Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximation Algorithm for Minimum Weight Connected $m$-Fold Dominating
  Set   Using connected dominating set (CDS) to serve as a virtual backbone in a
wireless networks can save energy and reduce interference. Since nodes may fail
due to accidental damage or energy depletion, it is desirable that the virtual
backbone has some fault-tolerance. A $k$-connected $m$-fold dominating set
($(k,m)$-CDS) of a graph $G$ is a node set $D$ such that every node in
$V\setminus D$ has at least $m$ neighbors in $D$ and the subgraph of $G$
induced by $D$ is $k$-connected. Using $(k,m)$-CDS can tolerate the failure of
$\min\{k-1,m-1\}$ nodes. In this paper, we study Minimum Weight $(1,m)$-CDS
problem ($(1,m)$-MWCDS), and present an
$(H(\delta+m)+2H(\delta-1))$-approximation algorithm, where $\delta$ is the
maximum degree of the graph and $H(\cdot)$ is the Harmonic number. Notice that
there is a $1.35\ln n$-approximation algorithm for the $(1,1)$-MWCDS problem,
where $n$ is the number of nodes in the graph. Though our constant in $O(\ln
\cdot)$ is larger than 1.35, $n$ is replaced by $\delta$. Such a replacement
enables us to obtain a $(6.67+\varepsilon)$-approximation for the $(1,m)$-MWCDS
problem on unit disk graphs.

36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th