Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fixed Parameter Approximations for k-Center Problems in Low Highway
  Dimension Graphs   We consider the $k$-Center problem and some generalizations. For $k$-Center a
set of $k$ center vertices needs to be found in a graph $G$ with edge lengths,
such that the distance from any vertex of $G$ to its nearest center is
minimized. This problem naturally occurs in transportation networks, and
therefore we model the inputs as graphs with bounded highway dimension, as
proposed by Abraham et al. [SODA 2010].
  We show both approximation and fixed-parameter hardness results, and how to
overcome them using fixed-parameter approximations, where the two paradigms are
combined. In particular, we prove that for any $\varepsilon>0$ computing a
$(2-\varepsilon)$-approximation is W[2]-hard for parameter $k$ and NP-hard for
graphs with highway dimension $O(\log^2 n)$. The latter does not rule out
fixed-parameter $(2-\varepsilon)$-approximations for the highway dimension
parameter $h$, but implies that such an algorithm must have at least doubly
exponential running time in $h$ if it exists, unless the ETH fails. On the
positive side, we show how to get below the approximation factor of $2$ by
combining the parameters $k$ and $h$: we develop a fixed-parameter
$3/2$-approximation with running time $2^{O(kh\log h)}\cdot n^{O(1)}$.
Additionally we prove that, unless P=NP, our techniques cannot be used to
compute fixed-parameter $(2-\varepsilon)$-approximations for only the parameter
$h$.
  We also provide similar fixed-parameter approximations for the weighted
$k$-Center and $(k,\mathcal{F})$-Partition problems, which generalize
$k$-Center.

3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
2
The categories of this paper are: math
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph