Emergent Mind
Abstract
We build boolean circuits of size $O(nm2)$ 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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