Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximating the Regular Graphic TSP in near linear time   We present a randomized approximation algorithm for computing traveling
salesperson tours in undirected regular graphs. Given an $n$-vertex,
$k$-regular graph, the algorithm computes a tour of length at most
$\left(1+\frac{7}{\ln k-O(1)}\right)n$, with high probability, in $O(nk \log
k)$ time. This improves upon a recent result by Vishnoi (\cite{Vishnoi12}, FOCS
2012) for the same problem, in terms of both approximation factor, and running
time. The key ingredient of our algorithm is a technique that uses
edge-coloring algorithms to sample a cycle cover with $O(n/\log k)$ cycles with
high probability, in near linear time.
  Additionally, we also give a deterministic
$\frac{3}{2}+O\left(\frac{1}{\sqrt{k}}\right)$ factor approximation algorithm
running in time $O(nk)$.

14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th