[{"type":"conference","arxiv":1,"OA_place":"repository","department":[{"_id":"MoHe"}],"date_updated":"2026-05-04T11:54:09Z","_id":"21719","date_published":"2026-01-07T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["10719040"],"isbn":["9781611978971"],"eissn":["15579468"]},"quality_controlled":"1","external_id":{"arxiv":["2601.09139"]},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2601.09139"}],"volume":"2026-January","doi":"10.1137/1.9781611978971.45","publication_status":"published","day":"07","project":[{"_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","grant_number":"101019564","call_identifier":"H2020","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"}],"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."}],"language":[{"iso":"eng"}],"OA_type":"green","page":"1128-1180","date_created":"2026-04-12T22:01:51Z","year":"2026","oa_version":"Preprint","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.","status":"public","oa":1,"publication":"Proceedings of the 2026 Annual ACM SIAM Symposium on Discrete Algorithms","publisher":"Society for Industrial and Applied Mathematics","ec_funded":1,"conference":{"name":"SODA: Symposium on Discrete Algorithms"},"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>","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>","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.","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.","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.","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>."},"scopus_import":"1","month":"01","author":[{"full_name":"Goranci, Gramoz","last_name":"Goranci","first_name":"Gramoz"},{"full_name":"Henzinger, Monika H","last_name":"Henzinger","first_name":"Monika H","orcid":"0000-0002-5008-6530","id":"540c9bbd-f2de-11ec-812d-d04a5be85630"},{"first_name":"Peter","last_name":"Kiss","full_name":"Kiss, Peter"},{"first_name":"Ali","full_name":"Momeni, Ali","last_name":"Momeni"},{"id":"45d5e826-47af-11f1-84e5-ba87c23fe681","first_name":"Gernot","full_name":"Zöcklein, Gernot","last_name":"Zöcklein"}],"article_processing_charge":"No","title":"Dynamic hierarchical j-tree decomposition and its applications"},{"month":"06","author":[{"last_name":"Kalinin","full_name":"Kalinin, Nikita","first_name":"Nikita","id":"4b14526e-14d2-11ed-ba64-c14c9553d137"},{"last_name":"Andersson","full_name":"Andersson, Joel D","first_name":"Joel D","id":"4a893819-d954-11f0-89b1-e360bad9ccc5"}],"researchdata_availability":"no","citation":{"ieee":"N. Kalinin and J. D. Andersson, “Learning rate scheduling with matrix factorization for private training,” in <i>7th Symposium on Foundations of Responsible Computing</i>, Cambridge, MA; United States, 2026, vol. 368.","short":"N. Kalinin, J.D. Andersson, in:, 7th Symposium on Foundations of Responsible Computing, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026.","ama":"Kalinin N, Andersson JD. Learning rate scheduling with matrix factorization for private training. In: <i>7th Symposium on Foundations of Responsible Computing</i>. Vol 368. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2026. doi:<a href=\"https://doi.org/10.4230/LIPIcs.FORC.2026.2\">10.4230/LIPIcs.FORC.2026.2</a>","apa":"Kalinin, N., &#38; Andersson, J. D. (2026). Learning rate scheduling with matrix factorization for private training. In <i>7th Symposium on Foundations of Responsible Computing</i> (Vol. 368). Cambridge, MA; United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.FORC.2026.2\">https://doi.org/10.4230/LIPIcs.FORC.2026.2</a>","ista":"Kalinin N, Andersson JD. 2026. Learning rate scheduling with matrix factorization for private training. 7th Symposium on Foundations of Responsible Computing. FORC: Symposium on Foundations of Responsible Computing, LIPIcs, vol. 368, 2:1-2:21.","mla":"Kalinin, Nikita, and Joel D. Andersson. “Learning Rate Scheduling with Matrix Factorization for Private Training.” <i>7th Symposium on Foundations of Responsible Computing</i>, vol. 368, 2:1-2:21, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026, doi:<a href=\"https://doi.org/10.4230/LIPIcs.FORC.2026.2\">10.4230/LIPIcs.FORC.2026.2</a>.","chicago":"Kalinin, Nikita, and Joel D Andersson. “Learning Rate Scheduling with Matrix Factorization for Private Training.” In <i>7th Symposium on Foundations of Responsible Computing</i>, Vol. 368. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026. <a href=\"https://doi.org/10.4230/LIPIcs.FORC.2026.2\">https://doi.org/10.4230/LIPIcs.FORC.2026.2</a>."},"scopus_import":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"conference":{"name":"FORC: Symposium on Foundations of Responsible Computing","end_date":"2026-06-05","start_date":"2026-06-03","location":"Cambridge, MA; United States"},"ec_funded":1,"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","publication":"7th Symposium on Foundations of Responsible Computing","supplementarymaterial":"no","file_date_updated":"2026-06-29T06:55:23Z","article_processing_charge":"No","title":"Learning rate scheduling with matrix factorization for private training","das_tickbox":"0","has_accepted_license":"1","oa_version":"Published Version","oa":1,"status":"public","acknowledgement":"We thank Rasmus Pagh, Christoph Lampert and Jalaj Upadhyay for valuable\r\ncomments on an early draft. We thank Ryan Mckenna for a fruitful discussion on the experiment\r\ndesign. We thank Antti Honkela for sharing insights on learning rate scheduling and DP.\r\nNikita P. Kalinin: Funded in part by the Austrian Science Fund (FWF) [10.55776/COE12].\r\nJoel Daniel Andersson: Funded by the European Union. Views and opinions expressed are however\r\nthose of the author(s) only and do not necessarily reflect those of the European Union or the European\r\nResearch Council Executive Agency. Neither the European Union nor the granting authority can be\r\nheld responsible for them. This project has received funding from the European Research Council\r\n(ERC) under the European Union’s Horizon 2020 research and innovation programme (MoDynStruct,\r\nNo. 101019564). Additional funding by Providentia, a Data Science Distinguished Investigator grant\r\nfrom Novo Nordisk Fonden, with additional support from VILLUM Investigator grant 54451.\r\n","doi":"10.4230/LIPIcs.FORC.2026.2","publication_status":"published","intvolume":"       368","ddc":["000"],"volume":368,"external_id":{"arxiv":["2511.17994"]},"article_number":"2:1-2:21","date_created":"2026-06-28T22:01:34Z","OA_type":"gold","year":"2026","day":"01","alternative_title":["LIPIcs"],"project":[{"grant_number":"101019564","call_identifier":"H2020","name":"The design and evaluation of modern fully dynamic data structures","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62"}],"abstract":[{"lang":"eng","text":"We study differentially private model training with stochastic gradient descent under learning rate scheduling and correlated noise. Although correlated noise, in particular via matrix factorizations, has been shown to improve accuracy, prior theoretical work focused primarily on the prefix-sum workload. That workload assumes a constant learning rate, whereas in practice learning rate schedules are widely used to accelerate training and improve convergence. We close this gap by deriving general upper and lower bounds for a broad class of learning rate schedules in both single- and multi-epoch settings. Building on these results, we propose a learning-rate-aware factorization that achieves improvements over prefix-sum factorizations under both MaxSE and MeanSE error metrics. Our theoretical analysis yields memory-efficient constructions suitable for practical deployment, and experiments on CIFAR-10 and IMDB datasets confirm that schedule-aware factorizations improve accuracy in private training."}],"language":[{"iso":"eng"}],"department":[{"_id":"ChLa"},{"_id":"GradSch"},{"_id":"MoHe"}],"OA_place":"publisher","arxiv":1,"corr_author":"1","type":"conference","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2026-06-01T00:00:00Z","publication_identifier":{"eissn":["1868-8969"],"isbn":["9783959774192"]},"quality_controlled":"1","keyword":["differential privacy","machine learning","matrix factorization"],"_id":"22146","file":[{"file_name":"2026_LIPIcsFORC_Kalinin.pdf","date_updated":"2026-06-29T06:55:23Z","date_created":"2026-06-29T06:55:23Z","checksum":"c661f016d3861a1c1b590b87a744d087","creator":"dernst","file_id":"22149","success":1,"content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_size":1231914}],"date_updated":"2026-06-29T06:56:34Z"},{"oa":1,"status":"public","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.","has_accepted_license":"1","das_tickbox":"0","oa_version":"Published Version","supplementarymaterial":"no","file_date_updated":"2026-07-06T06:57:16Z","article_processing_charge":"No","title":"An improved quality hierarchical congestion approximator in near-linear time","author":[{"last_name":"Henzinger","full_name":"Henzinger, Monika H","first_name":"Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","orcid":"0000-0002-5008-6530"},{"full_name":"Münk, Robin","last_name":"Münk","first_name":"Robin"},{"first_name":"Harald","full_name":"Räcke, Harald","last_name":"Räcke"}],"month":"06","scopus_import":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"citation":{"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>","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>","short":"M. Henzinger, R. Münk, H. Räcke, in:, 58th Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, 2026, pp. 1417–1428.","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.","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>.","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.","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>."},"researchdata_availability":"no","ec_funded":1,"publisher":"Association for Computing Machinery","conference":{"start_date":"2026-06-22","location":"Salt Lake City, UT, United States","end_date":"2026-06-26","name":"STOC: Symposium on the Theory of Computing"},"publication":"58th Annual ACM Symposium on Theory of Computing","keyword":["Congestion Approximators","Hierarchical Graph Decompositions"],"quality_controlled":"1","date_published":"2026-06-09T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"isbn":["9798400725364"],"issn":["0737-8017"]},"_id":"22245","date_updated":"2026-07-06T06:59:52Z","file":[{"relation":"main_file","content_type":"application/pdf","file_size":919005,"access_level":"open_access","checksum":"2bef46be8da6d19a641697bb0d8ade65","date_created":"2026-07-06T06:57:16Z","date_updated":"2026-07-06T06:57:16Z","file_name":"2026_STOC_HenzingerMo.pdf","success":1,"creator":"dernst","file_id":"22250"}],"department":[{"_id":"MoHe"}],"arxiv":1,"OA_place":"publisher","corr_author":"1","type":"conference","year":"2026","date_created":"2026-07-05T22:01:36Z","OA_type":"gold","page":"1417-1428","abstract":[{"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.","lang":"eng"}],"language":[{"iso":"eng"}],"project":[{"name":"The design and evaluation of modern fully dynamic data structures","call_identifier":"H2020","grant_number":"101019564","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62"},{"_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103","name":"Static and Dynamic Hierarchical Graph Decompositions","grant_number":"I05982"}],"day":"09","ddc":["000"],"doi":"10.1145/3798129.3800851","publication_status":"published","external_id":{"arxiv":["2511.03716"]}},{"status":"public","oa":1,"article_type":"original","acknowledgement":"1Salil Vadhan was supported by NSF grant BCS-2218803, a grant from the Sloan Foundation, and\r\na Simons Investigator Award. Work began while a Visiting Researcher at the Bocconi University\r\nDepartment of Computing Sciences, supported by Luca Trevisan’s ERC Project GA-834861.\r\n2Monika Henzinger and Roodabeh Safavi were supported by the European Research Council (ERC)\r\nunder the European Union’s Horizon 2020 research and innovation programme (Grant agreement\r\nNo. 101019564), and the Austrian Science Fund (FWF) under grants DOI 10.55776/Z422, DOI\r\n10.55776/I5982, and DOI 10.55776/P33775. For open access purposes, the author has applied a CC BY\r\npublic copyright license to any author-accepted manuscript version arising from this submission.\r\nViews and opinions expressed are however those of the author(s)\r\nonly and do not necessarily reflect those of the European Union\r\nor the European Research Council Executive Agency. Neither the\r\nEuropean Union nor the granting authority can be held responsible for them.","has_accepted_license":"1","das_tickbox":"0","PlanS_conform":"1","oa_version":"Published Version","supplementarymaterial":"no","title":"Concurrent composition for differentially private continual mechanisms","article_processing_charge":"Yes","issue":"2","file_date_updated":"2026-07-16T09:09:53Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"scopus_import":"1","citation":{"ama":"Henzinger M, Safavi Hemami R, Vadhan S. Concurrent composition for differentially private continual mechanisms. <i>Proceedings of the ACM on Management of Data</i>. 2026;4(2):1-26. doi:<a href=\"https://doi.org/10.1145/3801895\">10.1145/3801895</a>","apa":"Henzinger, M., Safavi Hemami, R., &#38; Vadhan, S. (2026). Concurrent composition for differentially private continual mechanisms. <i>Proceedings of the ACM on Management of Data</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3801895\">https://doi.org/10.1145/3801895</a>","ieee":"M. Henzinger, R. Safavi Hemami, and S. Vadhan, “Concurrent composition for differentially private continual mechanisms,” <i>Proceedings of the ACM on Management of Data</i>, vol. 4, no. 2. Association for Computing Machinery, pp. 1–26, 2026.","short":"M. Henzinger, R. Safavi Hemami, S. Vadhan, Proceedings of the ACM on Management of Data 4 (2026) 1–26.","ista":"Henzinger M, Safavi Hemami R, Vadhan S. 2026. Concurrent composition for differentially private continual mechanisms. Proceedings of the ACM on Management of Data. 4(2), 1–26.","mla":"Henzinger, Monika, et al. “Concurrent Composition for Differentially Private Continual Mechanisms.” <i>Proceedings of the ACM on Management of Data</i>, vol. 4, no. 2, Association for Computing Machinery, 2026, pp. 1–26, doi:<a href=\"https://doi.org/10.1145/3801895\">10.1145/3801895</a>.","chicago":"Henzinger, Monika, Roodabeh Safavi Hemami, and Salil Vadhan. “Concurrent Composition for Differentially Private Continual Mechanisms.” <i>Proceedings of the ACM on Management of Data</i>. Association for Computing Machinery, 2026. <a href=\"https://doi.org/10.1145/3801895\">https://doi.org/10.1145/3801895</a>."},"researchdata_availability":"no","author":[{"id":"540c9bbd-f2de-11ec-812d-d04a5be85630","orcid":"0000-0002-5008-6530","first_name":"Monika H","full_name":"Henzinger, Monika H","last_name":"Henzinger"},{"full_name":"Safavi Hemami, Roodabeh","last_name":"Safavi Hemami","id":"72ed2640-8972-11ed-ae7b-f9c81ec75154","first_name":"Roodabeh"},{"full_name":"Vadhan, Salil","last_name":"Vadhan","first_name":"Salil"}],"month":"06","publication":"Proceedings of the ACM on Management of Data","publisher":"Association for Computing Machinery","ec_funded":1,"quality_controlled":"1","keyword":["differential privacy","concurrent composition","continual release","continual observation","data streaming","continual mechanisms","concurrent parallel composition","concurrent filter composition"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["2836-6573"]},"date_published":"2026-06-01T00:00:00Z","date_updated":"2026-07-16T09:14:49Z","file":[{"file_size":655405,"access_level":"open_access","relation":"main_file","content_type":"application/pdf","success":1,"creator":"dernst","file_id":"22345","checksum":"c6c5e256d02b90682c0690c3bee94040","date_created":"2026-07-16T09:09:53Z","date_updated":"2026-07-16T09:09:53Z","file_name":"2026_ACMMgmtData_Henzinger.pdf"}],"_id":"22318","OA_place":"publisher","arxiv":1,"department":[{"_id":"MoHe"}],"type":"journal_article","corr_author":"1","abstract":[{"text":"Many intended uses of differential privacy involve a continual mechanism that is set up to run continuously\r\nover a long period of time, making more statistical releases as either queries come in or the dataset is updated.\r\nIn this paper, we give the first general treatment of privacy against adaptive adversaries for mechanisms that\r\nsupport dataset updates and a variety of queries, all arbitrarily interleaved. It also models a very general notion\r\nof neighboring, that includes both event-level and user-level privacy. We prove several concurrent composition\r\ntheorems for continual mechanisms, which ensure privacy even when an adversary can interleave its queries\r\nand dataset updates to the different composed mechanisms. Previous concurrent composition theorems for\r\ndifferential privacy were only for the case when the dataset is static, with no adaptive updates. We also give\r\nthe first interactive and continual generalizations of the “parallel composition theorem” for noninteractive\r\ndifferential privacy. Specifically, we show that the analogue of the noninteractive parallel composition theorem\r\nholds if either there are no adaptive dataset updates or each of the composed mechanisms satisfies pure\r\ndifferential privacy, but it fails to hold for composing approximately differentially private mechanisms with\r\ndataset updates. Thus, we prove a tight new composition theorem for this case. In addition, we prove concurrent\r\nfilter compositions theorems for the scenarios in which the privacy parameters are adaptively chosen. We\r\nextend these results to other measures of differential privacy, including Rényi DP and 𝑓 -DP.\r\nWe then formalize a set of general conditions on a continual mechanism M that runs multiple continual submechanisms such that the privacy guarantees of M follow directly using the above concurrent composition\r\ntheorems on the sub-mechanisms, without further privacy loss. This enables us to give a simpler and modular\r\nprivacy analysis of a recent continual histogram mechanism of Henzinger, Sricharan, and Steiner. In the\r\ncase of approximate DP, ours is the first proof that shows that its privacy holds against adaptive adversaries.\r\nWe also provide a framework that simplifies the analysis of local differential privacy when the protocol\r\nincludes multi-round server-user interactions. Using this result, we simplify the privacy analysis of the core\r\ndecomposition protocol of Dhulipala, Henzinger, Li, Liu, Sricharan, and Zhu [5].","lang":"eng"}],"project":[{"_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","call_identifier":"H2020","name":"The design and evaluation of modern fully dynamic data structures","grant_number":"101019564"},{"_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103","grant_number":"I05982","name":"Static and Dynamic Hierarchical Graph Decompositions"},{"name":"Fast Algorithms for a Reactive Network Layer","grant_number":"P33775","_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe"},{"grant_number":"Z00422","name":"Efficient algorithms","_id":"34def286-11ca-11ed-8bc3-da5948e1613c"}],"language":[{"iso":"eng"}],"day":"01","year":"2026","page":"1-26","date_created":"2026-07-13T14:59:14Z","OA_type":"gold","ddc":["000"],"publication_status":"published","doi":"10.1145/3801895","intvolume":"         4","external_id":{"arxiv":["2411.03299"]},"volume":4},{"das_tickbox":"0","has_accepted_license":"1","oa_version":"Published Version","PlanS_conform":"1","status":"public","oa":1,"article_type":"original","acknowledgement":"Bardiya Aryanfard and Monika Henzinger were supported by the European Research Council (ERC)\r\nunder the European Union’s Horizon 2020 research and innovation programme (Grant agreement\r\nNo. 101019564). For open access purposes, the author has applied a CC BY public copyright\r\nlicense to any author-accepted manuscript version arising from this submission. Funded by the\r\nEuropean union. Views and opinions expressed are however those of the author(s) only and do\r\nnot necessarily reflect those of the European Union or the European Research Council Executive\r\nAgency. Neither the European Union nor the granting authority can be held responsible for them","citation":{"chicago":"Aryanfard, Bardiya, Monika Henzinger, David Saulpic, and A. R. Sricharan. “Improved Lower Bounds for Privacy under Continual Release.” <i>Proceedings of the ACM on Management of Data</i>. Association for Computing Machinery, 2026. <a href=\"https://doi.org/10.1145/3801903\">https://doi.org/10.1145/3801903</a>.","mla":"Aryanfard, Bardiya, et al. “Improved Lower Bounds for Privacy under Continual Release.” <i>Proceedings of the ACM on Management of Data</i>, vol. 4, no. 2, Association for Computing Machinery, 2026, pp. 1–27, doi:<a href=\"https://doi.org/10.1145/3801903\">10.1145/3801903</a>.","ista":"Aryanfard B, Henzinger M, Saulpic D, Sricharan AR. 2026. Improved lower bounds for privacy under continual release. Proceedings of the ACM on Management of Data. 4(2), 1–27.","ama":"Aryanfard B, Henzinger M, Saulpic D, Sricharan AR. Improved lower bounds for privacy under continual release. <i>Proceedings of the ACM on Management of Data</i>. 2026;4(2):1-27. doi:<a href=\"https://doi.org/10.1145/3801903\">10.1145/3801903</a>","apa":"Aryanfard, B., Henzinger, M., Saulpic, D., &#38; Sricharan, A. R. (2026). Improved lower bounds for privacy under continual release. <i>Proceedings of the ACM on Management of Data</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3801903\">https://doi.org/10.1145/3801903</a>","ieee":"B. Aryanfard, M. Henzinger, D. Saulpic, and A. R. Sricharan, “Improved lower bounds for privacy under continual release,” <i>Proceedings of the ACM on Management of Data</i>, vol. 4, no. 2. Association for Computing Machinery, pp. 1–27, 2026.","short":"B. Aryanfard, M. Henzinger, D. Saulpic, A.R. Sricharan, Proceedings of the ACM on Management of Data 4 (2026) 1–27."},"researchdata_availability":"no","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"scopus_import":"1","month":"06","author":[{"first_name":"Bardiya","id":"1e8f4084-31df-11ee-b195-f706b4b77091","full_name":"Aryanfard, Bardiya","last_name":"Aryanfard"},{"first_name":"Monika H","orcid":"0000-0002-5008-6530","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","last_name":"Henzinger","full_name":"Henzinger, Monika H"},{"last_name":"Saulpic","full_name":"Saulpic, David","first_name":"David","id":"f8e48cf0-b0ff-11ed-b0e9-b4c35598f964"},{"first_name":"A. R.","full_name":"Sricharan, A. R.","last_name":"Sricharan"}],"publication":"Proceedings of the ACM on Management of Data","publisher":"Association for Computing Machinery","ec_funded":1,"supplementarymaterial":"no","title":"Improved lower bounds for privacy under continual release","article_processing_charge":"Yes","file_date_updated":"2026-07-16T09:29:08Z","issue":"2","OA_place":"publisher","arxiv":1,"department":[{"_id":"MoHe"},{"_id":"GradSch"}],"type":"journal_article","corr_author":"1","publication_identifier":{"issn":["2836-6573"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2026-06-01T00:00:00Z","quality_controlled":"1","file":[{"checksum":"21a48a620e415a31a3874077c55bc6c3","date_created":"2026-07-16T09:29:08Z","date_updated":"2026-07-16T09:29:08Z","file_name":"2026_ACMMgmtData_Aryanfard.pdf","success":1,"file_id":"22349","creator":"dernst","relation":"main_file","content_type":"application/pdf","file_size":934963,"access_level":"open_access"}],"date_updated":"2026-07-16T09:30:31Z","_id":"22322","publication_status":"published","doi":"10.1145/3801903","intvolume":"         4","ddc":["000"],"external_id":{"arxiv":["2512.15981"]},"volume":4,"day":"01","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"We study the problem of continually releasing statistics of an evolving dataset under differential privacy. In the event-level setting, we show the first polynomial lower bounds on the additive error for insertions-only graph problems such as maximum matching, degree histogram and k-core number computation. These results represent an exponential improvement on the polylogarithmic lower bounds of Fichtenberger, Henzinger and Ost [ESA 2021] for the former two problems, and are the first lower bounds in the continual release setting for the latter problem. Our results run counter to the intuition that the difference between insertions-only vs fully dynamic updates causes the gap between polylogarithmic and polynomial additive error. Indeed, we show that for estimating the size of the maximum matching or k-core number of a vertex, allowing small multiplicative approximations is what brings the additive error down to polylogarithmic. We complement these results with improved upper bounds on the additive error when no multiplicative approximation is allowed.\r\nBeyond graphs, our techniques also show that polynomial additive error is unavoidable for the Simultaneous Norm Estimation problem in the insertions-only setting. When multiplicative approximations are allowed, we circumvent this lower bound by giving the first continual mechanism with polylogarithmic additive error under (1 + ζ) multiplicative approximations, for any ζ > 0, for estimating all monotone symmetric norms simultaneously.\r\nIn the item-level setting, we show polynomial lower bounds on the product of the multiplicative and the additive error of continual mechanisms for a large range of graph problems. To the best of our knowledge, these are the first lower bounds shown for any differentially private mechanism under continual release with multiplicative error. To obtain these results, we prove a new lower bound on the product of multiplicative and additive error for the 1-Way-Marginals problem, and give reductions from 1-Way-Marginals to our desired graph problems. This generalizes the prior results of Hardt and Talwar [STOC 2010] and Bun, Ullman and Vadhan [STOC 2014, SIAM J. Comput. 2018], who gave lower bounds on the additive error for the special case of mechanisms with no multiplicative error."}],"project":[{"_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","call_identifier":"H2020","name":"The design and evaluation of modern fully dynamic data structures","grant_number":"101019564"}],"OA_type":"gold","date_created":"2026-07-14T05:33:58Z","page":"1-27","year":"2026"},{"corr_author":"1","type":"conference","department":[{"_id":"MoHe"},{"_id":"GradSch"}],"arxiv":1,"OA_place":"publisher","_id":"22327","date_updated":"2026-07-22T07:49:22Z","file":[{"success":1,"creator":"dernst","file_id":"22353","date_created":"2026-07-16T11:18:44Z","checksum":"e56da70c1b2e7e663d2d8106cf07a30a","file_name":"2026_ACMPODC_Breitkopf.pdf","date_updated":"2026-07-16T11:18:44Z","file_size":702140,"access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"quality_controlled":"1","date_published":"2026-07-01T00:00:00Z","publication_identifier":{"isbn":["9798400725128"]},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","external_id":{"arxiv":["2605.18707"]},"ddc":["000"],"publication_status":"published","doi":"10.1145/3796701.3815913","year":"2026","OA_type":"gold","date_created":"2026-07-14T05:40:17Z","page":"414 - 424","project":[{"name":"The design and evaluation of modern fully dynamic data structures","call_identifier":"H2020","grant_number":"101019564","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62"},{"_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103","name":"Static and Dynamic Hierarchical Graph Decompositions","grant_number":"I05982"}],"language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"Population protocols are a model of distributed computing where\r\n𝑛 agents, each a simple finite-state machine, interact in pairs to\r\nsolve a common task against a (adversarial) interaction scheduler.\r\nThis model was intensively studied in recent years; in particular,\r\nthe problem of relative majority received much attention: Each\r\nagent starts with an input opinion (or color) out of 𝑘 possibilities,\r\nand the goal is for each agent to eventually output the color with\r\nthe largest support in the population. Before our work, the state\r\ncomplexity (the minimum number of states required per agent) was\r\nonly known to be between Ω(𝑘\r\n2\r\n) and𝑂(𝑘\r\n7\r\n). Our main contribution\r\nis a population protocol that solves the relative majority problem\r\nwith 𝑘\r\n3\r\nstates. We achieve this result with a new protocol called\r\nCircles. While prior approaches in the literature relied on duels of\r\nagents to find the majority color — an approach that proved effective\r\nfor the case with two colors — Circles partitions the agents into\r\ncircular linked lists of decreasing sizes, with the property that no\r\ntwo agents with the same initial color lie in the same circle. We\r\nshow that Circles always correctly computes the desired structure\r\nagainst the most adversarial of schedulers (weakly fair). We then\r\nshow that a trivial extension of Circles solves the relative majority\r\nproblem. We extend our protocol to handle various tie-breaking\r\nmechanisms or to support the case where the agents do not share a\r\nprior ordering of the colors. Finally, we show that a modification of\r\nCircles solves the ranking problem with 2 · 𝑘^4\r\nstates, where each\r\nagent must output the rank of its initial color in the population."