Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Warning Propagation on random graphs   Warning Propagation is a combinatorial message passing algorithm that unifies
and generalises a wide variety of recursive combinatorial procedures. Special
cases include the Unit Clause Propagation and Pure Literal algorithms for
satisfiability as well as the peeling process for identifying the $k$-core of a
random graph. Here we analyse Warning Propagation in full generality on the
binomial random graph. We prove that under a mild stability assumption Warning
Propagation converges rapidly. In effect, the analysis of the fixed point of
the message passing process on a random graph reduces to analysing the process
on a Galton-Watson tree. This result corroborates and generalises a heuristic
first put forward by Pittel, Spencer and Wormald in their seminal $k$-core
paper (JCTB 1996).

15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio