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arXiv · 1310.6271

Optimal Sorting Networks

Daniel Bundala·Jakub Závodný
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Abstract

This paper settles the optimality of sorting networks given in The Art of Computer Programming vol. 3 more than 40 years ago. The book lists efficient sorting networks with n <= 16 inputs. In this paper we give general combinatorial arguments showing that if a sorting network with a given depth exists then there exists one with a special form. We then construct propositional formulas whose satisfiability is necessary for the existence of such a network. Using a SAT solver we conclude that the listed networks have optimal depth. For n <= 10 inputs where optimality was known previously, our algorithm is four orders of magnitude faster than those in prior work.

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Daniel Bundala, Jakub Závodný. 2013-12-22. Optimal Sorting Networks. https://arxiv.org/abs/1310.6271

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