[{"type":"conference","arxiv":1,"article_processing_charge":"No","quality_controlled":"1","doi":"10.1137/1.9781611978971.25","publication_identifier":{"issn":["1071-9040"],"eisbn":["9781611978971"],"eissn":["1557-9468"]},"status":"public","ec_funded":1,"page":"613-663","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","scopus_import":"1","conference":{"end_date":"2026-01-14","start_date":"2026-01-11","name":"SODA: Symposium on Discrete Algorithms","location":"Vancouver, Canada"},"date_updated":"2026-05-04T11:36:47Z","OA_type":"green","day":"07","citation":{"short":"A. El-Hayek, M. Henzinger, J. Li, in:, Proceedings of the Annual ACM SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, 2026, pp. 613–663.","ista":"El-Hayek A, Henzinger M, Li J. 2026. Deterministic and exact fully-dynamic minimum cut of superpolylogarithmic size in subpolynomial time. Proceedings of the Annual ACM SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms vol. 2026, 613–663.","chicago":"El-Hayek, Antoine, Monika Henzinger, and Jason Li. “Deterministic and Exact Fully-Dynamic Minimum Cut of Superpolylogarithmic Size in Subpolynomial Time.” In <i>Proceedings of the Annual ACM SIAM Symposium on Discrete Algorithms</i>, 2026:613–63. Society for Industrial and Applied Mathematics, 2026. <a href=\"https://doi.org/10.1137/1.9781611978971.25\">https://doi.org/10.1137/1.9781611978971.25</a>.","ama":"El-Hayek A, Henzinger M, Li J. Deterministic and exact fully-dynamic minimum cut of superpolylogarithmic size in subpolynomial time. In: <i>Proceedings of the Annual ACM SIAM Symposium on Discrete Algorithms</i>. Vol 2026. Society for Industrial and Applied Mathematics; 2026:613-663. doi:<a href=\"https://doi.org/10.1137/1.9781611978971.25\">10.1137/1.9781611978971.25</a>","apa":"El-Hayek, A., Henzinger, M., &#38; Li, J. (2026). Deterministic and exact fully-dynamic minimum cut of superpolylogarithmic size in subpolynomial time. In <i>Proceedings of the Annual ACM SIAM Symposium on Discrete Algorithms</i> (Vol. 2026, pp. 613–663). Vancouver, Canada: Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/1.9781611978971.25\">https://doi.org/10.1137/1.9781611978971.25</a>","mla":"El-Hayek, Antoine, et al. “Deterministic and Exact Fully-Dynamic Minimum Cut of Superpolylogarithmic Size in Subpolynomial Time.” <i>Proceedings of the Annual ACM SIAM Symposium on Discrete Algorithms</i>, vol. 2026, Society for Industrial and Applied Mathematics, 2026, pp. 613–63, doi:<a href=\"https://doi.org/10.1137/1.9781611978971.25\">10.1137/1.9781611978971.25</a>.","ieee":"A. El-Hayek, M. Henzinger, and J. Li, “Deterministic and exact fully-dynamic minimum cut of superpolylogarithmic size in subpolynomial time,” in <i>Proceedings of the Annual ACM SIAM Symposium on Discrete Algorithms</i>, Vancouver, Canada, 2026, vol. 2026, pp. 613–663."},"publication":"Proceedings of the Annual ACM SIAM Symposium on Discrete Algorithms","department":[{"_id":"MoHe"},{"_id":"GradSch"}],"publisher":"Society for Industrial and Applied Mathematics","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2512.13105"}],"OA_place":"repository","_id":"21720","title":"Deterministic and exact fully-dynamic minimum cut of superpolylogarithmic size in subpolynomial time","author":[{"id":"888a098e-fcac-11ee-aff7-d347be57b725","full_name":"El-Hayek, Antoine","orcid":"0000-0003-4268-7368","last_name":"El-Hayek","first_name":"Antoine"},{"last_name":"Henzinger","first_name":"Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H"},{"full_name":"Li, Jason","last_name":"Li","first_name":"Jason"}],"external_id":{"arxiv":["2512.13105"]},"publication_status":"published","project":[{"name":"The design and evaluation of modern fully dynamic data structures","call_identifier":"H2020","grant_number":"101019564","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62"},{"grant_number":"I05982","name":"Static and Dynamic Hierarchical Graph Decompositions","_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103"}],"volume":2026,"abstract":[{"lang":"eng","text":"We present an exact fully-dynamic minimum cut algorithm that runs in 𝑛𝑜⁡(1) deterministic update time when the minimum cut size is at most 2Θ⁡(log3/4−𝑐⁡𝑛) for any 𝑐 >0, improving on the previous algorithm of Jin, Sun, and Thorup (SODA 2024) whose minimum cut size limit is (log⁡𝑛)𝑜⁡(1). Combined with graph sparsification, we obtain the first (1 +𝜖)-approximate fully-dynamic minimum cut algorithm on weighted graphs, for any 𝜖 ≥2−Θ⁡(log3/4−𝑐⁡𝑛), in 𝑛𝑜⁡(1) randomized update time.\r\nOur main technical contribution is a deterministic local minimum cut algorithm, which replaces the randomized LocalKCut procedure from El-Hayek, Henzinger, and Li (SODA 2025)."}],"month":"01","oa":1,"acknowledgement":"Funded by the European union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (MoDynStruct, No. 101019564) and the Austrian Science Fund (FWF) grant DOI 10.55776/I5982. For open access purposes, the author has applied a CC BY public copyright license to any author-accepted manuscript version arising from this submission.","language":[{"iso":"eng"}],"intvolume":"      2026","year":"2026","date_published":"2026-01-07T00:00:00Z","date_created":"2026-04-12T22:01:51Z"}]