Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient Algorithms for Discrepancy Minimization in Convex Sets   A result of Spencer states that every collection of $n$ sets over a universe
of size $n$ has a coloring of the ground set with $\{-1,+1\}$ of discrepancy
$O(\sqrt{n})$. A geometric generalization of this result was given by Gluskin
(see also Giannopoulos) who showed that every symmetric convex body $K\subseteq
R^n$ with Gaussian measure at least $e^{-\epsilon n}$, for a small
$\epsilon>0$, contains a point $y\in K$ where a constant fraction of
coordinates of $y$ are in $\{-1,1\}$. This is often called a partial coloring
result. While both these results were inherently non-algorithmic, recently
Bansal (see also Lovett-Meka) gave a polynomial time algorithm for Spencer's
setting and Rothvo\ss gave a randomized polynomial time algorithm obtaining the
same guarantee as the result of Gluskin and Giannopoulos.
  This paper has several related results. First we prove another constructive
version of the result of Gluskin and Giannopoulos via an optimization of a
linear function. This implies a linear programming based algorithm for
combinatorial discrepancy obtaining the same result as Spencer. Our second
result gives a new approach to obtains partial colorings and shows that every
convex body $K\subseteq R^n$, possibly non-symmetric, with Gaussian measure at
least $e^{-\epsilon n}$, for a small $\epsilon>0$, contains a point $y\in K$
where a constant fraction of coordinates of $y$ are in $\{-1,1\}$. Finally, we
give a simple proof that shows that for any $\delta >0$ there exists a constant
$c>0$ such that given a body $K$ with $\gamma_n(K)\geq \delta$, a uniformly
random $x$ from $\{-1,1\}^n$ is in $cK$ with constant probability. This gives
an algorithmic version of a special case of the result of Banaszczyk.

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The categories of this paper are: econ
3
The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas