[{"doi":"10.1145/3816252","OA_place":"publisher","oa_version":"Published Version","publisher":"ACM","citation":{"mla":"Goranci, Gramoz, et al. “Incremental Approximate Maximum Flow via Residual Graph Sparsification.” <i>ACM Transactions on Algorithms</i>, vol. 22, no. 3, 31, ACM, 2026, doi:<a href=\"https://doi.org/10.1145/3816252\">10.1145/3816252</a>.","short":"G. Goranci, M. Henzinger, H. Räcke, A.R. Sricharan, ACM Transactions on Algorithms 22 (2026).","chicago":"Goranci, Gramoz, Monika Henzinger, Harald Räcke, and A. R. Sricharan. “Incremental Approximate Maximum Flow via Residual Graph Sparsification.” <i>ACM Transactions on Algorithms</i>. ACM, 2026. <a href=\"https://doi.org/10.1145/3816252\">https://doi.org/10.1145/3816252</a>.","apa":"Goranci, G., Henzinger, M., Räcke, H., &#38; Sricharan, A. R. (2026). Incremental approximate maximum flow via residual graph sparsification. <i>ACM Transactions on Algorithms</i>. ACM. <a href=\"https://doi.org/10.1145/3816252\">https://doi.org/10.1145/3816252</a>","ista":"Goranci G, Henzinger M, Räcke H, Sricharan AR. 2026. Incremental approximate maximum flow via residual graph sparsification. ACM Transactions on Algorithms. 22(3), 31.","ieee":"G. Goranci, M. Henzinger, H. Räcke, and A. R. Sricharan, “Incremental approximate maximum flow via residual graph sparsification,” <i>ACM Transactions on Algorithms</i>, vol. 22, no. 3. ACM, 2026.","ama":"Goranci G, Henzinger M, Räcke H, Sricharan AR. Incremental approximate maximum flow via residual graph sparsification. <i>ACM Transactions on Algorithms</i>. 2026;22(3). doi:<a href=\"https://doi.org/10.1145/3816252\">10.1145/3816252</a>"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"last_name":"Goranci","first_name":"Gramoz","full_name":"Goranci, Gramoz"},{"id":"540c9bbd-f2de-11ec-812d-d04a5be85630","last_name":"Henzinger","orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H","first_name":"Monika H"},{"last_name":"Räcke","full_name":"Räcke, Harald","first_name":"Harald"},{"last_name":"Sricharan","first_name":"A. R.","full_name":"Sricharan, A. R."}],"external_id":{"arxiv":["2502.09105"]},"article_number":"31","title":"Incremental approximate maximum flow via residual graph sparsification","date_published":"2026-07-06T00:00:00Z","researchdata_availability":"no","status":"public","OA_type":"gold","article_type":"original","type":"journal_article","abstract":[{"text":"We give an algorithm that, with high probability, maintains a (1-ε)-approximate s-t maximum flow in undirected, uncapacitated n-vertex graphs undergoing m edge insertions in Õ(m+ n F^*/ε) total update time, where F^{*} is the maximum flow on the final graph. This is the first algorithm to achieve polylogarithmic amortized update time for dense graphs (m = Ω(n²)), and more generally, for graphs where F^* = Õ(m/n). At the heart of our incremental algorithm is the residual graph sparsification technique of Karger and Levine [SICOMP '15], originally designed for computing exact maximum flows in the static setting. Our main contributions are (i) showing how to maintain such sparsifiers for approximate maximum flows in the incremental setting and (ii) generalizing the cut sparsification framework of Fung et al. [SICOMP '19] from undirected graphs to balanced directed graphs.","lang":"eng"}],"ddc":["000"],"department":[{"_id":"MoHe"}],"date_updated":"2026-08-20T06:28:01Z","volume":22,"arxiv":1,"month":"07","quality_controlled":"1","publication":"ACM Transactions on Algorithms","has_accepted_license":"1","acknowledgement":"M. Henzinger: This project has received funding from the European Research Council (ERC) under the European Union’s\r\nHorizon 2020 research and innovation programme (MoDynStruct, No. 101019564)   and the Austrian Science Fund\r\n(FWF) grant DOI 10.55776/Z422, grant DOI 10.55776/I5982, and grant DOI 10.55776/P33775 with additional funding from the\r\nnetidee SCIENCE Stiftung, 2020–2024. Views and opinions expressed are those of the author(s) only and do not necessarily\r\nreflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor\r\nthe granting authority can be held responsible for them","PlanS_conform":"1","oa":1,"file_date_updated":"2026-08-20T06:19:51Z","supplementarymaterial":"yes","publication_status":"published","intvolume":"        22","_id":"22716","language":[{"iso":"eng"}],"day":"06","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"21280"}]},"corr_author":"1","file":[{"date_created":"2026-08-20T06:19:51Z","file_size":2272512,"relation":"main_file","access_level":"open_access","checksum":"97969d26dab25c3a35be3ae4dd0fd9ee","content_type":"application/pdf","file_name":"2026_TransactionsAlgorithms_Goranci.pdf","creator":"dernst","success":1,"file_id":"22740","date_updated":"2026-08-20T06:19:51Z"}],"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"year":"2026","date_created":"2026-08-16T22:01:43Z","article_processing_charge":"Yes","project":[{"name":"The design and evaluation of modern fully dynamic data structures","call_identifier":"H2020","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","grant_number":"101019564"},{"name":"Efficient algorithms","_id":"34def286-11ca-11ed-8bc3-da5948e1613c","grant_number":"Z00422"},{"_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103","grant_number":"I05982","name":"Static and Dynamic Hierarchical Graph Decompositions"},{"_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe","grant_number":"P33775","name":"Fast Algorithms for a Reactive Network Layer"}],"scopus_import":"1","issue":"3","publication_identifier":{"eissn":["1549-6333"],"issn":["1549-6325"]},"ec_funded":1,"das_tickbox":"0"}]