Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: MAX CUT in Weighted Random Intersection Graphs and Discrepancy of Sparse
  Random Set Systems   Let $V$ be a set of $n$ vertices, ${\cal M}$ a set of $m$ labels, and let
$\mathbf{R}$ be an $m \times n$ matrix of independent Bernoulli random
variables with success probability $p$. A random instance
$G(V,E,\mathbf{R}^T\mathbf{R})$ of the weighted random intersection graph model
is constructed by drawing an edge with weight $[\mathbf{R}^T\mathbf{R}]_{v,u}$
between any two vertices $u,v$ for which this weight is larger than 0. In this
paper we study the average case analysis of Weighted Max Cut, assuming the
input is a weighted random intersection graph, i.e. given
$G(V,E,\mathbf{R}^T\mathbf{R})$ we wish to find a partition of $V$ into two
sets so that the total weight of the edges having one endpoint in each set is
maximized. We initially prove concentration of the weight of a maximum cut of
$G(V,E,\mathbf{R}^T\mathbf{R})$ around its expected value, and then show that,
when the number of labels is much smaller than the number of vertices, a random
partition of the vertices achieves asymptotically optimal cut weight with high
probability (whp). Furthermore, in the case $n=m$ and constant average degree,
we show that whp, a majority type algorithm outputs a cut with weight that is
larger than the weight of a random cut by a multiplicative constant strictly
larger than 1. Then, we highlight a connection between the computational
problem of finding a weighted maximum cut in $G(V,E,\mathbf{R}^T\mathbf{R})$
and the problem of finding a 2-coloring with minimum discrepancy for a set
system $\Sigma$ with incidence matrix $\mathbf{R}$. We exploit this connection
by proposing a (weak) bipartization algorithm for the case $m=n,
p=\frac{\Theta(1)}{n}$ that, when it terminates, its output can be used to find
a 2-coloring with minimum discrepancy in $\Sigma$. Finally, we prove that, whp
this 2-coloring corresponds to a bipartition with maximum cut-weight in
$G(V,E,\mathbf{R}^T\mathbf{R})$.

13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int