Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal dynamic program for r-domination problems over tree
  decompositions   There has been recent progress in showing that the exponential dependence on
treewidth in dynamic programming algorithms for solving NP-hard problems are
optimal under the Strong Exponential Time Hypothesis (SETH). We extend this
work to $r$-domination problems. In $r$-dominating set, one wished to find a
minimum subset $S$ of vertices such that every vertex of $G$ is within $r$ hops
of some vertex in $S$. In connected $r$-dominating set, one additionally
requires that the set induces a connected subgraph of $G$. We give a
$O((2r+1)^{\mathrm{tw}} n)$ time algorithm for $r$-dominating set and a
$O((2r+2)^{\mathrm{tw}} n^{O(1)})$ time algorithm for connected $r$-dominating
set in $n$-vertex graphs of treewidth $\mathrm{tw}$. We show that the running
time dependence on $r$ and $\mathrm{tw}$ is the best possible under SETH. This
adds to earlier observations that a "+1" in the denominator is required for
connectivity constraints.

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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: physics