Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distributed Domination on Graph Classes of Bounded Expansion   We provide a new constant factor approximation algorithm for the (connected)
distance-$r$ dominating set problem on graph classes of bounded expansion.
Classes of bounded expansion include many familiar classes of sparse graphs
such as planar graphs and graphs with excluded (topological) minors, and
notably, these classes form the most general subgraph closed classes of graphs
for which a sequential constant factor approximation algorithm for the
distance-$r$ dominating set problem is currently known. Our algorithm can be
implemented in the \congestbc model of distributed computing and uses
$\mathcal{O}(r^2 \log n)$ communication rounds.
  Our techniques, which may be of independent interest, are based on a
distributed computation of sparse neighborhood covers of small radius on
bounded expansion classes. We show how to compute an $r$-neighborhood cover of
radius~$2r$ and overlap $f(r)$ on every class of bounded expansion in
$\mathcal{O}(r^2 \log n)$ communication rounds for some function~$f$.% in the
$\mathcal{CONGEST}_{\mathrm{BC}}$ model.
  Finally, we show how to use the greater power of the $\mathcal{LOCAL}$ model
to turn any distance-$r$ dominating set into a constantly larger connected
distance-$r$ dominating set in $3r+1$ rounds on any class of bounded expansion.
Combining this algorithm, e.g., with the constant factor approximation
algorithm for dominating sets on planar graphs of Lenzen et al.\ gives a
constant factor approximation algorithm for connected dominating sets on planar
graphs in a constant number of rounds in the $\mathcal{LOCAL}$ model, where the
approximation ratio is only $6$ times larger than that of Lenzen et al.'s
algorithm.

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The categories of this paper are: q-alg
9
The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: math
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The categories of this paper are: cmp-lg