(q-\varepsilon)$-percentage of all elements and the performance ratio is
$O(b/\varepsilon)$ with a high probability, where $b=\max_e\binom{f}{r_{e}}$
and $f$ is the maximum number of sets containing a common element. The
algorithm is based on a novel non-linear program. Furthermore, in the case when
the covering requirement $r\equiv 1$, a bicriteria
$O(f/\varepsilon)$-approximation can be achieved even when monotonicity
requirement is dropped off from the cost function.

23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat