Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximately counting independent sets in bipartite graphs via graph
  containers   By implementing algorithmic versions of Sapozhenko's graph container methods,
we give new algorithms for approximating the number of independent sets in
bipartite graphs. Our first algorithm applies to $d$-regular, bipartite graphs
satisfying a weak expansion condition: when $d$ is constant, and the graph is a
bipartite $\Omega( \log^2 d/d)$-expander, we obtain an FPTAS for the number of
independent sets. Previously such a result for $d>5$ was known only for graphs
satisfying the much stronger expansion conditions of random bipartite graphs.
The algorithm also applies to weighted independent sets: for a $d$-regular,
bipartite $\alpha$-expander, with $\alpha>0$ fixed, we give an FPTAS for the
hard-core model partition function at fugacity $\lambda=\Omega(\log d /
d^{1/4})$. Finally we present an algorithm that applies to all $d$-regular,
bipartite graphs, runs in time $\exp\left( O\left( n \cdot \frac{ \log^3 d }{d
} \right) \right)$, and outputs a $(1 + o(1))$-approximation to the number of
independent sets.

25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg