Sorting Short Integers

02/19/2021

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by   Michal Koucký, et al.

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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.