}],"day":"01","oa_version":"Published Version","has_accepted_license":"1","das_tickbox":"0","acknowledgement":"Funded by the European union. Views and opinions expressed are\r\nhowever those of the author(s) only and do not necessarily reflect\r\nthose of the European Union or the European Research Council\r\nExecutive Agency. Neither the European Union nor the granting authority can be held responsible for them. This project has received\r\nfunding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme\r\n(MoDynStruct, No. 101019564) and the Austrian Science\r\nFund (FWF) grant DOI 10.55776/I5982. For open access purposes,\r\nthe author has applied a CC BY public copyright license to any\r\nauthor-accepted manuscript version arising from this submission.","oa":1,"status":"public","publisher":"Association for Computing Machinery","conference":{"end_date":"2026-07-10","location":"Egham, United Kingdom","start_date":"2026-07-06","name":"PODC: Symposium on Principles of Distributed Computing"},"ec_funded":1,"publication":"Proceedings of the ACM Symposium on Principles of Distributed Computing","author":[{"first_name":"Tom-Lukas","last_name":"Breitkopf","full_name":"Breitkopf, Tom-Lukas"},{"last_name":"Dallot","full_name":"Dallot, Julien","first_name":"Julien"},{"full_name":"El-Hayek, Antoine","last_name":"El-Hayek","orcid":"0000-0003-4268-7368","id":"888a098e-fcac-11ee-aff7-d347be57b725","first_name":"Antoine"},{"first_name":"Stefan","full_name":"Schmid, Stefan","last_name":"Schmid"}],"month":"07","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"scopus_import":"1","researchdata_availability":"no","citation":{"apa":"Breitkopf, T.-L., Dallot, J., El-Hayek, A., &#38; Schmid, S. (2026). Ranking opinions with few states in population protocols. In <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i> (pp. 414–424). Egham, United Kingdom: Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3796701.3815913\">https://doi.org/10.1145/3796701.3815913</a>","ama":"Breitkopf T-L, Dallot J, El-Hayek A, Schmid S. Ranking opinions with few states in population protocols. In: <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i>. Association for Computing Machinery; 2026:414-424. doi:<a href=\"https://doi.org/10.1145/3796701.3815913\">10.1145/3796701.3815913</a>","ieee":"T.-L. Breitkopf, J. Dallot, A. El-Hayek, and S. Schmid, “Ranking opinions with few states in population protocols,” in <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i>, Egham, United Kingdom, 2026, pp. 414–424.","short":"T.-L. Breitkopf, J. Dallot, A. El-Hayek, S. Schmid, in:, Proceedings of the ACM Symposium on Principles of Distributed Computing, Association for Computing Machinery, 2026, pp. 414–424.","ista":"Breitkopf T-L, Dallot J, El-Hayek A, Schmid S. 2026. Ranking opinions with few states in population protocols. Proceedings of the ACM Symposium on Principles of Distributed Computing. PODC: Symposium on Principles of Distributed Computing, 414–424.","mla":"Breitkopf, Tom-Lukas, et al. “Ranking Opinions with Few States in Population Protocols.” <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i>, Association for Computing Machinery, 2026, pp. 414–24, doi:<a href=\"https://doi.org/10.1145/3796701.3815913\">10.1145/3796701.3815913</a>.","chicago":"Breitkopf, Tom-Lukas, Julien Dallot, Antoine El-Hayek, and Stefan Schmid. “Ranking Opinions with Few States in Population Protocols.” In <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i>, 414–24. Association for Computing Machinery, 2026. <a href=\"https://doi.org/10.1145/3796701.3815913\">https://doi.org/10.1145/3796701.3815913</a>."},"file_date_updated":"2026-07-16T11:18:44Z","title":"Ranking opinions with few states in population protocols","article_processing_charge":"Yes","supplementarymaterial":"no"},{"related_material":{"record":[{"relation":"part_of_dissertation","id":"20051","status":"public"},{"id":"18557","relation":"part_of_dissertation","status":"public"},{"status":"public","relation":"part_of_dissertation","id":"19982"},{"id":"21720","relation":"part_of_dissertation","status":"public"},{"id":"22374","relation":"part_of_dissertation","status":"public"},{"status":"public","relation":"part_of_dissertation","id":"22373"}]},"author":[{"full_name":"El-Hayek, Antoine","last_name":"El-Hayek","orcid":"0000-0003-4268-7368","id":"888a098e-fcac-11ee-aff7-d347be57b725","first_name":"Antoine"}],"month":"07","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"citation":{"ista":"El-Hayek A. 2026. Handling updates and failures: Dynamic graph algorithms and distributed computing on dynamic networks. Institute of Science and Technology Austria.","mla":"El-Hayek, Antoine. <i>Handling Updates and Failures: Dynamic Graph Algorithms and Distributed Computing on Dynamic Networks</i>. Institute of Science and Technology Austria, 2026, doi:<a href=\"https://doi.org/10.15479/AT-ISTA-22281\">10.15479/AT-ISTA-22281</a>.","chicago":"El-Hayek, Antoine. “Handling Updates and Failures: Dynamic Graph Algorithms and Distributed Computing on Dynamic Networks.” Institute of Science and Technology Austria, 2026. <a href=\"https://doi.org/10.15479/AT-ISTA-22281\">https://doi.org/10.15479/AT-ISTA-22281</a>.","ieee":"A. El-Hayek, “Handling updates and failures: Dynamic graph algorithms and distributed computing on dynamic networks,” Institute of Science and Technology Austria, 2026.","short":"A. El-Hayek, Handling Updates and Failures: Dynamic Graph Algorithms and Distributed Computing on Dynamic Networks, Institute of Science and Technology Austria, 2026.","apa":"El-Hayek, A. (2026). <i>Handling updates and failures: Dynamic graph algorithms and distributed computing on dynamic networks</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT-ISTA-22281\">https://doi.org/10.15479/AT-ISTA-22281</a>","ama":"El-Hayek A. Handling updates and failures: Dynamic graph algorithms and distributed computing on dynamic networks. 2026. doi:<a href=\"https://doi.org/10.15479/AT-ISTA-22281\">10.15479/AT-ISTA-22281</a>"},"ec_funded":1,"publisher":"Institute of Science and Technology Austria","doi_confirm":"1","file_date_updated":"2026-07-20T11:29:38Z","title":"Handling updates and failures: Dynamic graph algorithms and distributed computing on dynamic networks","article_processing_charge":"No","has_accepted_license":"1","oa_version":"Published Version","oa":1,"status":"public","acknowledgement":"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)\r\n\"The Design and Evaluation of Modern Fully Dynamic Data Structures\" , from the\r\nAustrian Science Fund (FWF) grant DOI 10.55776/I5982 \"Static and Dynamic Hierarchical\r\nGraph Decompositions\", and from the Austrian Science Fund (FWF) and netIDEE SCIENCE\r\nproject P 33775-N, \"Fast Algorithms for a Reactive Network Layer\".\r\n","ddc":["000"],"doi":"10.15479/AT-ISTA-22281","publisher_comment":"Sections 2.4 and 7.1 and chapter 6 are not CC-BY 4.0, they are All Rights Reserved.","publication_status":"published","year":"2026","date_created":"2026-07-13T09:39:59Z","page":"244","abstract":[{"text":"In this thesis, we took a look at networks, and more specifically, at networks that change over time, whether those are networks in the distributed algorithms sense of the word, or the graph algorithm sense. \r\n\r\nIn distributed algorithms, we looked at two main problems. First, the broadcast problem: given n agents, each agent is tasked to forward a (unique) message to every other agent. Agents collaborate and can copy and forward all messages they have received up until that point. Broadcast is achieved when one agent has successfully broadcast its message to everyone else. We studied the case where the communication network is controlled by an adversary, under the condition that the graph is rooted in every round of communication. We show that the adversary can delay broadcast for at most  l\r\n(1 + √\r\n2)n\r\nm\r\n rounds, improving on the $O(n\\log\\log n)$ previous upper bound~\\cite{fugger2020radius}, and asymptotically matching the $\\sim 1.5n$ lower bound~\\cite{schwarz2017linear}.\r\n\r\nWe then looked at the stochastic version of the problem: here, the adversary -- parametrized by $k$ where $k=0$ signifies that the adversary has no control,  and $k=n$ that the adversary has full control -- can choose parts of the graph, and the graph is then completed stochastically. Here, we are able to look at a stronger version of broadcast: instead of having $n$ messages trying to be broadcast in parallel, we can assume that only one message needs to be broadcasted. We show the bound $\\Theta(k+\\log n)$.\r\n\r\nThen, we looked at undecided states dynamics in population protocols: given a population of $n$ agents, where each initially holds an opinion among $k$ different ones. In each round, two agents are chosen uniformly at random, and can interact. If they have different opinions, they forget their opinions and become undecided. If one of them is undecided while the other has an opinion, they undecided agent copies they opinion of the decided one. The question is then, how many interactions does it take for the whole population to share the same opinion? We show a $\\Omega(kn\\log \\frac {\\sqrt n} {k \\log n})$ lower bound  for any $k = o\\left(\\frac {\\sqrt n}{\\log n}\\right)$.\r\nThis is tight for any $ k \\le n^{\\frac 1 2 - \\epsilon}$, where $\\epsilon >0$ can be any small constant, matching the known $O(kn\\log n)$ upper bound for $k = O\\left(\\frac {\\sqrt n} {\\log ^2 n}\\right)$~\\cite{DBLP:conf/podc/AmirABBHKL23}.\r\n\r\nFinally, in dynamic algorithms, we study the minimum cut problem: we are given a graph, whose vertex set we want to partition into two subsets such that the number of edges crossing from one subset to the other is minimized. Then, the graph can be updated via edge insertions or deletions, and we must update the solution without recomputing everything from scratch. We present an exact fully-dynamic minimum cut algorithm that runs in $n^{o(1)}$ deterministic update time when the minimum cut size is at most $2^{\\Theta(\\log^{3/4-c}n)}$ for any $c>0$, improving on the previous algorithm~\\cite{DBLP:conf/soda/JinST24} whose minimum cut size limit is $(\\log n)^{o(1)}$. Using sparsification and randomization techniques, we are able to extend this to all values of the minimum cut in weighted graphs, at the cost of a $(1+o(1))$-approximation ratio.","lang":"eng"}],"alternative_title":["ISTA Thesis"],"language":[{"iso":"eng"}],"degree_awarded":"PhD","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"},{"name":"Fast Algorithms for a Reactive Network Layer","grant_number":"P33775","_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe"}],"day":"13","department":[{"_id":"GradSch"},{"_id":"MoHe"}],"OA_place":"publisher","corr_author":"1","supervisor":[{"full_name":"Henzinger, Monika H","last_name":"Henzinger","first_name":"Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","orcid":"0000-0002-5008-6530"}],"type":"dissertation","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","date_published":"2026-07-13T00:00:00Z","publication_identifier":{"issn":["2663-337X"]},"_id":"22281","date_updated":"2026-07-24T12:48:29Z","file":[{"success":1,"creator":"aelhayek","file_id":"22356","checksum":"923e4ca769c9ef2f6b0b005444faf462","date_created":"2026-07-17T11:39:47Z","date_updated":"2026-07-17T11:39:47Z","file_name":"2026_El-Hayek_Antoine_Thesis.pdf","file_size":5465973,"access_level":"open_access","relation":"main_file","content_type":"application/pdf"},{"checksum":"262689f9df27dd6c2c7c7861f1de7329","date_created":"2026-07-17T11:40:34Z","date_updated":"2026-07-20T11:29:38Z","file_name":"2026_El-Hayek_Antoine_Thesis.zip","creator":"aelhayek","file_id":"22357","relation":"source_file","content_type":"application/x-zip-compressed","file_size":9116107,"access_level":"closed"}]},{"status":"public","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.","oa_version":"Preprint","title":"Deterministic and exact fully-dynamic minimum cut of superpolylogarithmic size in subpolynomial time","article_processing_charge":"No","scopus_import":"1","citation":{"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>.","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>.","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.","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.","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>","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>"},"author":[{"id":"888a098e-fcac-11ee-aff7-d347be57b725","orcid":"0000-0003-4268-7368","first_name":"Antoine","last_name":"El-Hayek","full_name":"El-Hayek, Antoine"},{"last_name":"Henzinger","full_name":"Henzinger, Monika H","orcid":"0000-0002-5008-6530","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","first_name":"Monika H"},{"first_name":"Jason","full_name":"Li, Jason","last_name":"Li"}],"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"22281"}]},"month":"01","publication":"Proceedings of the Annual ACM SIAM Symposium on Discrete Algorithms","conference":{"name":"SODA: Symposium on Discrete Algorithms","end_date":"2026-01-14","start_date":"2026-01-11","location":"Vancouver, Canada"},"ec_funded":1,"publisher":"Society for Industrial and Applied Mathematics","quality_controlled":"1","date_published":"2026-01-07T00:00:00Z","publication_identifier":{"issn":["1071-9040"],"eissn":["1557-9468"],"eisbn":["9781611978971"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2026-07-24T12:48:29Z","_id":"21720","arxiv":1,"OA_place":"repository","department":[{"_id":"MoHe"},{"_id":"GradSch"}],"type":"conference","language":[{"iso":"eng"}],"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)."}],"project":[{"call_identifier":"H2020","name":"The design and evaluation of modern fully dynamic data structures","grant_number":"101019564","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62"},{"name":"Static and Dynamic Hierarchical Graph Decompositions","grant_number":"I05982","_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103"}],"day":"07","year":"2026","date_created":"2026-04-12T22:01:51Z","page":"613-663","OA_type":"green","doi":"10.1137/1.9781611978971.25","intvolume":"      2026","publication_status":"published","external_id":{"arxiv":["2512.13105"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2512.13105","open_access":"1"}],"volume":2026},{"ddc":["000"],"intvolume":"       334","publication_status":"published","doi":"10.4230/lipics.icalp.2025.91","volume":334,"external_id":{"arxiv":["2502.09105"]},"year":"2025","OA_type":"gold","date_created":"2026-02-17T08:26:06Z","page":"91:1-91:20","project":[{"name":"The design and evaluation of modern fully dynamic data structures","call_identifier":"H2020","grant_number":"101019564","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62"},{"name":"Efficient algorithms","grant_number":"Z00422","_id":"34def286-11ca-11ed-8bc3-da5948e1613c"},{"grant_number":"I05982","name":"Static and Dynamic Hierarchical Graph Decompositions","_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103"},{"grant_number":"P33775","name":"Fast Algorithms for a Reactive Network Layer","_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe"}],"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"}],"alternative_title":["LIPIcs"],"language":[{"iso":"eng"}],"day":"30","department":[{"_id":"MoHe"}],"OA_place":"publisher","arxiv":1,"corr_author":"1","type":"conference","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"isbn":["9783959773720"]},"date_published":"2025-06-30T00:00:00Z","_id":"21280","date_updated":"2026-02-18T09:06:12Z","file":[{"date_created":"2026-02-18T09:02:33Z","checksum":"c178cf554e44204b9f64ebd9b54cf7ba","file_name":"2025_ICALP_Goranci.pdf","date_updated":"2026-02-18T09:02:33Z","success":1,"creator":"dernst","file_id":"21315","relation":"main_file","content_type":"application/pdf","file_size":944824,"access_level":"open_access"}],"author":[{"full_name":"Goranci, Gramoz","last_name":"Goranci","first_name":"Gramoz"},{"first_name":"Monika H","orcid":"0000-0002-5008-6530","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","full_name":"Henzinger, Monika H","last_name":"Henzinger"},{"last_name":"Räcke","full_name":"Räcke, Harald","first_name":"Harald"},{"last_name":"Sricharan","full_name":"Sricharan, A.","first_name":"A."}],"month":"06","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"scopus_import":"1","citation":{"ama":"Goranci G, Henzinger M, Räcke H, Sricharan A. Incremental approximate maximum flow via residual graph sparsification. In: <i>52nd International Colloquium on Automata, Languages, and Programming</i>. Vol 334. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2025:91:1-91:20. doi:<a href=\"https://doi.org/10.4230/lipics.icalp.2025.91\">10.4230/lipics.icalp.2025.91</a>","apa":"Goranci, G., Henzinger, M., Räcke, H., &#38; Sricharan, A. (2025). Incremental approximate maximum flow via residual graph sparsification. In <i>52nd International Colloquium on Automata, Languages, and Programming</i> (Vol. 334, p. 91:1-91:20). Aarhus, Denmark: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/lipics.icalp.2025.91\">https://doi.org/10.4230/lipics.icalp.2025.91</a>","short":"G. Goranci, M. Henzinger, H. Räcke, A. Sricharan, in:, 52nd International Colloquium on Automata, Languages, and Programming, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025, p. 91:1-91:20.","ieee":"G. Goranci, M. Henzinger, H. Räcke, and A. Sricharan, “Incremental approximate maximum flow via residual graph sparsification,” in <i>52nd International Colloquium on Automata, Languages, and Programming</i>, Aarhus, Denmark, 2025, vol. 334, p. 91:1-91:20.","mla":"Goranci, Gramoz, et al. “Incremental Approximate Maximum Flow via Residual Graph Sparsification.” <i>52nd International Colloquium on Automata, Languages, and Programming</i>, vol. 334, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025, p. 91:1-91:20, doi:<a href=\"https://doi.org/10.4230/lipics.icalp.2025.91\">10.4230/lipics.icalp.2025.91</a>.","chicago":"Goranci, Gramoz, Monika Henzinger, Harald Räcke, and A. Sricharan. “Incremental Approximate Maximum Flow via Residual Graph Sparsification.” In <i>52nd International Colloquium on Automata, Languages, and Programming</i>, 334:91:1-91:20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. <a href=\"https://doi.org/10.4230/lipics.icalp.2025.91\">https://doi.org/10.4230/lipics.icalp.2025.91</a>.","ista":"Goranci G, Henzinger M, Räcke H, Sricharan A. 2025. Incremental approximate maximum flow via residual graph sparsification. 52nd International Colloquium on Automata, Languages, and Programming. ICALP: Automata, Languages and Programming, LIPIcs, vol. 334, 91:1-91:20."},"ec_funded":1,"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","conference":{"name":"ICALP: Automata, Languages and Programming","end_date":"2025-07-11","start_date":"2025-07-08","location":"Aarhus, Denmark"},"publication":"52nd International Colloquium on Automata, Languages, and Programming","file_date_updated":"2026-02-18T09:02:33Z","article_processing_charge":"No","title":"Incremental approximate maximum flow via residual graph sparsification","has_accepted_license":"1","oa_version":"Published Version","oa":1,"status":"public","acknowledgement":"Monika Henzinger and A. R. Sricharan: This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation\r\nprogramme (MoDynStruct, No. 101019564) and the Austrian Science Fund (FWF) grant DOI\r\n10.55776/Z422, grant DOI 10.55776/I5982, and grant DOI 10.55776/P33775 with additional funding from the netidee SCIENCE Stiftung, 2020–2024. Harald Räcke: This project has received funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 498605858 and 470029389."},{"article_type":"original","acknowledgement":"The first author thanks Chandra Chekuri for useful discussions about this paper. This work was done in part at the University of Vienna. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No. 101019564 “The Design of Modern Fully Dynamic Data Structures (MoDynStruct)” and from the Austrian Science Fund (FWF) project “Fast Algorithms for a Reactive Network Layer (ReactNet)”, P 33775-N, with additional funding from the netidee SCIENCE Stiftung, 2020–2024.","status":"public","oa":1,"oa_version":"Preprint","article_processing_charge":"No","title":"Multiplicative auction algorithm for approximate maximum weight bipartite matching","isi":1,"publication":"Mathematical Programming","publisher":"Springer Nature","ec_funded":1,"scopus_import":"1","citation":{"chicago":"Zheng, Da Wei, and Monika Henzinger. “Multiplicative Auction Algorithm for Approximate Maximum Weight Bipartite Matching.” <i>Mathematical Programming</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s10107-024-02066-3\">https://doi.org/10.1007/s10107-024-02066-3</a>.","mla":"Zheng, Da Wei, and Monika Henzinger. “Multiplicative Auction Algorithm for Approximate Maximum Weight Bipartite Matching.” <i>Mathematical Programming</i>, vol. 210, Springer Nature, 2025, pp. 881–94, doi:<a href=\"https://doi.org/10.1007/s10107-024-02066-3\">10.1007/s10107-024-02066-3</a>.","ista":"Zheng DW, Henzinger M. 2025. Multiplicative auction algorithm for approximate maximum weight bipartite matching. Mathematical Programming. 210, 881–894.","apa":"Zheng, D. W., &#38; Henzinger, M. (2025). Multiplicative auction algorithm for approximate maximum weight bipartite matching. <i>Mathematical Programming</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10107-024-02066-3\">https://doi.org/10.1007/s10107-024-02066-3</a>","ama":"Zheng DW, Henzinger M. Multiplicative auction algorithm for approximate maximum weight bipartite matching. <i>Mathematical Programming</i>. 2025;210:881-894. doi:<a href=\"https://doi.org/10.1007/s10107-024-02066-3\">10.1007/s10107-024-02066-3</a>","short":"D.W. Zheng, M. Henzinger, Mathematical Programming 210 (2025) 881–894.","ieee":"D. W. Zheng and M. Henzinger, “Multiplicative auction algorithm for approximate maximum weight bipartite matching,” <i>Mathematical Programming</i>, vol. 210. Springer Nature, pp. 881–894, 2025."},"author":[{"full_name":"Zheng, Da Wei","last_name":"Zheng","first_name":"Da Wei"},{"id":"540c9bbd-f2de-11ec-812d-d04a5be85630","orcid":"0000-0002-5008-6530","first_name":"Monika H","full_name":"Henzinger, Monika H","last_name":"Henzinger"}],"related_material":{"record":[{"relation":"earlier_version","id":"13236","status":"public"}]},"month":"03","date_updated":"2025-09-09T12:39:58Z","_id":"15121","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2025-03-01T00:00:00Z","publication_identifier":{"issn":["0025-5610"],"eissn":["1436-4646"]},"type":"journal_article","corr_author":"1","arxiv":1,"OA_place":"repository","department":[{"_id":"MoHe"}],"language":[{"iso":"eng"}],"project":[{"grant_number":"101019564","call_identifier":"H2020","name":"The design and evaluation of modern fully dynamic data structures","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62"},{"_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe","grant_number":"P33775","name":"Fast Algorithms for a Reactive Network Layer"}],"abstract":[{"lang":"eng","text":"We present an auction algorithm using multiplicative instead of constant weight updates to compute a (1-E)-approximate maximum weight matching (MWM) in a bipartite graph with n vertices and m edges in time 0(mE-1), beating the running time of the fastest known approximation algorithm of Duan and Pettie [JACM ’14] that runs in 0(mE-1 log E-1). Our algorithm is very simple and it can be extended to give a dynamic data structure that maintains a (1-E)-approximate maximum weight matching under (1) one-sided vertex deletions (with incident edges) and (2) one-sided vertex insertions (with incident edges sorted by weight) to the other side. The total time time used is 0(mE-1), where m is the sum of the number of initially existing and inserted edges."}],"day":"01","year":"2025","OA_type":"green","page":"881-894","date_created":"2024-03-17T23:00:58Z","external_id":{"isi":["001176048100003"],"arxiv":["2301.09217"]},"volume":210,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2301.09217","open_access":"1"}],"doi":"10.1007/s10107-024-02066-3","intvolume":"       210","publication_status":"published"},{"date_updated":"2025-04-14T13:50:49Z","_id":"19038","date_published":"2025-01-20T00:00:00Z","publication_identifier":{"issn":["1071-9040"],"isbn":["979-833131200-8"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","type":"conference","arxiv":1,"OA_place":"repository","department":[{"_id":"MoHe"}],"day":"20","project":[{"_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","grant_number":"101019564","call_identifier":"H2020","name":"The design and evaluation of modern fully dynamic data structures"},{"name":"Efficient algorithms","grant_number":"Z00422","_id":"34def286-11ca-11ed-8bc3-da5948e1613c"},{"_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103","grant_number":"I05982","name":"Static and Dynamic Hierarchical Graph Decompositions"},{"_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe","name":"Fast Algorithms for a Reactive Network Layer","grant_number":"P33775"}],"abstract":[{"lang":"eng","text":"Differentially private weighted prefix sum under continual observation is a crucial component in the production-level deployment of private next-word prediction for Gboard, which, according to Google, has over a billion users. More specifically, Google uses a differentially private mechanism to sum weighted gradients in its private follow-the-regularized leader algorithm. Apart from efficiency, the additive error of the private mechanism is crucial as multiplied with the square root of the model’s dimension d (with d ranging up to 10 trillion, for example, Switch Transformers or M6-10T), it determines the accuracy of the learning system. So, any improvement in leading constant matters significantly in practice. In this paper, we show a novel connection between mechanisms for continual weighted prefix sum and a concept in representation theory known as the group matrix introduced in correspondence between Dedekind and Frobenius (Sitzungsber. Preuss. Akad. Wiss. Berlin, 1897) and generalized by Schur (Journal für die reine und angewandte Mathematik, 1904). To the best of our knowledge, this is the first application of group algebra in the analysis of differentially private algorithms. Using this connection, we analyze a class of matrix norms known as factorization norms that give upper and lower bounds for the additive error under general ℓp-norms of the matrix mechanism. This allows us to give 1. the first efficient factorization that matches the best-known non-constructive upper bound on the factorization norm by Mathias (SIAM Journal of Matrix Analysis and Applications, 1993) for the matrix used in Google’s deployment, and also improves on the previous best-known constructive bound of Fichtenberger, Henzinger, and Upadhyay (ICML 2023) and Henzinger, Upadhyay, and Upadhyay (SODA 2023); thereby, partially resolving an open question in operator theory, 2. the first upper bound on the additive error for a large class of weight functions for weighted prefix sum problems, including the sliding window matrix (Bolot, Fawaz, Muthukrishnan, Nikolov, and Taft (ICDT 2013). We also improve the bound on factorizing the striped matrix used for outputting a synthetic graph that approximates all cuts (Fichtenberger, Henzinger, and Upadhyay (ICML 2023)); 3. a general improved upper bound on the factorization norms that depend on algebraic properties of the weighted sum matrices and that applies to a more general class of weighting functions than the ones considered in Henzinger, Upadhyay, and Upadhyay (SODA 2024). Using the known connection between these factorization norms and the ℓp-error of continual weighted sum, we give an upper bound on the ℓp-error for the continual weighted sum problem for p ≥ 2."}],"language":[{"iso":"eng"}],"OA_type":"green","page":"2951 - 2970","date_created":"2025-02-17T09:31:03Z","year":"2025","external_id":{"arxiv":["2412.02840"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2412.02840","open_access":"1"}],"volume":5,"publication_status":"published","doi":"10.1137/1.9781611978322.95","intvolume":"         5","acknowledgement":"Monika Henzinger: This project has received funding from the European Research Council(ERC) under the European Union’s Horizon 2020 research and innovation programme (Grantagreement No. 101019564) and the Austrian Science Fund (FWF) grant DOI 10.55776/Z422,grant DOI 10.55776/I5982, and grant DOI 10.55776/P33775 with additional funding from the netidee SCIENCEStiftung, 2020–2024.Jalaj Upadhyay’s research was funded by the Rutgers Decanal Grant no. 302918 and an unrestricted giftfrom Google. This work was done in part while visiting the Institute of Science and Technology Austria (ISTA).The authors would like to thank Sarvagya Upadhyay for the initial discussion and feedback on the early draft of the paper. The authors would like to thank the anonymous reviewers, Brendan McMahan and Abhradeep Thakurta for the discussions that helped improve the presentation of the final version of the paper.","status":"public","oa":1,"oa_version":"Preprint","title":"Improved differentially private continual observation using group algebra","article_processing_charge":"No","publication":"Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms","conference":{"end_date":"2025-01-15","start_date":"2025-01-12","location":"New Orleans, LA, United States","name":"SODA: Symposium on Discrete Algorithms"},"publisher":"Association for Computing Machinery","ec_funded":1,"citation":{"mla":"Henzinger, Monika, and Jalaj Upadhyay. “Improved Differentially Private Continual Observation Using Group Algebra.” <i>Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms</i>, vol. 5, Association for Computing Machinery, 2025, pp. 2951–70, doi:<a href=\"https://doi.org/10.1137/1.9781611978322.95\">10.1137/1.9781611978322.95</a>.","ista":"Henzinger M, Upadhyay J. 2025. Improved differentially private continual observation using group algebra. Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms vol. 5, 2951–2970.","chicago":"Henzinger, Monika, and Jalaj Upadhyay. “Improved Differentially Private Continual Observation Using Group Algebra.” In <i>Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms</i>, 5:2951–70. Association for Computing Machinery, 2025. <a href=\"https://doi.org/10.1137/1.9781611978322.95\">https://doi.org/10.1137/1.9781611978322.95</a>.","ama":"Henzinger M, Upadhyay J. Improved differentially private continual observation using group algebra. In: <i>Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms</i>. Vol 5. Association for Computing Machinery; 2025:2951-2970. doi:<a href=\"https://doi.org/10.1137/1.9781611978322.95\">10.1137/1.9781611978322.95</a>","apa":"Henzinger, M., &#38; Upadhyay, J. (2025). Improved differentially private continual observation using group algebra. In <i>Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms</i> (Vol. 5, pp. 2951–2970). New Orleans, LA, United States: Association for Computing Machinery. <a href=\"https://doi.org/10.1137/1.9781611978322.95\">https://doi.org/10.1137/1.9781611978322.95</a>","ieee":"M. Henzinger and J. Upadhyay, “Improved differentially private continual observation using group algebra,” in <i>Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms</i>, New Orleans, LA, United States, 2025, vol. 5, pp. 2951–2970.","short":"M. Henzinger, J. Upadhyay, in:, Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms, Association for Computing Machinery, 2025, pp. 2951–2970."},"scopus_import":"1","month":"01","author":[{"last_name":"Henzinger","full_name":"Henzinger, Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","orcid":"0000-0002-5008-6530","first_name":"Monika H"},{"full_name":"Upadhyay, Jalaj","last_name":"Upadhyay","first_name":"Jalaj"}]},{"status":"public","oa":1,"acknowledgement":"This project has received funding from the European Research Council (ERC) under the\r\nEuropean Union’s Horizon 2020 research and innovation programme (MoDynStruct, No. 101019564) and the Austrian Science Fund (FWF) grant DOI 10.55776/Z422, grant DOI 10.55776/I5982, and grant DOI 10.55776/P33775 with additional funding from the netidee SCIENCE Stiftung, 2020–2024. This work was further supported by the Federal Ministry of Education and Research (BMBF) project, 6G-RIC: 6G Research and Innovation Cluster, grant 16KISK020K.","has_accepted_license":"1","oa_version":"Published Version","article_processing_charge":"No","title":"On b-matching and fully-dynamic maximum k-edge coloring","file_date_updated":"2025-06-23T11:23:29Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"scopus_import":"1","citation":{"ama":"El-Hayek A, Hanauer K, Henzinger M. On b-matching and fully-dynamic maximum k-edge coloring. In: <i>4th Symposium on Algorithmic Foundations of Dynamic Networks</i>. Vol 330. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2025. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SAND.2025.4\">10.4230/LIPIcs.SAND.2025.4</a>","apa":"El-Hayek, A., Hanauer, K., &#38; Henzinger, M. (2025). On b-matching and fully-dynamic maximum k-edge coloring. In <i>4th Symposium on Algorithmic Foundations of Dynamic Networks</i> (Vol. 330). Liverpool, United Kingdom: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SAND.2025.4\">https://doi.org/10.4230/LIPIcs.SAND.2025.4</a>","ieee":"A. El-Hayek, K. Hanauer, and M. Henzinger, “On b-matching and fully-dynamic maximum k-edge coloring,” in <i>4th Symposium on Algorithmic Foundations of Dynamic Networks</i>, Liverpool, United Kingdom, 2025, vol. 330.","short":"A. El-Hayek, K. Hanauer, M. Henzinger, in:, 4th Symposium on Algorithmic Foundations of Dynamic Networks, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025.","mla":"El-Hayek, Antoine, et al. “On B-Matching and Fully-Dynamic Maximum k-Edge Coloring.” <i>4th Symposium on Algorithmic Foundations of Dynamic Networks</i>, vol. 330, 4, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SAND.2025.4\">10.4230/LIPIcs.SAND.2025.4</a>.","chicago":"El-Hayek, Antoine, Kathrin Hanauer, and Monika Henzinger. “On B-Matching and Fully-Dynamic Maximum k-Edge Coloring.” In <i>4th Symposium on Algorithmic Foundations of Dynamic Networks</i>, Vol. 330. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. <a href=\"https://doi.org/10.4230/LIPIcs.SAND.2025.4\">https://doi.org/10.4230/LIPIcs.SAND.2025.4</a>.","ista":"El-Hayek A, Hanauer K, Henzinger M. 2025. On b-matching and fully-dynamic maximum k-edge coloring. 4th Symposium on Algorithmic Foundations of Dynamic Networks. SAND: Symposium on Algorithmic Foundations of Dynamic Networks, LIPIcs, vol. 330, 4."},"author":[{"last_name":"El-Hayek","full_name":"El-Hayek, Antoine","first_name":"Antoine","orcid":"0000-0003-4268-7368","id":"888a098e-fcac-11ee-aff7-d347be57b725"},{"last_name":"Hanauer","full_name":"Hanauer, Kathrin","first_name":"Kathrin"},{"last_name":"Henzinger","full_name":"Henzinger, Monika H","orcid":"0000-0002-5008-6530","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","first_name":"Monika H"}],"month":"06","publication":"4th Symposium on Algorithmic Foundations of Dynamic Networks","isi":1,"conference":{"name":"SAND: Symposium on Algorithmic Foundations of Dynamic Networks","start_date":"2025-06-09","end_date":"2025-06-11","location":"Liverpool, United Kingdom"},"ec_funded":1,"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","quality_controlled":"1","date_published":"2025-06-02T00:00:00Z","publication_identifier":{"isbn":["9783959773683"],"issn":["1868-8969"]},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_updated":"2025-09-30T13:37:28Z","file":[{"date_updated":"2025-06-23T11:23:29Z","file_name":"2025_LIPIcs_ElHayek.pdf","checksum":"ad93a1e052adb29d7bfe8bd551bab193","date_created":"2025-06-23T11:23:29Z","file_id":"19872","creator":"dernst","success":1,"content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_size":995666}],"_id":"19858","OA_place":"publisher","arxiv":1,"department":[{"_id":"MoHe"}],"type":"conference","corr_author":"1","article_number":"4","language":[{"iso":"eng"}],"alternative_title":["LIPIcs"],"abstract":[{"lang":"eng","text":"Given a graph G that undergoes a sequence of edge insertions and deletions, we study the Maximum k-Edge Coloring problem (MkEC): Having access to k different colors, color as many edges of G as possible such that no two adjacent edges share the same color. While this problem is different from simply maintaining a b-matching with b = k, the two problems are related. However, maximum b-matching can be solved efficiently in the static setting, whereas MkEC is NP-hard and even APX-hard for k ≥ 2. \r\nWe present new results on both problems: For b-matching, we show a new integrality gap result and we adapt Wajc’s matching sparsification scheme [David Wajc, 2020] for the case where b is a constant.\r\nUsing these as basis, we give three new algorithms for the dynamic MkEC problem: Our MatchO algorithm builds on the dynamic (2+ε)-approximation algorithm of Bhattacharya, Gupta, and Mohan [Sayan Bhattacharya et al., 2017] for b-matching and achieves a (2+ε)(k+1)/k-approximation in O(poly(log n, ε^-1)) update time against an oblivious adversary. Our MatchA algorithm builds on the dynamic (7+ε)-approximation algorithm by Bhattacharya, Henzinger, and Italiano [Sayan Bhattacharya et al., 2015] for fractional b-matching and achieves a (7+ε)(3k+3)/(3k-1)-approximation in O(poly(log n, ε^-1)) update time against an adaptive adversary. Moreover, our reductions use the dynamic b-matching algorithm as a black box, so any future improvement in the approximation ratio for dynamic b-matching will automatically translate into a better approximation ratio for our algorithms. Finally, we present a greedy algorithm with O(Δ+k) update time, which guarantees a 2.16 approximation factor."}],"project":[{"name":"The design and evaluation of modern fully dynamic data structures","call_identifier":"H2020","grant_number":"101019564","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62"},{"name":"Efficient algorithms","grant_number":"Z00422","_id":"34def286-11ca-11ed-8bc3-da5948e1613c"},{"grant_number":"I05982","name":"Static and Dynamic Hierarchical Graph Decompositions","_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103"},{"grant_number":"P33775","name":"Fast Algorithms for a Reactive Network Layer","_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe"}],"day":"02","year":"2025","date_created":"2025-06-22T22:02:06Z","OA_type":"gold","ddc":["000"],"doi":"10.4230/LIPIcs.SAND.2025.4","publication_status":"published","intvolume":"       330","external_id":{"arxiv":["2310.01149"],"isi":["001532136900004"]},"volume":330},{"date_created":"2025-07-21T08:17:04Z","OA_type":"hybrid","page":"549-552","year":"2025","day":"13","language":[{"iso":"eng"}],"abstract":[{"text":"This paper revisits a fundamental distributed computing problem in the population protocol model. Provided n agents each starting with an input color in [k], the relative majority problem asks to find the predominant color. In the population protocol model, at each time step, a scheduler selects two agents that first learn each other's states and then update their states based on what they learned.\r\nWe present the Circles protocol that solves the relative majority problem with k3 states. It is always-correct under weakly fair scheduling. Not only does it improve upon the best known upper bound of O(k7), but it also shows a strikingly simpler design inspired by energy minimization in chemical settings.","lang":"eng"}],"project":[{"grant_number":"101019564","call_identifier":"H2020","name":"The design and evaluation of modern fully dynamic data structures","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62"},{"grant_number":"I05982","name":"Static and Dynamic Hierarchical Graph Decompositions","_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103"},{"grant_number":"P33775","name":"Fast Algorithms for a Reactive Network Layer","_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe"}],"doi":"10.1145/3732772.3733512","publication_status":"published","ddc":["000"],"external_id":{"isi":["001525534800069"]},"date_published":"2025-06-13T00:00:00Z","publication_identifier":{"isbn":["9798400718854"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","_id":"20052","file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_size":549706,"date_updated":"2025-08-05T07:32:01Z","file_name":"2025_PODC_Breitkopf.pdf","checksum":"e99679ffb28877b7cea4d54860302790","date_created":"2025-08-05T07:32:01Z","file_id":"20123","creator":"dernst","success":1}],"date_updated":"2026-02-16T11:46:37Z","department":[{"_id":"MoHe"}],"OA_place":"publisher","corr_author":"1","type":"conference","file_date_updated":"2025-08-05T07:32:01Z","title":"Brief announcement: Minimizing energy solves relative majority with a cubic number of states in population protocols","article_processing_charge":"No","month":"06","author":[{"last_name":"Breitkopf","full_name":"Breitkopf, Tom-Lukas","first_name":"Tom-Lukas"},{"last_name":"Dallot","full_name":"Dallot, Julien","first_name":"Julien"},{"last_name":"El-Hayek","full_name":"El-Hayek, Antoine","orcid":"0000-0003-4268-7368","id":"888a098e-fcac-11ee-aff7-d347be57b725","first_name":"Antoine"},{"first_name":"Stefan","full_name":"Schmid, Stefan","last_name":"Schmid"}],"citation":{"mla":"Breitkopf, Tom-Lukas, et al. “Brief Announcement: Minimizing Energy Solves Relative Majority with a Cubic Number of States in Population Protocols.” <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i>, Association for Computing Machinery, 2025, pp. 549–52, doi:<a href=\"https://doi.org/10.1145/3732772.3733512\">10.1145/3732772.3733512</a>.","ista":"Breitkopf T-L, Dallot J, El-Hayek A, Schmid S. 2025. Brief announcement: Minimizing energy solves relative majority with a cubic number of states in population protocols. Proceedings of the ACM Symposium on Principles of Distributed Computing. PODC: Symposium on Principles of Distributed Computing, 549–552.","chicago":"Breitkopf, Tom-Lukas, Julien Dallot, Antoine El-Hayek, and Stefan Schmid. “Brief Announcement: Minimizing Energy Solves Relative Majority with a Cubic Number of States in Population Protocols.” In <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i>, 549–52. Association for Computing Machinery, 2025. <a href=\"https://doi.org/10.1145/3732772.3733512\">https://doi.org/10.1145/3732772.3733512</a>.","ama":"Breitkopf T-L, Dallot J, El-Hayek A, Schmid S. Brief announcement: Minimizing energy solves relative majority with a cubic number of states in population protocols. In: <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i>. Association for Computing Machinery; 2025:549-552. doi:<a href=\"https://doi.org/10.1145/3732772.3733512\">10.1145/3732772.3733512</a>","apa":"Breitkopf, T.-L., Dallot, J., El-Hayek, A., &#38; Schmid, S. (2025). Brief announcement: Minimizing energy solves relative majority with a cubic number of states in population protocols. In <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i> (pp. 549–552). Huatulco, Mexico: Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3732772.3733512\">https://doi.org/10.1145/3732772.3733512</a>","ieee":"T.-L. Breitkopf, J. Dallot, A. El-Hayek, and S. Schmid, “Brief announcement: Minimizing energy solves relative majority with a cubic number of states in population protocols,” in <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i>, Huatulco, Mexico, 2025, pp. 549–552.","short":"T.-L. Breitkopf, J. Dallot, A. El-Hayek, S. Schmid, in:, Proceedings of the ACM Symposium on Principles of Distributed Computing, Association for Computing Machinery, 2025, pp. 549–552."