Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finding Minimum Spanning Forests in a Graph   We introduce a graph partitioning problem motivated by computational topology
and propose two algorithms that produce approximate solutions. Specifically,
given a weighted, undirected graph $G$ and a positive integer $k$, we desire to
find $k$ disjoint trees within $G$ such that each vertex of $G$ is contained in
one of the trees and the weight of the largest tree is as small as possible. We
are unable to find this problem in the graph partitioning literature, but we
show that the problem is NP-complete. We then propose two approximation
algorithms, one that uses a spectral clustering approach and another that
employs a dynamic programming strategy, which produce near-optimal partitions
on a family of test graphs. We describe these algorithms and analyze their
empirical performance.

13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg