最优排序网络的探索：两层前缀的有效生成
The Quest for Optimal Sorting Networks: Efficient Generation of Two-Layer Prefixes
摘要：
以前的工作确定深度最优的$n$通道排序网络的$9\leq n \leq 16$是基于利用前两层的对称性。然而，通常应用的朴素生成和测试方法不能扩展。本文重新讨论了两层前缀模对称的生成问题。提出了一种改进的对称性概念，并给出了一种基于正则语言和图同构的非对称表示集的生成方法。实证评估表明，新方法优于生成和测试的方法的数量级和容易扩展，直到$n=40$。
英文摘要：
Previous work identifying depth-optimal $n$-channel sorting networks for $9\leq n \leq 16$ 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 $n=40$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