},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"publisher":"Association for Computing Machinery","ec_funded":1,"conference":{"start_date":"2025-06-16","location":"Huatulco, Mexico","end_date":"2025-06-20","name":"PODC: Symposium on Principles of Distributed Computing"},"publication":"Proceedings of the ACM Symposium on Principles of Distributed Computing","isi":1,"oa":1,"status":"public","acknowledgement":"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, and grant DOI 10.55776/P33775 with additional funding from the netidee SCIENCE Stiftung, 2020–2024 and the German Research Foundation (DFG), grant 470029389 (FlexNets). ","has_accepted_license":"1","oa_version":"Published Version"},{"day":"01","language":[{"iso":"eng"}],"abstract":[{"text":"We study privately releasing column sums of a d-dimensional table with entries from a universe χ undergoing T row updates, called histogram under continual release. Our mechanisms give better additive ℓ∞-error than existing mechanisms for a large class of queries and input streams. Our first contribution is an output-sensitive mechanism in the insertions-only model (χ = {0, 1}) for maintaining (i) the histogram or (ii) queries that do not require maintaining the entire histogram, such as the maximum or minimum column sum, the median, or any quantiles. The mechanism has an additive error of O(d log2 (dq∗) + log T) whp, where q∗ is the maximum output value over all time steps on this dataset. The mechanism does not require q∗ as input. This breaks the Ω(d log T) bound of prior work when q∗ ≪ T. Our second contribution is a mechanism for the turnstile model that admits negative entry updates (χ = {−1, 0, 1}). This mechanism has an additive error of O(d log2(dK) + log T) whp, where K is the number of times two consecutive data rows differ, and the mechanism does not require K as input. This is useful when monitoring inputs that only vary under unusual circumstances. For d = 1 this gives the first\r\nprivate mechanism with error O(log2 K + log T) for continual counting in the turnstile model, improving on the O(log2 n + log T) error bound by Dwork et al. (2015), where n is the number of ones in the stream, as well as allowing negative entries, while Dwork et al. (2015) can only handle nonnegative entries (χ = {0, 1}). ","lang":"eng"}],"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":"34def286-11ca-11ed-8bc3-da5948e1613c","grant_number":"Z00422","name":"Efficient algorithms"},{"_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103","name":"Static and Dynamic Hierarchical Graph Decompositions","grant_number":"I05982"},{"_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe","grant_number":"P33775","name":"Fast Algorithms for a Reactive Network Layer"}],"alternative_title":["PMLR"],"OA_type":"green","page":"1990-1998","date_created":"2025-09-07T22:01:35Z","year":"2025","publication_status":"published","intvolume":"       258","external_id":{"arxiv":["2302.11341"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2302.11341","open_access":"1"}],"volume":258,"publication_identifier":{"eissn":["2640-3498"]},"date_published":"2025-05-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","date_updated":"2025-09-09T07:09:22Z","_id":"20301","arxiv":1,"OA_place":"repository","department":[{"_id":"MoHe"}],"type":"conference","title":"Differentially private continual release of histograms and related queries","article_processing_charge":"No","citation":{"ieee":"M. Henzinger, A. R. Sricharan, and T. A. Steiner, “Differentially private continual release of histograms and related queries,” in <i>The 28th International Conference on Artificial Intelligence and Statistics</i>, Mai Khao, Thailand, 2025, vol. 258, pp. 1990–1998.","short":"M. Henzinger, A.R. Sricharan, T.A. Steiner, in:, The 28th International Conference on Artificial Intelligence and Statistics, ML Research Press, 2025, pp. 1990–1998.","apa":"Henzinger, M., Sricharan, A. R., &#38; Steiner, T. A. (2025). Differentially private continual release of histograms and related queries. In <i>The 28th International Conference on Artificial Intelligence and Statistics</i> (Vol. 258, pp. 1990–1998). Mai Khao, Thailand: ML Research Press.","ama":"Henzinger M, Sricharan AR, Steiner TA. Differentially private continual release of histograms and related queries. In: <i>The 28th International Conference on Artificial Intelligence and Statistics</i>. Vol 258. ML Research Press; 2025:1990-1998.","chicago":"Henzinger, Monika, A. R. Sricharan, and Teresa Anna Steiner. “Differentially Private Continual Release of Histograms and Related Queries.” In <i>The 28th International Conference on Artificial Intelligence and Statistics</i>, 258:1990–98. ML Research Press, 2025.","mla":"Henzinger, Monika, et al. “Differentially Private Continual Release of Histograms and Related Queries.” <i>The 28th International Conference on Artificial Intelligence and Statistics</i>, vol. 258, ML Research Press, 2025, pp. 1990–98.","ista":"Henzinger M, Sricharan AR, Steiner TA. 2025. Differentially private continual release of histograms and related queries. The 28th International Conference on Artificial Intelligence and Statistics. AISTATS: Conference on Artificial Intelligence and Statistics, PMLR, vol. 258, 1990–1998."},"scopus_import":"1","month":"05","author":[{"orcid":"0000-0002-5008-6530","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","first_name":"Monika H","full_name":"Henzinger, Monika H","last_name":"Henzinger"},{"last_name":"Sricharan","full_name":"Sricharan, A. R.","first_name":"A. R."},{"first_name":"Teresa Anna","full_name":"Steiner, Teresa Anna","last_name":"Steiner"}],"publication":"The 28th International Conference on Artificial Intelligence and Statistics","publisher":"ML Research Press","ec_funded":1,"conference":{"name":"AISTATS: Conference on Artificial Intelligence and Statistics","end_date":"2025-05-05","location":"Mai Khao, Thailand","start_date":"2025-05-03"},"status":"public","oa":1,"acknowledgement":"MH: 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/Z422, grant DOI 10.55776/I5982, and grant DOI 10.55776/P33775 with additional funding from the netidee SCIENCE Stiftung, 2020–2024. TAS: This work was supported by a research grant (VIL51463)\r\nfrom VILLUM FONDEN.","oa_version":"Preprint"},{"has_accepted_license":"1","oa_version":"Published Version","status":"public","oa":1,"acknowledgement":"Monika Henzinger and Evangelos Kosinas: 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 https://www.doi.org/10.55776/Z422 and grant https://www.doi.org/10.55776/I5982. Harald Räcke and Robin Münk: This project has received funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 498605858.","scopus_import":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"citation":{"mla":"Henzinger, Monika, et al. “Efficient Contractions of Dynamic Graphs - with Applications.” <i>33rd Annual European Symposium on Algorithms</i>, vol. 351, 36, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025, doi:<a href=\"https://doi.org/10.4230/LIPIcs.ESA.2025.36\">10.4230/LIPIcs.ESA.2025.36</a>.","ista":"Henzinger M, Kosinas E, Münk R, Räcke H. 2025. Efficient contractions of dynamic graphs - with applications. 33rd Annual European Symposium on Algorithms. ESA: European Symposium on Algorithms vol. 351, 36.","chicago":"Henzinger, Monika, Evangelos Kosinas, Robin Münk, and Harald Räcke. “Efficient Contractions of Dynamic Graphs - with Applications.” In <i>33rd Annual European Symposium on Algorithms</i>, Vol. 351. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. <a href=\"https://doi.org/10.4230/LIPIcs.ESA.2025.36\">https://doi.org/10.4230/LIPIcs.ESA.2025.36</a>.","ieee":"M. Henzinger, E. Kosinas, R. Münk, and H. Räcke, “Efficient contractions of dynamic graphs - with applications,” in <i>33rd Annual European Symposium on Algorithms</i>, Warsaw, Poland, 2025, vol. 351.","short":"M. Henzinger, E. Kosinas, R. Münk, H. Räcke, in:, 33rd Annual European Symposium on Algorithms, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025.","apa":"Henzinger, M., Kosinas, E., Münk, R., &#38; Räcke, H. (2025). Efficient contractions of dynamic graphs - with applications. In <i>33rd Annual European Symposium on Algorithms</i> (Vol. 351). Warsaw, Poland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.ESA.2025.36\">https://doi.org/10.4230/LIPIcs.ESA.2025.36</a>","ama":"Henzinger M, Kosinas E, Münk R, Räcke H. Efficient contractions of dynamic graphs - with applications. In: <i>33rd Annual European Symposium on Algorithms</i>. Vol 351. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2025. doi:<a href=\"https://doi.org/10.4230/LIPIcs.ESA.2025.36\">10.4230/LIPIcs.ESA.2025.36</a>"},"author":[{"last_name":"Henzinger","full_name":"Henzinger, Monika H","orcid":"0000-0002-5008-6530","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","first_name":"Monika H"},{"full_name":"Kosinas, Evangelos","last_name":"Kosinas","first_name":"Evangelos","id":"4c7f9625-dbbc-11ee-9d86-bdcc2db5a949"},{"last_name":"Münk","full_name":"Münk, Robin","first_name":"Robin"},{"first_name":"Harald","last_name":"Räcke","full_name":"Räcke, Harald"}],"month":"10","publication":"33rd Annual European Symposium on Algorithms","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","conference":{"end_date":"2025-09-17","location":"Warsaw, Poland","start_date":"2025-09-15","name":"ESA: European Symposium on Algorithms"},"ec_funded":1,"title":"Efficient contractions of dynamic graphs - with applications","article_processing_charge":"No","file_date_updated":"2025-10-27T08:03:36Z","OA_place":"publisher","arxiv":1,"department":[{"_id":"MoHe"}],"type":"conference","corr_author":"1","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2025-10-01T00:00:00Z","publication_identifier":{"isbn":["9783959773959"],"issn":["1868-8969"]},"date_updated":"2025-10-27T08:05:46Z","file":[{"creator":"dernst","file_id":"20542","success":1,"file_name":"2025_LIPIcs.ESA_HenzingerM.pdf","date_updated":"2025-10-27T08:03:36Z","date_created":"2025-10-27T08:03:36Z","checksum":"d2daf9a467e96fb5e7084a8a85321776","access_level":"open_access","file_size":934846,"content_type":"application/pdf","relation":"main_file"}],"_id":"20534","ddc":["000"],"intvolume":"       351","publication_status":"published","doi":"10.4230/LIPIcs.ESA.2025.36","external_id":{"arxiv":["2509.05157"]},"volume":351,"article_number":"36","language":[{"iso":"eng"}],"abstract":[{"text":"A non-trivial minimum cut (NMC) sparsifier is a multigraph Ĝ that preserves all non-trivial minimum cuts of a given undirected graph G. We introduce a flexible data structure for fully dynamic graphs that can efficiently provide an NMC sparsifier upon request at any point during the sequence of updates. We employ simple dynamic forest data structures to achieve a fast from-scratch construction of the sparsifier at query time. Based on the strength of the adversary and desired type of time bounds, the data structure comes with different guarantees. Specifically, let G be a fully dynamic simple graph with n vertices and minimum degree δ. Then our data structure supports an insertion/deletion of an edge to/from G in n^o(1) worst-case time. Furthermore, upon request, it can return w.h.p. an NMC sparsifier of G that has O(n/δ) vertices and O(n) edges, in Ô(n) time. The probabilistic guarantees hold against an adaptive adversary. Alternatively, the update and query times can be improved to Õ(1) and Õ(n) respectively, if amortized-time guarantees are sufficient, or if the adversary is oblivious. Throughout the paper, we use Õ to hide polylogarithmic factors and Ô to hide subpolynomial (i.e., n^o(1)) factors.\r\nWe discuss two applications of our new data structure. First, it can be used to efficiently report a cactus representation of all minimum cuts of a fully dynamic simple graph. Building this cactus for the NMC sparsifier instead of the original graph allows for a construction time that is sublinear in the number of edges. Against an adaptive adversary, we can with high probability output the cactus representation in worst-case Ô(n) time. Second, our data structure allows us to efficiently compute the maximal k-edge-connected subgraphs of undirected simple graphs, by repeatedly applying a minimum cut algorithm on the NMC sparsifier. Specifically, we can compute with high probability the maximal k-edge-connected subgraphs of a simple graph with n vertices and m edges in Õ(m+n²/k) time. This improves the best known time bounds for k = Ω(n^{1/8}) and naturally extends to the case of fully dynamic graphs.","lang":"eng"}],"project":[{"_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","grant_number":"101019564","name":"The design and evaluation of modern fully dynamic data structures","call_identifier":"H2020"},{"name":"Efficient algorithms","grant_number":"Z00422","_id":"34def286-11ca-11ed-8bc3-da5948e1613c"},{"grant_number":"I05982","name":"Static and Dynamic Hierarchical Graph Decompositions","_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103"}],"day":"01","year":"2025","date_created":"2025-10-26T23:01:34Z","OA_type":"gold"},{"month":"10","author":[{"last_name":"Dhulipala","full_name":"Dhulipala, Laxman","first_name":"Laxman"},{"last_name":"Henzinger","full_name":"Henzinger, Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","orcid":"0000-0002-5008-6530","first_name":"Monika H"},{"first_name":"George Z.","last_name":"Li","full_name":"Li, George Z."},{"first_name":"Quanquan C.","last_name":"Liu","full_name":"Liu, Quanquan C."},{"last_name":"Sricharan","full_name":"Sricharan, A. R.","first_name":"A. R."},{"last_name":"Zhu","full_name":"Zhu, Leqi","first_name":"Leqi","id":"a2117c59-cee4-11ed-b9d0-874ecf0f8ac5"}],"citation":{"ama":"Dhulipala L, Henzinger M, Li GZ, Liu QC, Sricharan AR, Zhu L. Near-optimal differentially private graph algorithms via the Multidimensional AboveThreshold Mechanism. In: <i>33rd Annual European Symposium on Algorithms</i>. Vol 351. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2025. doi:<a href=\"https://doi.org/10.4230/LIPIcs.ESA.2025.91\">10.4230/LIPIcs.ESA.2025.91</a>","apa":"Dhulipala, L., Henzinger, M., Li, G. Z., Liu, Q. C., Sricharan, A. R., &#38; Zhu, L. (2025). Near-optimal differentially private graph algorithms via the Multidimensional AboveThreshold Mechanism. In <i>33rd Annual European Symposium on Algorithms</i> (Vol. 351). Warsaw, Poland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.ESA.2025.91\">https://doi.org/10.4230/LIPIcs.ESA.2025.91</a>","short":"L. Dhulipala, M. Henzinger, G.Z. Li, Q.C. Liu, A.R. Sricharan, L. Zhu, in:, 33rd Annual European Symposium on Algorithms, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025.","ieee":"L. Dhulipala, M. Henzinger, G. Z. Li, Q. C. Liu, A. R. Sricharan, and L. Zhu, “Near-optimal differentially private graph algorithms via the Multidimensional AboveThreshold Mechanism,” in <i>33rd Annual European Symposium on Algorithms</i>, Warsaw, Poland, 2025, vol. 351.","chicago":"Dhulipala, Laxman, Monika Henzinger, George Z. Li, Quanquan C. Liu, A. R. Sricharan, and Leqi Zhu. “Near-Optimal Differentially Private Graph Algorithms via the Multidimensional AboveThreshold Mechanism.” In <i>33rd Annual European Symposium on Algorithms</i>, Vol. 351. