Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sorting Short Integers   We build boolean circuits of size $O(nm^2)$ and depth $O(\log(n) + m
\log(m))$ for sorting $n$ integers each of $m$-bits. We build also circuits
that sort $n$ integers each of $m$-bits according to their first $k$ bits that
are of size $O(nmk(1 + \log^*(n) - \log^*(m)))$ and depth $O(\log^{3}(n))$.
This improves on the result of Asharov et al. arXiv:2010.09884 and resolves
some of their open questions.

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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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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: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: q-fin