Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The statistical mechanics of random set packing and a generalization of
  the Karp-Sipser algorithm   We analyse the asymptotic behaviour of random instances of the Maximum Set
Packing (MSP) optimization problem, also known as Maximum Matching or Maximum
Strong Independent Set on Hypergraphs. We give an analytical prediction of the
MSPs size using the 1RSB cavity method from statistical mechanics of disordered
systems. We also propose a heuristic algorithm, a generalization of the
celebrated Karp-Sipser one, which allows us to rigorously prove that the
replica symmetric cavity method prediction is exact for certain problem
ensembles and breaks down when a core survives the leaf removal process. The
$e$-phenomena threshold discovered by Karp and Sipser, marking the onset of
core emergence and of replica symmetry breaking, is elegantly generalized to
$c_s = \frac{e}{d-1}$ for one of the ensembles considered, where $d$ is the
size of the sets.

5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th