Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Searching for dense subsets in a graph via the partition function   For a set $S$ of vertices of a graph $G$, we define its density $0 \leq
\sigma(S) \leq 1$ as the ratio of the number of edges of $G$ spanned by the
vertices of $S$ to ${|S| \choose 2}$. We show that, given a graph $G$ with $n$
vertices and an integer $m$, the partition function $\sum_S \exp\{ \gamma m
\sigma(S) \}$, where the sum is taken over all $m$-subsets $S$ of vertices and
$0 < \gamma <1$ is fixed in advance, can be approximated within relative error
$0 < \epsilon < 1$ in quasi-polynomial $n^{O(\ln m - \ln \epsilon)}$ time. We
discuss numerical experiments and observe that for the random graph $G(n, 1/2)$
one can afford a much larger $\gamma$, provided the ratio $n/m$ is sufficiently
large.

18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys