Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The guillotine approach for TSP with neighborhoods revisited   The Euclidean TSP with neighborhoods (TSPN) is the following problem: Given a
set R of k regions, find a shortest tour that visits at least one point from
each region. We study the special cases of disjoint, connected, alpha-fat
regions (i.e., every region P contains a disk of diameter diam(P)/alpha) and
disjoint unit disks.
  For the latter, Dumitrescu and Mitchell proposed an algorithm based on
Mitchell's guillotine subdivision approach for the Euclidean TSP and claimed it
to be a PTAS. However, their proof contains a severe gap, which we will close
in the following. Bodlaender et al. remark that their techniques for the
minimum corridor connection problem carry over to the TSPN and yield an
alternative PTAS for this problem.
  For disjoint connected alpha-fat regions of varying size, Mitchell proposed a
slightly different PTAS candidate. We will expose several further problems and
gaps in this approach. Some of them we can close, but overall, for alpha-fat
regions, the existence of a PTAS for the TSPN remains open.

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The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
2
The categories of this paper are: math
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat