The Quest for Optimal Sorting Networks: Efficient Generation of Two-Layer Prefixes - Codish, Michael; Cruz-Filipe, Luis; Schneider-Kamp, Peter (2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, 2014)
Previous work identifying depth-optimal n-channel sorting networks for 9 ≤ n ≤ 16 is based on exploiting symmetries of the first two layers. However, the naive generate-and-test approach typically applied does not scale. This paper revisits the problem of generating two-layer prefixes modulo symmetries. An improved notion of symmetry is provided and a novel technique based on regular languages and graph isomorphism is shown to generate the set of non-symmetric representations. An empirical evaluation demonstrates that the new method outperforms the generate-and-test approach by orders of magnitude and easily scales until n = 40.