{"file":[{"access_level":"open_access","file_id":"20012","date_updated":"2025-07-14T06:13:10Z","checksum":"cf0ab9cb9c6abda188de13dc3f9a4c9b","file_name":"2025_STOC_Anastos.pdf","success":1,"creator":"dernst","file_size":706445,"content_type":"application/pdf","relation":"main_file","date_created":"2025-07-14T06:13:10Z"}],"doi":"10.1145/3717823.3718173","department":[{"_id":"MaKw"}],"OA_type":"hybrid","day":"15","date_updated":"2025-07-14T06:33:50Z","title":"Smoothed analysis for graph isomorphism","status":"public","has_accepted_license":"1","corr_author":"1","scopus_import":"1","_id":"20007","publisher":"Association for Computing Machinery","external_id":{"arxiv":["2410.06095"]},"publication":"Proceedings of the 57th Annual ACM Symposium on Theory of Computing","language":[{"iso":"eng"}],"arxiv":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"conference":{"name":"STOC: Symposium on Theory of Computing","location":"Prague, Czechia","start_date":"2025-06-23","end_date":"2025-06-27"},"abstract":[{"lang":"eng","text":"There is no known polynomial-time algorithm for graph isomorphism testing, but elementary combinatorial “refinement” algorithms seem to be very efficient in practice. Some philosophical justification for this phenomenon is provided by a classical theorem of Babai, Erdős and Selkow: an extremely simple polynomial-time combinatorial algorithm (variously known as “naïve refinement”, “naïve vertex classification”, “colour refinement” or the “1-dimensional Weisfeiler–Leman algorithm”) yields a so-called canonical labelling scheme for “almost all graphs”. More precisely, for a typical outcome of a random graph G(n,1/2), this simple combinatorial algorithm assigns labels to vertices in a way that easily permits isomorphism-testing against any other graph."}],"acknowledgement":"All authors were supported by ERC Starting Grant “RANDSTRUCT” No. 101076777. Michael Anastos was also supported in part by the Austrian Science Fund (FWF)[10.55776/ESP3863424] and by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 101034413. For Open Access purposes, the authors have applied a CC BY public copyright license to any author accepted manuscript version arising from this submission.","page":"2098-2106","oa":1,"month":"06","quality_controlled":"1","OA_place":"publisher","ec_funded":1,"file_date_updated":"2025-07-14T06:13:10Z","year":"2025","citation":{"apa":"Anastos, M., Kwan, M. A., &#38; Moore, B. (2025). Smoothed analysis for graph isomorphism. In <i>Proceedings of the 57th Annual ACM Symposium on Theory of Computing</i> (pp. 2098–2106). Prague, Czechia: Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3717823.3718173\">https://doi.org/10.1145/3717823.3718173</a>","mla":"Anastos, Michael, et al. “Smoothed Analysis for Graph Isomorphism.” <i>Proceedings of the 57th Annual ACM Symposium on Theory of Computing</i>, Association for Computing Machinery, 2025, pp. 2098–106, doi:<a href=\"https://doi.org/10.1145/3717823.3718173\">10.1145/3717823.3718173</a>.","chicago":"Anastos, Michael, Matthew Alan Kwan, and Benjamin Moore. “Smoothed Analysis for Graph Isomorphism.” In <i>Proceedings of the 57th Annual ACM Symposium on Theory of Computing</i>, 2098–2106. Association for Computing Machinery, 2025. <a href=\"https://doi.org/10.1145/3717823.3718173\">https://doi.org/10.1145/3717823.3718173</a>.","short":"M. Anastos, M.A. Kwan, B. Moore, in:, Proceedings of the 57th Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, 2025, pp. 2098–2106.","ista":"Anastos M, Kwan MA, Moore B. 2025. Smoothed analysis for graph isomorphism. Proceedings of the 57th Annual ACM Symposium on Theory of Computing. STOC: Symposium on Theory of Computing, 2098–2106.","ieee":"M. Anastos, M. A. Kwan, and B. Moore, “Smoothed analysis for graph isomorphism,” in <i>Proceedings of the 57th Annual ACM Symposium on Theory of Computing</i>, Prague, Czechia, 2025, pp. 2098–2106.","ama":"Anastos M, Kwan MA, Moore B. Smoothed analysis for graph isomorphism. In: <i>Proceedings of the 57th Annual ACM Symposium on Theory of Computing</i>. Association for Computing Machinery; 2025:2098-2106. doi:<a href=\"https://doi.org/10.1145/3717823.3718173\">10.1145/3717823.3718173</a>"},"date_published":"2025-06-15T00:00:00Z","publication_status":"published","article_processing_charge":"Yes (via OA deal)","date_created":"2025-07-13T22:01:23Z","project":[{"grant_number":"101076777","_id":"bd95085b-d553-11ed-ba76-e55d3349be45","name":"Randomness and structure in combinatorics"},{"grant_number":"101034413","call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"},{"_id":"8f906bd2-16d5-11f0-9cad-e07be8aa9ac9","name":"Combinatorial Optimisation Problems on Sparse Random Graphs","grant_number":"ESP3863424"}],"ddc":["000"],"oa_version":"Published Version","publication_identifier":{"issn":["0737-8017"],"isbn":["9798400715105"]},"type":"conference","author":[{"id":"0b2a4358-bb35-11ec-b7b9-e3279b593dbb","last_name":"Anastos","full_name":"Anastos, Michael","first_name":"Michael"},{"id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","last_name":"Kwan","full_name":"Kwan, Matthew Alan","first_name":"Matthew Alan","orcid":"0000-0002-4003-7567"},{"full_name":"Moore, Benjamin","first_name":"Benjamin","last_name":"Moore","id":"6dc1a1be-bf1c-11ed-8d2b-d044840f49d6"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"}