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. <a href=\"https://doi.org/10.4230/LIPIcs.ESA.2025.91\">https://doi.org/10.4230/LIPIcs.ESA.2025.91</a>.","mla":"Dhulipala, Laxman, et al. “Near-Optimal Differentially Private Graph Algorithms via the Multidimensional AboveThreshold Mechanism.” <i>33rd Annual European Symposium on Algorithms</i>, vol. 351, 91, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025, doi:<a href=\"https://doi.org/10.4230/LIPIcs.ESA.2025.91\">10.4230/LIPIcs.ESA.2025.91</a>.","ista":"Dhulipala L, Henzinger M, Li GZ, Liu QC, Sricharan AR, Zhu L. 2025. Near-optimal differentially private graph algorithms via the Multidimensional AboveThreshold Mechanism. 33rd Annual European Symposium on Algorithms. ESA: European Symposium on Algorithms, LIPIcs, vol. 351, 91."},"scopus_import":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"conference":{"start_date":"2025-09-15","location":"Warsaw, Poland","end_date":"2025-09-17","name":"ESA: European Symposium on Algorithms"},"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","ec_funded":1,"publication":"33rd Annual European Symposium on Algorithms","file_date_updated":"2025-10-27T06:58:43Z","title":"Near-optimal differentially private graph algorithms via the Multidimensional AboveThreshold Mechanism","article_processing_charge":"No","has_accepted_license":"1","oa_version":"Published Version","oa":1,"status":"public","acknowledgement":"Monika Henzinger and A. R. Sricharan: This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation\r\nprogramme (MoDynStruct, No. 101019564) and the Austrian Science Fund (FWF) grant DOI\r\n10.55776/Z422 and grant DOI 10.55776/I5982. Laxman Dhulipala and George Z. Li: supported by NSF award number CNS-2317194. Quanquan C. Liu: supported by a Google Academic Research Award and by an NSF award number CCF-2453323.","intvolume":"       351","publication_status":"published","doi":"10.4230/LIPIcs.ESA.2025.91","ddc":["000"],"volume":351,"external_id":{"arxiv":["2508.02182"]},"article_number":"91","OA_type":"gold","date_created":"2025-10-26T23:01:35Z","year":"2025","day":"01","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"Many differentially private and classical non-private graph algorithms rely crucially on determining whether some property of each vertex meets a threshold. For example, for the k-core decomposition problem, the classic peeling algorithm iteratively removes a vertex if its induced degree falls below a threshold. The sparse vector technique (SVT) is generally used to transform non-private threshold queries into private ones with only a small additive loss in accuracy. However, a naive application of SVT in the graph setting leads to an amplification of the error by a factor of n due to composition, as SVT is applied to every vertex. In this paper, we resolve this problem by formulating a novel generalized sparse vector technique which we call the Multidimensional AboveThreshold (MAT) Mechanism which generalizes SVT (applied to vectors with one dimension) to vectors with multiple dimensions. When applied to vectors with n dimensions, we solve a number of important graph problems with better bounds than previous work.\r\nSpecifically, we apply our MAT mechanism to obtain a set of improved bounds for a variety of problems including k-core decomposition, densest subgraph, low out-degree ordering, and vertex coloring. We give a tight local edge differentially private (LEDP) algorithm for k-core decomposition that results in an approximation with O(ε^{-1} log n) additive error and no multiplicative error in O(n) rounds. We also give a new (2+η)-factor multiplicative, O(ε^{-1} log n) additive error algorithm in O(log² n) rounds for any constant η > 0. Both of these results are asymptotically tight against our new lower bound of Ω(log n) for any constant-factor approximation algorithm for k-core decomposition. Our new algorithms for k-core decomposition also directly lead to new algorithms for the related problems of densest subgraph and low out-degree ordering. Finally, we give novel LEDP differentially private defective coloring algorithms that use number of colors given in terms of the arboricity of the graph."}],"project":[{"_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","name":"The design and evaluation of modern fully dynamic data structures","call_identifier":"H2020","grant_number":"101019564"},{"_id":"34def286-11ca-11ed-8bc3-da5948e1613c","grant_number":"Z00422","name":"Efficient algorithms"},{"_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103","grant_number":"I05982","name":"Static and Dynamic Hierarchical Graph Decompositions"}],"alternative_title":["LIPIcs"],"department":[{"_id":"MoHe"}],"OA_place":"publisher","arxiv":1,"corr_author":"1","type":"conference","publication_identifier":{"isbn":["9783959773959"],"issn":["1868-8969"]},"date_published":"2025-10-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","_id":"20535","file":[{"access_level":"open_access","file_size":870317,"content_type":"application/pdf","relation":"main_file","file_id":"20539","creator":"dernst","success":1,"date_updated":"2025-10-27T06:58:43Z","file_name":"2025_LIPIcs.ESA_Dhulipala.pdf","checksum":"19146e935b5b6ad5d33c8d08280ad8e7","date_created":"2025-10-27T06:58:43Z"}],"date_updated":"2025-10-27T07:02:06Z"},{"oa_version":"Published Version","has_accepted_license":"1","acknowledgement":"This work was supported under the Australian Research Council Discovery Projects\r\nfunding scheme (project number DP180102870). This project has received funding from the\r\nEuropean Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No. 101019564) “The Design of Modern Fully Dynamic Data Structures (MoDynStruct)” and from the Austrian Science Fund (FWF) project Z 422-N and project “Fast Algorithms for a Reactive Network Layer (ReactNet)” P 33775-N, with additional funding from the netidee SCIENCE Stiftung, 2020–2024.","status":"public","oa":1,"publication":"19th International Symposium on Algorithms and Data Structures","ec_funded":1,"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","conference":{"name":"WADS: Algorithms and Data Structures Symposium","start_date":"2025-08-11","location":"Toronto, Canada","end_date":"2025-08-15"},"citation":{"mla":"Safavi Hemami, Roodabeh, and Martin P. Seybold. “B-Treaps Revised: Write Efficient Randomized Block Search Trees with High Load.” <i>19th International Symposium on Algorithms and Data Structures</i>, vol. 349, 47, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025, doi:<a href=\"https://doi.org/10.4230/LIPIcs.WADS.2025.47\">10.4230/LIPIcs.WADS.2025.47</a>.","ista":"Safavi Hemami R, Seybold MP. 2025. B-Treaps revised: Write efficient randomized block search trees with high load. 19th International Symposium on Algorithms and Data Structures. WADS: Algorithms and Data Structures Symposium, LIPIcs, vol. 349, 47.","chicago":"Safavi Hemami, Roodabeh, and Martin P. Seybold. “B-Treaps Revised: Write Efficient Randomized Block Search Trees with High Load.” In <i>19th International Symposium on Algorithms and Data Structures</i>, Vol. 349. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. <a href=\"https://doi.org/10.4230/LIPIcs.WADS.2025.47\">https://doi.org/10.4230/LIPIcs.WADS.2025.47</a>.","ieee":"R. Safavi Hemami and M. P. Seybold, “B-Treaps revised: Write efficient randomized block search trees with high load,” in <i>19th International Symposium on Algorithms and Data Structures</i>, Toronto, Canada, 2025, vol. 349.","short":"R. Safavi Hemami, M.P. Seybold, in:, 19th International Symposium on Algorithms and Data Structures, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025.","ama":"Safavi Hemami R, Seybold MP. B-Treaps revised: Write efficient randomized block search trees with high load. In: <i>19th International Symposium on Algorithms and Data Structures</i>. Vol 349. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2025. doi:<a href=\"https://doi.org/10.4230/LIPIcs.WADS.2025.47\">10.4230/LIPIcs.WADS.2025.47</a>","apa":"Safavi Hemami, R., &#38; Seybold, M. P. (2025). B-Treaps revised: Write efficient randomized block search trees with high load. In <i>19th International Symposium on Algorithms and Data Structures</i> (Vol. 349). Toronto, Canada: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.WADS.2025.47\">https://doi.org/10.4230/LIPIcs.WADS.2025.47</a>"},"scopus_import":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"month":"08","author":[{"id":"72ed2640-8972-11ed-ae7b-f9c81ec75154","first_name":"Roodabeh","last_name":"Safavi Hemami","full_name":"Safavi Hemami, Roodabeh"},{"full_name":"Seybold, Martin P.","last_name":"Seybold","first_name":"Martin P."}],"title":"B-Treaps revised: Write efficient randomized block search trees with high load","article_processing_charge":"No","file_date_updated":"2025-10-27T07:09:41Z","type":"conference","corr_author":"1","OA_place":"publisher","arxiv":1,"department":[{"_id":"MoHe"}],"file":[{"access_level":"open_access","file_size":1081870,"content_type":"application/pdf","relation":"main_file","creator":"dernst","file_id":"20540","success":1,"file_name":"2025_LIPIcs.WADS_Safavi.pdf","date_updated":"2025-10-27T07:09:41Z","date_created":"2025-10-27T07:09:41Z","checksum":"196af33762831a78e87f4f95ecd8677b"}],"date_updated":"2025-10-27T07:10:49Z","_id":"20536","publication_identifier":{"isbn":["9783959773980"],"issn":["1868-8969"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2025-08-29T00:00:00Z","quality_controlled":"1","external_id":{"arxiv":["2303.04722"]},"volume":349,"intvolume":"       349","publication_status":"published","doi":"10.4230/LIPIcs.WADS.2025.47","ddc":["000"],"day":"29","abstract":[{"lang":"eng","text":"Uniquely represented (UR) data structures represent each logical state with a unique storage state. We study the problem of maintaining a dynamic set of n keys from a totally ordered universe in this context. UR structures are also called \"strongly history independent\" structures in the literature.\r\nWe introduce a two-layer data structure called (α,ε)-Randomized Block Search Tree (RBST) that is uniquely represented and suitable for external memory (EM). Though RBSTs naturally generalize the well-known binary Treaps, several new ideas are needed to analyze the expected search, update, and storage efficiency in terms of block-reads, block-writes, and blocks stored. We prove that searches have O(ε^{-1} + log_α n) block-reads, that dynamic updates perform O(ε^{-1} + log_α(n)/α) block-writes and O(ε^{-2}+(1+(ε^{-1}+log n)/α)log_α n) block-reads, and that (α, ε)-RBSTs have an asymptotic load-factor of at least (1-ε) for every ε ∈ (0,1/2].\r\nThus (α, ε)-RBSTs improve on the known, uniquely represented B-Treap [Golovin; ICALP'09]. Compared with non-UR structures, the RBST is also, to the best of our knowledge, the first external memory structure that is storage-efficient and has a non-amortized, write-efficient update bound."}],"project":[{"grant_number":"101019564","name":"The design and evaluation of modern fully dynamic data structures","call_identifier":"H2020","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62"},{"grant_number":"Z00422","name":"Efficient algorithms","_id":"34def286-11ca-11ed-8bc3-da5948e1613c"},{"name":"Fast Algorithms for a Reactive Network Layer","grant_number":"P33775","_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe"}],"language":[{"iso":"eng"}],"alternative_title":["LIPIcs"],"OA_type":"gold","date_created":"2025-10-26T23:01:35Z","year":"2025","article_number":"47"},{"oa":1,"status":"public","acknowledgement":"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/I5862,grant DOI 10.55776/I5982, and grant DOI 10.55776/P33775 with\r\nadditional funding from the netidee SCIENCE Stiftung, 2020–2024\r\nand the German Research Foundation (DFG), grant 470029389\r\n(FlexNets).","has_accepted_license":"1","oa_version":"Published Version","file_date_updated":"2025-08-04T09:10:55Z","title":"An almost tight lower bound for plurality consensus with undecided state dynamics in the population protocol model","article_processing_charge":"Yes (via OA deal)","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"22281"}]},"author":[{"first_name":"Antoine","orcid":"0000-0003-4268-7368","id":"888a098e-fcac-11ee-aff7-d347be57b725","last_name":"El-Hayek","full_name":"El-Hayek, Antoine"},{"first_name":"Robert","full_name":"Elsässer, Robert","last_name":"Elsässer"},{"first_name":"Stefan","last_name":"Schmid","full_name":"Schmid, Stefan"}],"month":"06","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"citation":{"apa":"El-Hayek, A., Elsässer, R., &#38; Schmid, S. (2025). An almost tight lower bound for plurality consensus with undecided state dynamics in the population protocol model. In <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i>. Huatulco, Mexico: Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3732772.3733505\">https://doi.org/10.1145/3732772.3733505</a>","ama":"El-Hayek A, Elsässer R, Schmid S. An almost tight lower bound for plurality consensus with undecided state dynamics in the population protocol model. In: <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i>. Association for Computing Machinery; 2025. doi:<a href=\"https://doi.org/10.1145/3732772.3733505\">10.1145/3732772.3733505</a>","ieee":"A. El-Hayek, R. Elsässer, and S. Schmid, “An almost tight lower bound for plurality consensus with undecided state dynamics in the population protocol model,” in <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i>, Huatulco, Mexico, 2025.","short":"A. El-Hayek, R. Elsässer, S. Schmid, in:, Proceedings of the ACM Symposium on Principles of Distributed Computing, Association for Computing Machinery, 2025.","ista":"El-Hayek A, Elsässer R, Schmid S. 2025. An almost tight lower bound for plurality consensus with undecided state dynamics in the population protocol model. Proceedings of the ACM Symposium on Principles of Distributed Computing. PODC: Symposium on Principles of Distributed Computing.","chicago":"El-Hayek, Antoine, Robert Elsässer, and Stefan Schmid. “An Almost Tight Lower Bound for Plurality Consensus with Undecided State Dynamics in the Population Protocol Model.” In <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i>. Association for Computing Machinery, 2025. <a href=\"https://doi.org/10.1145/3732772.3733505\">https://doi.org/10.1145/3732772.3733505</a>.","mla":"El-Hayek, Antoine, et al. “An Almost Tight Lower Bound for Plurality Consensus with Undecided State Dynamics in the Population Protocol Model.” <i>Proceedings of the ACM Symposium on Principles of Distributed Computing</i>, Association for Computing Machinery, 2025, doi:<a href=\"https://doi.org/10.1145/3732772.3733505\">10.1145/3732772.3733505</a>."},"conference":{"end_date":"2025-06-20","start_date":"2025-06-16","location":"Huatulco, Mexico","name":"PODC: Symposium on Principles of Distributed Computing"},"ec_funded":1,"publisher":"Association for Computing Machinery","publication":"Proceedings of the ACM Symposium on Principles of Distributed Computing","isi":1,"quality_controlled":"1","publication_identifier":{"isbn":[" 9798400718854"]},"date_published":"2025-06-13T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"20051","date_updated":"2026-07-24T12:48:28Z","file":[{"success":1,"file_id":"20115","creator":"dernst","checksum":"52976d226f3f691aa519d71c1c718fa5","date_created":"2025-08-04T09:10:55Z","date_updated":"2025-08-04T09:10:55Z","file_name":"2025_PODC_ElHayek.pdf","file_size":2200347,"access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"department":[{"_id":"MoHe"}],"OA_place":"publisher","arxiv":1,"corr_author":"1","type":"conference","year":"2025","OA_type":"hybrid","date_created":"2025-07-21T08:16:15Z","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"We revisit the majority problem in the population protocol communication model, as first studied by Angluin et al. (Distributed Computing 2008). We consider a more general version of this problem known as plurality consensus, which has already been studied intensively in the literature. In this problem, each node in a system of n nodes, has initially one of k different opinions, and they need to agree on the (relative) majority opinion. In particular, we consider the important and intensively studied model of Undecided State Dynamics.\r\nOur main contribution is an almost tight lower bound on the stabilization time: we prove that there exists an initial configuration, even with bias \\Delta = \\omega(\\sqrt{n\\log n}), where stabilization requires \\Omega(kn\\log \\frac {\\sqrt n} {k \\log n}) interactions, or equivalently, \\Omega(k\\log \\frac {\\sqrt n} {k \\log n}) parallel time for any k = o\\left(\\frac {\\sqrt n}{\\log n}\\right). This bound is tight for any k \\le n^{\\frac 1 2 - \\epsilon}, where \\epsilon >0 can be any small constant, as Amir et al.~(PODC'23) gave a O(k\\log n) parallel time upper bound for k = O\\left(\\frac {\\sqrt n} {\\log ^2 n}\\right)."}],"project":[{"grant_number":"101019564","call_identifier":"H2020","name":"The design and evaluation of modern fully dynamic data structures","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62"},{"_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103","grant_number":"I05982","name":"Static and Dynamic Hierarchical Graph Decompositions"},{"_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe","name":"Fast Algorithms for a Reactive Network Layer","grant_number":"P33775"}],"day":"13","ddc":["000"],"doi":"10.1145/3732772.3733505","publication_status":"published","external_id":{"arxiv":["2505.02765"],"isi":["001525534800066"]}},{"title":"Fully dynamic approximate minimum cut in subpolynomial time per operation","article_processing_charge":"No","citation":{"ama":"El-Hayek A, Henzinger M, Li J. Fully dynamic approximate minimum cut in subpolynomial time per operation. In: <i>Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms</i>. Society for Industrial and Applied Mathematics; 2025:750-784. doi:<a href=\"https://doi.org/10.1137/1.9781611978322.22\">10.1137/1.9781611978322.22</a>","apa":"El-Hayek, A., Henzinger, M., &#38; Li, J. (2025). Fully dynamic approximate minimum cut in subpolynomial time per operation. In <i>Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms</i> (pp. 750–784). New Orleans, LA, United States: Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/1.9781611978322.22\">https://doi.org/10.1137/1.9781611978322.22</a>","short":"A. El-Hayek, M. Henzinger, J. Li, in:, Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, 2025, pp. 750–784.","ieee":"A. El-Hayek, M. Henzinger, and J. Li, “Fully dynamic approximate minimum cut in subpolynomial time per operation,” in <i>Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms</i>, New Orleans, LA, United States, 2025, pp. 750–784.","mla":"El-Hayek, Antoine, et al. “Fully Dynamic Approximate Minimum Cut in Subpolynomial Time per Operation.” <i>Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms</i>, Society for Industrial and Applied Mathematics, 2025, pp. 750–84, doi:<a href=\"https://doi.org/10.1137/1.9781611978322.22\">10.1137/1.9781611978322.22</a>.","ista":"El-Hayek A, Henzinger M, Li J. 2025. Fully dynamic approximate minimum cut in subpolynomial time per operation. Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms, 750–784.","chicago":"El-Hayek, Antoine, Monika Henzinger, and Jason Li. “Fully Dynamic Approximate Minimum Cut in Subpolynomial Time per Operation.” In <i>Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms</i>, 750–84. Society for Industrial and Applied Mathematics, 2025. <a href=\"https://doi.org/10.1137/1.9781611978322.22\">https://doi.org/10.1137/1.9781611978322.22</a>."},"author":[{"full_name":"El-Hayek, Antoine","last_name":"El-Hayek","id":"888a098e-fcac-11ee-aff7-d347be57b725","orcid":"0000-0003-4268-7368","first_name":"Antoine"},{"last_name":"Henzinger","full_name":"Henzinger, Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","orcid":"0000-0002-5008-6530","first_name":"Monika H"},{"first_name":"Jason","full_name":"Li, Jason","last_name":"Li"}],"related_material":{"record":[{"id":"22281","relation":"dissertation_contains","status":"public"}]},"month":"01","publication":"Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms","publisher":"Society for Industrial and Applied Mathematics","conference":{"name":"SODA: Symposium on Discrete Algorithms","location":"New Orleans, LA, United States","end_date":"2025-01-15","start_date":"2025-01-12"},"ec_funded":1,"status":"public","oa":1,"acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’sHorizon 2020 research and innovation programme (MoDynStruct, No. 101019564) and the Austrian Science Fund(FWF) grant DOI 10.55776/Z422, grant DOI 10.55776/I5982, and grant DOI 10.55776/P33775 with additional funding from the netidee SCIENCE Stiftung, 2020–2024.","oa_version":"Preprint","abstract":[{"lang":"eng","text":"Dynamically maintaining the minimum cut in a graph G under edge insertions and deletion is a fundamental problem in dynamic graph algorithms for which no conditional lower bound on the time per operation exists. In an n-node graph the best known (1 + o (1))-approximate algorithm takes  update time [14]. If the minimum cut is guaranteed to be (log n )o (1), a deterministic exact algorithm with n o (1) update time exists [8].\r\nWe present the first fully dynamic algorithm for (1 + o (1))-approximate minimum cut with n o(1) update time. Our main technical contribution is to show that it suffices to consider small-volume cuts in suitably contracted graphs."}],"project":[{"grant_number":"101019564","call_identifier":"H2020","name":"The design and evaluation of modern fully dynamic data structures","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62"},{"name":"Efficient algorithms","grant_number":"Z00422","_id":"34def286-11ca-11ed-8bc3-da5948e1613c"},{"name":"Static and Dynamic Hierarchical Graph Decompositions","grant_number":"I05982","_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103"},{"grant_number":"P33775","name":"Fast Algorithms for a Reactive Network Layer","_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe"}],"language":[{"iso":"eng"}],"day":"07","year":"2025","date_created":"2025-07-10T13:08:57Z","page":"750-784","OA_type":"green","doi":"10.1137/1.9781611978322.22","publication_status":"published","external_id":{"arxiv":["2412.15069"]},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2412.15069"}],"quality_controlled":"1","date_published":"2025-01-07T00:00:00Z","publication_identifier":{"eisbn":["9781611978322"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2026-07-24T12:48:28Z","_id":"19982","OA_place":"repository","arxiv":1,"department":[{"_id":"MoHe"}],"type":"conference","corr_author":"1"},{"_id":"14769","date_updated":"2025-04-14T13:50:50Z","publication_identifier":{"eisbn":["9781611977929"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2024-01-04T00:00:00Z","quality_controlled":"1","corr_author":"1","type":"conference","department":[{"_id":"MoHe"}],"arxiv":1,"page":"220-233","date_created":"2024-01-09T16:22:47Z","year":"2024","day":"04","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"For a set of points in Rd, the Euclidean k-means problems consists of finding k centers such that the sum of distances squared from each data point to its closest center is minimized. Coresets are one the main tools developed recently to solve this problem in a big data context. They allow to compress the initial dataset while preserving its structure: running any algorithm on the coreset provides a guarantee almost equivalent to running it on the full data. In this work, we study coresets in a fully-dynamic setting: points are added and deleted with the goal to efficiently maintain a coreset with which a k-means solution can be computed. Based on an algorithm from Henzinger and Kale [ESA'20], we present an efficient and practical implementation of a fully dynamic coreset algorithm, that improves the running time by up to a factor of 20 compared to our non-optimized implementation of the algorithm by Henzinger and Kale, without sacrificing more than 7% on the quality of the k-means solution."}],"project":[{"_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","call_identifier":"H2020","name":"The design and evaluation of modern fully dynamic data structures","grant_number":"101019564"},{"grant_number":"Z00422","name":"Efficient algorithms","_id":"34def286-11ca-11ed-8bc3-da5948e1613c"},{"grant_number":"I05982","name":"Static and Dynamic Hierarchical Graph Decompositions","_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103"},{"_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe","grant_number":"P33775","name":"Fast Algorithms for a Reactive Network Layer"},{"name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2310.18034","open_access":"1"}],"external_id":{"arxiv":["2310.18034"]},"doi":"10.1137/1.9781611977929.17","publication_status":"published","acknowledgement":"This   project   has   received   funding   from   the   Euro-pean  Research  Council  (ERC)  under  the  EuropeanUnion’s  Horizon  2020  research  and  innovation  programme  (Grant  agreement  No.   101019564  “The  De-sign  of  Modern  Fully  Dynamic  Data  Structures  (Mo-DynStruct)”  and  the  Austrian  Science  Fund  (FWF)project Z 422-N, project “Static and Dynamic Hierar-chical  Graph  Decompositions”,  I  5982-N,  and  project“Fast  Algorithms  for  a  Reactive  Network  Layer  (Re-actNet)”, P 33775-N, with additional funding from thenetidee SCIENCE Stiftung, 2020–2024.D.  Sauplic  has  received  funding  from  the  Euro-pean  Union’s  Horizon  2020  research  and  innovation programme under the Marie Sklodowska-Curie    grant    agreementNo 101034413.","oa":1,"status":"public","oa_version":"Preprint","article_processing_charge":"No","title":"Experimental evaluation of fully dynamic k-means via coresets","publisher":"Society for Industrial and Applied Mathematics","conference":{"name":"ALENEX: Workshop on Algorithm Engineering and Experiments","location":"Alexandria, VA, United States","start_date":"2024-01-07","end_date":"2024-01-08"},"ec_funded":1,"publication":"2024 Proceedings of the Symposium on Algorithm Engineering and Experiments","month":"01","author":[{"full_name":"Henzinger, Monika H","last_name":"Henzinger","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","orcid":"0000-0002-5008-6530","first_name":"Monika H"},{"id":"f8e48cf0-b0ff-11ed-b0e9-b4c35598f964","first_name":"David","full_name":"Saulpic, David","last_name":"Saulpic"},{"full_name":"Sidl, Leonhard","last_name":"Sidl","first_name":"Leonhard","id":"8b563fd0-b441-11ee-9101-a3891c61efa6"}],"citation":{"ista":"Henzinger M, Saulpic D, Sidl L. 2024. Experimental evaluation of fully dynamic k-means via coresets. 2024 Proceedings of the Symposium on Algorithm Engineering and Experiments. ALENEX: Workshop on Algorithm Engineering and Experiments, 220–233.","chicago":"Henzinger, Monika, David Saulpic, and Leonhard Sidl. “Experimental Evaluation of Fully Dynamic K-Means via Coresets.” In <i>2024 Proceedings of the Symposium on Algorithm Engineering and Experiments</i>, 220–33. Society for Industrial and Applied Mathematics, 2024. <a href=\"https://doi.org/10.1137/1.9781611977929.17\">https://doi.org/10.1137/1.9781611977929.17</a>.","mla":"Henzinger, Monika, et al. “Experimental Evaluation of Fully Dynamic K-Means via Coresets.” <i>2024 Proceedings of the Symposium on Algorithm Engineering and Experiments</i>, Society for Industrial and Applied Mathematics, 2024, pp. 220–33, doi:<a href=\"https://doi.org/10.1137/1.9781611977929.17\">10.1137/1.9781611977929.17</a>.","ama":"Henzinger M, Saulpic D, Sidl L. Experimental evaluation of fully dynamic k-means via coresets. In: <i>2024 Proceedings of the Symposium on Algorithm Engineering and Experiments</i>. Society for Industrial and Applied Mathematics; 2024:220-233. doi:<a href=\"https://doi.org/10.1137/1.9781611977929.17\">10.1137/1.9781611977929.17</a>","apa":"Henzinger, M., Saulpic, D., &#38; Sidl, L. (2024). Experimental evaluation of fully dynamic k-means via coresets. In <i>2024 Proceedings of the Symposium on Algorithm Engineering and Experiments</i> (pp. 220–233). Alexandria, VA, United States: Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/1.9781611977929.17\">https://doi.org/10.1137/1.9781611977929.17</a>","short":"M. Henzinger, D. Saulpic, L. Sidl, in:, 2024 Proceedings of the Symposium on Algorithm Engineering and Experiments, Society for Industrial and Applied Mathematics, 2024, pp. 220–233.","ieee":"M. Henzinger, D. Saulpic, and L. Sidl, “Experimental evaluation of fully dynamic k-means via coresets,” in <i>2024 Proceedings of the Symposium on Algorithm Engineering and Experiments</i>, Alexandria, VA, United States, 2024, pp. 220–233."},"scopus_import":"1"}]