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Twentyfive comparators is optimal when sorting nine inputs (and twentynine for ten
, 2014
"... This paper describes a computerassisted nonexistence proof of 9input sorting networks consisting of 24 comparators, hence showing that the 25comparator sorting network found by Floyd in 1964 is optimal. As a corollary, we obtain that the 29comparator network found by Waksman in 1969 is optimal ..."
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This paper describes a computerassisted nonexistence proof of 9input sorting networks consisting of 24 comparators, hence showing that the 25comparator sorting network found by Floyd in 1964 is optimal. As a corollary, we obtain that the 29comparator network found by Waksman in 1969 is optimal when sorting 10 inputs. This closes the two smallest open instances of the optimalsize sorting network problem, which have been open since the results of Floyd and Knuth from 1966 proving optimality for sorting networks of up to 8 inputs. The proof involves a combination of two methodologies: one based on exploiting the abundance of symmetries in sorting networks, and the other based on an encoding of the problem to that of satisfiability of propositional logic. We illustrate that, while each of these can singlehandedly solve smaller instances of the problem, it is their combination that leads to the more efficient solution that scales to handle 9 inputs. 1
Faster Sorting Networks for 17, 19 and 20 Inputs
"... Abstract. We present new parallel sorting networks for 17 to 20 inputs. For 17, 19, and 20 inputs these new networks are faster (i.e., they require less computation steps) than the previously known best networks. Therefore, we improve upon the known upper bounds for minimal depth sorting networks ..."
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Abstract. We present new parallel sorting networks for 17 to 20 inputs. For 17, 19, and 20 inputs these new networks are faster (i.e., they require less computation steps) than the previously known best networks. Therefore, we improve upon the known upper bounds for minimal depth sorting networks on 17, 19, and 20 channels. The networks were obtained using a combination of handcrafted first layers and a SAT encoding of sorting networks. 1