Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constant Factor Approximation for Balanced Cut in the PIE model   We propose and study a new semi-random semi-adversarial model for Balanced
Cut, a planted model with permutation-invariant random edges (PIE). Our model
is much more general than planted models considered previously. Consider a set
of vertices V partitioned into two clusters $L$ and $R$ of equal size. Let $G$
be an arbitrary graph on $V$ with no edges between $L$ and $R$. Let
$E_{random}$ be a set of edges sampled from an arbitrary permutation-invariant
distribution (a distribution that is invariant under permutation of vertices in
$L$ and in $R$). Then we say that $G + E_{random}$ is a graph with
permutation-invariant random edges.
  We present an approximation algorithm for the Balanced Cut problem that finds
a balanced cut of cost $O(|E_{random}|) + n \text{polylog}(n)$ in this model.
In the regime when $|E_{random}| = \Omega(n \text{polylog}(n))$, this is a
constant factor approximation with respect to the cost of the planted cut.

2
The categories of this paper are: math
16
The categories of this paper are: stat
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys