Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Simple Algorithm for Minimum Cuts in Near-Linear Time   We consider the minimum cut problem in undirected, weighted graphs. We give a
simple algorithm to find a minimum cut that $2$-respects (cuts two edges of) a
spanning tree $T$ of a graph $G$. This procedure can be used in place of the
complicated subroutine given in Karger's near-linear time minimum cut algorithm
(J. ACM, 2000). We give a self-contained version of Karger's algorithm with the
new procedure, which is easy to state and relatively simple to implement. It
produces a minimum cut on an $m$-edge, $n$-vertex graph in $O(m \log^3 n)$ time
with high probability, matching the complexity of Karger's approach.

37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
2
The categories of this paper are: math
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat