Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximation algorithms for the maximum weight internal spanning tree
  problem   Given a vertex-weighted connected graph $G = (V, E)$, the maximum weight
internal spanning tree (MwIST for short) problem asks for a spanning tree $T$
of $G$ such that the total weight of the internal vertices in $T$ is maximized.
The un-weighted variant, denoted as MIST, is NP-hard and APX-hard, and the
currently best approximation algorithm has a proven performance ratio $13/17$.
The currently best approximation algorithm for MwIST only has a performance
ratio $1/3 - \epsilon$, for any $\epsilon > 0$. In this paper, we present a
simple algorithm based on a novel relationship between MwIST and the maximum
weight matching, and show that it achieves a better approximation ratio of
$1/2$. When restricted to claw-free graphs, a special case been previously
studied, we design a $7/12$-approximation algorithm.

11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph