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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Bundala, D., Závodný, J. (2014). Optimal Sorting Networks. In: Dediu, AH., Martín-Vide, C., Sierra-Rodríguez, JL., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2014. Lecture Notes in Computer Science, vol 8370. Springer, Cham. https://doi.org/10.1007/978-3-319-04921-2_19
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DOI: https://doi.org/10.1007/978-3-319-04921-2_19
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-04920-5
Online ISBN: 978-3-319-04921-2
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