[{"author":[{"first_name":"Gramoz","last_name":"Goranci","full_name":"Goranci, Gramoz"},{"last_name":"Henzinger","full_name":"Henzinger, Monika H","orcid":"0000-0002-5008-6530","first_name":"Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630"},{"first_name":"Peter","full_name":"Kiss, Peter","last_name":"Kiss"},{"last_name":"Momeni","full_name":"Momeni, Ali","first_name":"Ali"},{"full_name":"Zöcklein, Gernot","last_name":"Zöcklein","id":"45d5e826-47af-11f1-84e5-ba87c23fe681","first_name":"Gernot"}],"day":"07","project":[{"call_identifier":"H2020","grant_number":"101019564","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","name":"The design and evaluation of modern fully dynamic data structures"},{"name":"Static and Dynamic Hierarchical Graph Decompositions","grant_number":"I05982","_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103"}],"publisher":"Society for Industrial and Applied Mathematics","volume":"2026-January","citation":{"apa":"Goranci, G., Henzinger, M., Kiss, P., Momeni, A., &#38; Zöcklein, G. (2026). Dynamic hierarchical j-tree decomposition and its applications. In <i>Proceedings of the 2026 Annual ACM SIAM Symposium on Discrete Algorithms</i> (Vol. 2026–January, pp. 1128–1180). Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/1.9781611978971.45\">https://doi.org/10.1137/1.9781611978971.45</a>","short":"G. Goranci, M. Henzinger, P. Kiss, A. Momeni, G. Zöcklein, in:, Proceedings of the 2026 Annual ACM SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, 2026, pp. 1128–1180.","ama":"Goranci G, Henzinger M, Kiss P, Momeni A, Zöcklein G. Dynamic hierarchical j-tree decomposition and its applications. In: <i>Proceedings of the 2026 Annual ACM SIAM Symposium on Discrete Algorithms</i>. Vol 2026-January. Society for Industrial and Applied Mathematics; 2026:1128-1180. doi:<a href=\"https://doi.org/10.1137/1.9781611978971.45\">10.1137/1.9781611978971.45</a>","chicago":"Goranci, Gramoz, Monika Henzinger, Peter Kiss, Ali Momeni, and Gernot Zöcklein. “Dynamic Hierarchical J-Tree Decomposition and Its Applications.” In <i>Proceedings of the 2026 Annual ACM SIAM Symposium on Discrete Algorithms</i>, 2026–January:1128–80. Society for Industrial and Applied Mathematics, 2026. <a href=\"https://doi.org/10.1137/1.9781611978971.45\">https://doi.org/10.1137/1.9781611978971.45</a>.","mla":"Goranci, Gramoz, et al. “Dynamic Hierarchical J-Tree Decomposition and Its Applications.” <i>Proceedings of the 2026 Annual ACM SIAM Symposium on Discrete Algorithms</i>, vol. 2026–January, Society for Industrial and Applied Mathematics, 2026, pp. 1128–80, doi:<a href=\"https://doi.org/10.1137/1.9781611978971.45\">10.1137/1.9781611978971.45</a>.","ista":"Goranci G, Henzinger M, Kiss P, Momeni A, Zöcklein G. 2026. Dynamic hierarchical j-tree decomposition and its applications. Proceedings of the 2026 Annual ACM SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms vol. 2026–January, 1128–1180.","ieee":"G. Goranci, M. Henzinger, P. Kiss, A. Momeni, and G. Zöcklein, “Dynamic hierarchical j-tree decomposition and its applications,” in <i>Proceedings of the 2026 Annual ACM SIAM Symposium on Discrete Algorithms</i>, 2026, vol. 2026–January, pp. 1128–1180."},"page":"1128-1180","publication_status":"published","ec_funded":1,"scopus_import":"1","month":"01","oa_version":"Preprint","conference":{"name":"SODA: Symposium on Discrete Algorithms"},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2601.09139","open_access":"1"}],"status":"public","OA_place":"repository","quality_controlled":"1","doi":"10.1137/1.9781611978971.45","department":[{"_id":"MoHe"}],"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"Monika Henzinger: Funded by the European union. Views and opinions expressed\r\nare 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.\r\nPeter Kiss: This research was funded in whole or in part by the Austrian Science Fund (FWF)\r\n10.55776/ESP6088024.","arxiv":1,"publication_identifier":{"issn":["10719040"],"eissn":["15579468"],"isbn":["9781611978971"]},"year":"2026","date_updated":"2026-05-04T11:54:09Z","publication":"Proceedings of the 2026 Annual ACM SIAM Symposium on Discrete Algorithms","date_created":"2026-04-12T22:01:51Z","abstract":[{"lang":"eng","text":"We develop a new algorithmic framework for designing approximation algorithms for cut-based optimization problems on capacitated undirected graphs that undergo edge insertions and deletions. Specifically, our framework dynamically maintains a variant of the hierarchical 𝑗-tree decomposition of [Madry FOCS’10], achieving a poly-logarithmic approximation factor to the graph’s cut structure and supporting edge updates in 𝑂⁡(𝑛𝜀) amortized update time, for any arbitrarily small constant 𝜀 ∈(0,1).\r\nConsequently, we obtain new trade-offs between approximation and update/query time for fundamental cut-based optimization problems in the fully dynamic setting, including all-pairs minimum cuts, sparsest cut, multi-way cut, and multi-cut. For the last three problems, these trade-offs give the first fully-dynamic algorithms achieving poly-logarithmic approximation in sub-linear time per operation.\r\nThe main technical ingredient behind our dynamic hierarchy is a dynamic cut-sparsifier algorithm that can handle vertex splits with low recourse. This is achieved by white-boxing the dynamic cut sparsifier construction of [Abraham et al. FOCS’16], based on forest packing, together with new structural insights about the maintenance of these forests under vertex splits. Given the versatility of cut sparsification in both the static and dynamic graph algorithms literature, we believe this construction may be of independent interest."}],"external_id":{"arxiv":["2601.09139"]},"type":"conference","_id":"21719","OA_type":"green","language":[{"iso":"eng"}],"article_processing_charge":"No","title":"Dynamic hierarchical j-tree decomposition and its applications","date_published":"2026-01-07T00:00:00Z"}]