{"paper":{"title":"The Quest for Optimal Sorting Networks: Efficient Generation of Two-Layer Prefixes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"Luis Cruz-Filipe, Michael Codish, Peter Schneider-Kamp","submitted_at":"2014-04-03T15:02:11Z","abstract_excerpt":"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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0948","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}