Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximation Algorithms for Finding Maximum Induced Expanders   We initiate the study of approximating the largest induced expander in a
given graph $G$. Given a $\Delta$-regular graph $G$ with $n$ vertices, the goal
is to find the set with the largest induced expansion of size at least $\delta
\cdot n$. We design a bi-criteria approximation algorithm for this problem; if
the optimum has induced spectral expansion $\lambda$ our algorithm returns a
$\frac{\lambda}{\log^2\delta \exp(\Delta/\lambda)}$-(spectral) expander of size
at least $\delta n$ (up to constants).
  Our proof introduces and employs a novel semidefinite programming relaxation
for the largest induced expander problem. We expect to see further applications
of our SDP relaxation in graph partitioning problems. In particular, because of
the close connection to the small set expansion problem, one may be able to
obtain new insights into the unique games problem.

37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
2
The categories of this paper are: math
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an