The Quest for Optimal Sorting Networks: Efficient Generation of Two-Layer Prefixes

@article{Codish2014TheQF,
  title={The Quest for Optimal Sorting Networks: Efficient Generation of Two-Layer Prefixes},
  author={Michael Codish and Lu{\'i}s Cruz-Filipe and Peter Schneider-Kamp},
  journal={2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing},
  year={2014},
  pages={359-366}
}
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… CONTINUE READING
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