Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constant-Factor Approximation for TSP with Disks   We revisit the traveling salesman problem with neighborhoods (TSPN) and
present the first constant-ratio approximation for disks in the plane: Given a
set of $n$ disks in the plane, a TSP tour whose length is at most $O(1)$ times
the optimal can be computed in time that is polynomial in $n$. Our result is
the first constant-ratio approximation for a class of planar convex bodies of
arbitrary size and arbitrary intersections. In order to achieve a
$O(1)$-approximation, we reduce the traveling salesman problem with disks, up
to constant factors, to a minimum weight hitting set problem in a geometric
hypergraph. The connection between TSPN and hitting sets in geometric
hypergraphs, established here, is likely to have future applications.

22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int