Sorting Short Integers

Michal Koucký; Karel Král

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arXiv · 2102.10027

Sorting Short Integers

Michal Koucký·Karel Král

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Abstract

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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BibTeX RIS

Michal Koucký, Karel Král. 2021-02-19. Sorting Short Integers. https://arxiv.org/abs/2102.10027

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