Sorting Short Integers [article]

Michal Koucký, Karel Král
2021 arXiv   pre-print
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.
arXiv:2102.10027v5 fatcat:swvsfxdf6rfatfz3bxlo27ypsq