[{"license":"https://creativecommons.org/licenses/by/4.0/","year":"2026","ec_funded":1,"has_accepted_license":"1","scopus_import":"1","publisher":"Association for Computing Machinery","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"title":"An improved quality hierarchical congestion approximator in near-linear time","abstract":[{"lang":"eng","text":"A single-commodity congestion approximator for a graph is a compact data structure that approximately predicts the edge congestion required to route any set of single-commodity flow demands in a network. A hierarchical congestion approximator (HCA) consists of a laminar family of cuts in the graph and has numerous applications in approximating cut and flow problems in graphs, designing efficient routing schemes, and managing distributed networks.\r\nThere is a tradeoff between the running time for computing an HCA and its approximation quality. The best polynomial-time construction in an n-node graph gives an HCA with approximation quality O(log1.5n loglogn). Among near-linear time algorithms, the best previous result achieves approximation quality O(log4 n). We improve upon the latter result by giving the first near-linear time algorithm for computing an HCA with approximation quality O(log2 n loglogn). Additionally, our algorithm can be implemented in the parallel setting with polylogarithmic span and near-linear work, achieving the same approximation quality. This improves upon the best previous such algorithm, which has an O(log9n) approximation quality. We also present a lower bound of Ω(logn) for the approximation guarantee of hierarchical congestion approximators.\r\nCrucial for achieving a near-linear running time is a new partitioning routine that, unlike previous such routines, manages to avoid recursing on large subgraphs. To achieve the improved approximation quality, we introduce the new concept of border routability of a cut and provide an improved sparsest cut oracle for general vertex weights."}],"keyword":["Congestion Approximators","Hierarchical Graph Decompositions"],"das_tickbox":"0","status":"public","date_created":"2026-07-05T22:01:36Z","project":[{"_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","grant_number":"101019564","call_identifier":"H2020","name":"The design and evaluation of modern fully dynamic data structures"},{"_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103","grant_number":"I05982","name":"Static and Dynamic Hierarchical Graph Decompositions"}],"month":"06","citation":{"ama":"Henzinger M, Münk R, Räcke H. An improved quality hierarchical congestion approximator in near-linear time. In: <i>58th Annual ACM Symposium on Theory of Computing</i>. Association for Computing Machinery; 2026:1417-1428. doi:<a href=\"https://doi.org/10.1145/3798129.3800851\">10.1145/3798129.3800851</a>","mla":"Henzinger, Monika, et al. “An Improved Quality Hierarchical Congestion Approximator in Near-Linear Time.” <i>58th Annual ACM Symposium on Theory of Computing</i>, Association for Computing Machinery, 2026, pp. 1417–28, doi:<a href=\"https://doi.org/10.1145/3798129.3800851\">10.1145/3798129.3800851</a>.","ieee":"M. Henzinger, R. Münk, and H. Räcke, “An improved quality hierarchical congestion approximator in near-linear time,” in <i>58th Annual ACM Symposium on Theory of Computing</i>, Salt Lake City, UT, United States, 2026, pp. 1417–1428.","apa":"Henzinger, M., Münk, R., &#38; Räcke, H. (2026). An improved quality hierarchical congestion approximator in near-linear time. In <i>58th Annual ACM Symposium on Theory of Computing</i> (pp. 1417–1428). Salt Lake City, UT, United States: Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3798129.3800851\">https://doi.org/10.1145/3798129.3800851</a>","short":"M. Henzinger, R. Münk, H. Räcke, in:, 58th Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, 2026, pp. 1417–1428.","chicago":"Henzinger, Monika, Robin Münk, and Harald Räcke. “An Improved Quality Hierarchical Congestion Approximator in Near-Linear Time.” In <i>58th Annual ACM Symposium on Theory of Computing</i>, 1417–28. Association for Computing Machinery, 2026. <a href=\"https://doi.org/10.1145/3798129.3800851\">https://doi.org/10.1145/3798129.3800851</a>.","ista":"Henzinger M, Münk R, Räcke H. 2026. An improved quality hierarchical congestion approximator in near-linear time. 58th Annual ACM Symposium on Theory of Computing. STOC: Symposium on the Theory of Computing, 1417–1428."},"language":[{"iso":"eng"}],"doi":"10.1145/3798129.3800851","OA_place":"publisher","ddc":["000"],"article_processing_charge":"No","_id":"22245","quality_controlled":"1","oa":1,"conference":{"name":"STOC: Symposium on the Theory of Computing","start_date":"2026-06-22","end_date":"2026-06-26","location":"Salt Lake City, UT, United States"},"external_id":{"arxiv":["2511.03716"]},"OA_type":"gold","publication":"58th Annual ACM Symposium on Theory of Computing","corr_author":"1","acknowledgement":"We thank Evangelos Kosinas for helpful discussions on this topic.\r\nFunded by the European Union. Views and opinions expressed\r\nare however those of the author(s) only and do not necessarily\r\nreflect those of the European Union or the European Research\r\nCouncil Executive Agency. Neither the European Union nor the\r\ngranting authority can be held responsible for them.\r\nThis project has received funding from the European Research\r\nCouncil (ERC) under the European Union’s Horizon 2020 research\r\nand innovation programme (MoDynStruct, No. 101019564)\r\nand the Austrian Science Fund (FWF) grant DOI 10.55776/I5982. For\r\nopen access purposes, the author has applied a CC BY public copyright license to any author-accepted manuscript version arising\r\nfrom this submission.\r\nThis project has received funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 498605858.","date_updated":"2026-07-06T06:59:52Z","author":[{"id":"540c9bbd-f2de-11ec-812d-d04a5be85630","orcid":"0000-0002-5008-6530","last_name":"Henzinger","full_name":"Henzinger, Monika H","first_name":"Monika H"},{"last_name":"Münk","full_name":"Münk, Robin","first_name":"Robin"},{"first_name":"Harald","full_name":"Räcke, Harald","last_name":"Räcke"}],"publication_identifier":{"isbn":["9798400725364"],"issn":["0737-8017"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","researchdata_availability":"no","supplementarymaterial":"no","arxiv":1,"oa_version":"Published Version","publication_status":"published","file":[{"file_name":"2026_STOC_HenzingerMo.pdf","access_level":"open_access","file_size":919005,"checksum":"2bef46be8da6d19a641697bb0d8ade65","creator":"dernst","file_id":"22250","content_type":"application/pdf","success":1,"date_created":"2026-07-06T06:57:16Z","date_updated":"2026-07-06T06:57:16Z","relation":"main_file"}],"date_published":"2026-06-09T00:00:00Z","file_date_updated":"2026-07-06T06:57:16Z","day":"09","department":[{"_id":"MoHe"}],"type":"conference","page":"1417-1428"}]