Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A polynomial-time approximation algorithm for all-terminal network
  reliability   We give a fully polynomial-time randomized approximation scheme (FPRAS) for
the all-terminal network reliability problem, which is to determine the
probability that, in a undirected graph, assuming each edge fails
independently, the remaining graph is still connected. Our main contribution is
to confirm a conjecture by Gorodezky and Pak (Random Struct. Algorithms, 2014),
that the expected running time of the "cluster-popping" algorithm in
bi-directed graphs is bounded by a polynomial in the size of the input.

7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga