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Sorting Short Keys in Circuits of Size o(n log n)
[article]

2020
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arXiv
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pre-print

We consider the classical problem of sorting an input array containing n elements, where each element is described with a k-bit comparison-key and a w-bit payload. A long-standing open problem is whether there exist (k + w) · o(n log n)-sized boolean circuits for sorting. We show that one can overcome the nlog n barrier when the keys to be sorted are short. Specifically, we prove that there is a circuit with (k + w) · O(n k) ·(log^*n - log^* (w + k)) boolean gates capable of sorting any input

arXiv:2010.09884v2
fatcat:ji2762hgevbpxijglqczbp5sxu