Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deterministic Discrepancy Minimization via the Multiplicative Weight
  Update Method   A well-known theorem of Spencer shows that any set system with $n$ sets over
$n$ elements admits a coloring of discrepancy $O(\sqrt{n})$. While the original
proof was non-constructive, recent progress brought polynomial time algorithms
by Bansal, Lovett and Meka, and Rothvoss. All those algorithms are randomized,
even though Bansal's algorithm admitted a complicated derandomization.
  We propose an elegant deterministic polynomial time algorithm that is
inspired by Lovett-Meka as well as the Multiplicative Weight Update method. The
algorithm iteratively updates a fractional coloring while controlling the
exponential weights that are assigned to the set constraints.
  A conjecture by Meka suggests that Spencer's bound can be generalized to
symmetric matrices. We prove that $n \times n$ matrices that are block diagonal
with block size $q$ admit a coloring of discrepancy $O(\sqrt{n} \cdot
\sqrt{\log(q)})$.
  Bansal, Dadush and Garg recently gave a randomized algorithm to find a vector
$x$ with entries in $\lbrace{-1,1\rbrace}$ with $\|Ax\|_{\infty} \leq
O(\sqrt{\log n})$ in polynomial time, where $A$ is any matrix whose columns
have length at most 1. We show that our method can be used to deterministically
obtain such a vector.

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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th