{"paper":{"title":"Graph Isomorphism in Quasipolynomial Time","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC","math.CO","math.GR"],"primary_cat":"cs.DS","authors_text":"L\\'aszl\\'o Babai","submitted_at":"2015-12-11T08:04:26Z","abstract_excerpt":"We show that the Graph Isomorphism (GI) problem and the related problems of String Isomorphism (under group action) (SI) and Coset Intersection (CI) can be solved in quasipolynomial ($\\exp((\\log n)^{O(1)})$) time. The best previous bound for GI was $\\exp(O(\\sqrt{n\\log n}))$, where $n$ is the number of vertices (Luks, 1983); for the other two problems, the bound was similar, $\\exp(\\tilde{O}(\\sqrt{n}))$, where $n$ is the size of the permutation domain (Babai, 1983).\n  The algorithm builds on Luks's SI framework and attacks the barrier configurations for Luks's algorithm by group theoretic \"local"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03547","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"}