Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computational Complexity, Phase Transitions, and Message-Passing for
  Community Detection   We take a whirlwind tour of problems and techniques at the boundary of
computer science and statistical physics. We start with a brief description of
P, NP, and NP-completeness. We then discuss random graphs, including the
emergence of the giant component and the k-core, using techniques from
branching processes and differential equations. Using these tools as well as
the second moment method, we give upper and lower bounds on the critical clause
density for random k-SAT. We end with community detection in networks,
variational methods, the Bethe free energy, belief propagation, the
detectability transition, and the non-backtracking matrix.

2
The categories of this paper are: math
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph