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Optimal Sorting Networks

2014; Springer Science+Business Media; Linguagem: Inglês

10.1007/978-3-319-04921-2_19

1611-3349

Daniel Bundala, Jakub Závodný,

graph theory and CDMA systems

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.