Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A parallel algorithm for minimum weight set cover with small
  neighborhood property   This paper studies the minimum weight set cover (MinWSC) problem with a {\em
small neighborhood cover} (SNC) property proposed by Agarwal {\it et al.} in
\cite{Agarwal.}. A parallel algorithm for MinWSC with $\tau$-SNC property is
presented, obtaining approximation ratio $\tau(1+3\varepsilon)$ in
$O(L\log_{1+\varepsilon}\frac{n^3}{\varepsilon^2}+ 4\tau^{3}2^\tau L^2\log n)$
rounds, where $0< \varepsilon <\frac{1}{2}$ is a constant, $n$ is the number of
elements, and $L$ is a parameter related to SNC property. Our results not only
improve the approximation ratio obtained in \cite{Agarwal.}, but also answer
two questions proposed in \cite{Agarwal.}.

27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph