[{"month":"05","language":[{"iso":"eng"}],"title":"Charting the diameter computation landscape of intersection graphs in 3D and above","keyword":["Graph Diameter","Geometric Intersection Graphs","Unit Ball Graphs"],"has_accepted_license":"1","department":[{"_id":"MoHe"}],"doi":"10.4230/LIPIcs.SoCG.2026.29","status":"public","project":[{"_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103","grant_number":"I05982","name":"Static and Dynamic Hierarchical Graph Decompositions"}],"volume":367,"das_tickbox":"0","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","year":"2026","OA_type":"gold","article_processing_charge":"Yes","author":[{"full_name":"Chan, Timothy M.","first_name":"Timothy M.","last_name":"Chan"},{"first_name":"Hsien Chih","full_name":"Chang, Hsien Chih","last_name":"Chang"},{"first_name":"Jie","full_name":"Gao, Jie","last_name":"Gao"},{"last_name":"Kisfaludi-Bak","full_name":"Kisfaludi-Bak, Sándor","first_name":"Sándor"},{"last_name":"Le","full_name":"Le, Hung","first_name":"Hung"},{"last_name":"Zheng","id":"af77956b-e859-11ef-8dc9-d301b898e32f","first_name":"Da Wei","full_name":"Zheng, Da Wei"}],"publication_identifier":{"eissn":["1868-8969"],"isbn":["9783959774185"]},"day":"27","oa_version":"Published Version","arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"text":"Recent research on computing the diameter of geometric intersection graphs has made significant strides, primarily focusing on the 2D case [Duraj et al., 2024; Hsien-Chih Chang et al., 2024; Chan et al., 2025] where truly subquadratic-time algorithms were given for simple objects such as unit-disks and (axis-aligned) squares. However, in three or higher dimensions, there is no known truly subquadratic-time algorithm for any intersection graph of non-trivial objects, even basic ones such as unit balls or (axis-aligned) unit cubes. This was partially explained by the pioneering work of Bringmann et al. [Karl Bringmann et al., 2022] which gave several truly subquadratic lower bounds, notably for unit balls or unit cubes in 3D when the graph diameter Δ is at least Ω(log n), hinting at a pessimistic outlook for the complexity of the diameter problem in higher dimensions. In this paper, we substantially extend the landscape of diameter computation for objects in three and higher dimensions, giving a few positive results. Our highlighted findings include: \r\n1) A truly subquadratic-time algorithm for deciding if the diameter of unit cubes in 3D is at most 3 (Diameter-3 hereafter), the first algorithm of its kind for objects in 3D or higher dimensions. Our algorithm is based on a novel connection to pseudolines, which is of independent interest. \r\n2) A truly subquadratic time lower bound for Diameter-3 of unit balls in 3D under the Orthogonal Vector (OV) hypothesis, giving the first separation between unit balls and unit cubes in the small diameter regime. Previously, computing the diameter for both objects was known to be quadratic hard when the diameter is Ω(log n) [Karl Bringmann et al., 2022]. \r\n3) A near-linear-time algorithm for Diameter-2 of unit cubes in 3D, generalizing the previous result for unit squares in 2D [Karl Bringmann et al., 2022]. \r\n4) A truly subquadratic-time algorithm and lower bound for Diameter-2 and Diameter-3 of rectangular boxes (of arbitrary dimension and sizes), respectively.","lang":"eng"}],"ddc":["000"],"date_created":"2026-06-14T22:01:44Z","external_id":{"arxiv":["2603.21790"]},"_id":"22004","file":[{"creator":"dernst","file_size":918197,"success":1,"date_updated":"2026-06-22T08:34:11Z","content_type":"application/pdf","file_id":"22114","date_created":"2026-06-22T08:34:11Z","file_name":"2026_LIPIcSSoCG_Chan.pdf","relation":"main_file","checksum":"ffff03934cc182757d6db82d88f896e6","access_level":"open_access"}],"date_updated":"2026-06-22T08:37:44Z","file_date_updated":"2026-06-22T08:34:11Z","scopus_import":"1","acknowledgement":"Timothy M. Chan: Supported by NSF grant CCF-2224271.\r\nHsien-Chih Chang: Supported by NSF CAREER award CCF-2443017.\r\nJie Gao: Supported by NSF DMS-2220271, DMS-2311064, IIS-2229876, CCF-2118953, CNS-2515159.\r\nSándor Kisfaludi-Bak: Supported by the Research Council of Finland, Grant 363444.\r\nHung Le: Supported by an NSF grant CCF-2517033 and an NSF CAREER Award CCF-2237288. Da Wei Zheng: This project has received funding from the Austrian Science Fund (FWF) grant\r\nDOI 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.","publication_status":"published","article_number":"29:1-29:15","publication":"42nd International Symposium on Computational Geometry","date_published":"2026-05-27T00:00:00Z","oa":1,"type":"conference","OA_place":"publisher","quality_controlled":"1","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"conference":{"name":"SoCG: Symposium on Computational Geometry","end_date":"2026-06-05","location":"New Brunswick, NJ, United States","start_date":"2026-06-02"},"alternative_title":["LIPIcs"],"intvolume":" 367","citation":{"short":"T.M. Chan, H.C. Chang, J. Gao, S. Kisfaludi-Bak, H. Le, D.W. Zheng, in:, 42nd International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026.","ama":"Chan TM, Chang HC, Gao J, Kisfaludi-Bak S, Le H, Zheng DW. Charting the diameter computation landscape of intersection graphs in 3D and above. In: 42nd International Symposium on Computational Geometry. Vol 367. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2026. doi:10.4230/LIPIcs.SoCG.2026.29","ista":"Chan TM, Chang HC, Gao J, Kisfaludi-Bak S, Le H, Zheng DW. 2026. Charting the diameter computation landscape of intersection graphs in 3D and above. 42nd International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 367, 29:1-29:15.","apa":"Chan, T. M., Chang, H. C., Gao, J., Kisfaludi-Bak, S., Le, H., & Zheng, D. W. (2026). Charting the diameter computation landscape of intersection graphs in 3D and above. In 42nd International Symposium on Computational Geometry (Vol. 367). New Brunswick, NJ, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2026.29","ieee":"T. M. Chan, H. C. Chang, J. Gao, S. Kisfaludi-Bak, H. Le, and D. W. Zheng, “Charting the diameter computation landscape of intersection graphs in 3D and above,” in 42nd International Symposium on Computational Geometry, New Brunswick, NJ, United States, 2026, vol. 367.","chicago":"Chan, Timothy M., Hsien Chih Chang, Jie Gao, Sándor Kisfaludi-Bak, Hung Le, and Da Wei Zheng. “Charting the Diameter Computation Landscape of Intersection Graphs in 3D and Above.” In 42nd International Symposium on Computational Geometry, Vol. 367. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026. https://doi.org/10.4230/LIPIcs.SoCG.2026.29.","mla":"Chan, Timothy M., et al. “Charting the Diameter Computation Landscape of Intersection Graphs in 3D and Above.” 42nd International Symposium on Computational Geometry, vol. 367, 29:1-29:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026, doi:10.4230/LIPIcs.SoCG.2026.29."},"corr_author":"1"},{"ddc":["510"],"external_id":{"arxiv":["2408.09589"]},"date_created":"2026-02-08T23:02:49Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_type":"original","abstract":[{"lang":"eng","text":"One of the foundational theorems of extremal graph theory is Dirac’s theorem, which\r\nsays that if an n-vertex graph G has minimum degree at least n/2, then G has a\r\nHamilton cycle, and therefore a perfect matching (if n is even). Later work by Sárközy,\r\nSelkow and Szemerédi showed that in fact Dirac graphs have many Hamilton cycles\r\nand perfect matchings, culminating in a result of Cuckler and Kahn that gives a precise\r\ndescription of the numbers of Hamilton cycles and perfect matchings in a Dirac graph\r\nG (in terms of an entropy-like parameter of G). In this paper we extend Cuckler\r\nand Kahn’s result to perfect matchings in hypergraphs. For positive integers d < k,\r\nand for n divisible by k, let md (k, n) be the minimum d-degree that ensures the\r\nexistence of a perfect matching in an n-vertex k-uniform hypergraph. In general, it is\r\nan open question to determine (even asymptotically) the values of md (k, n), but we are\r\nnonetheless able to prove an analogue of the Cuckler–Kahn theorem, showing that if\r\nan n-vertex k-uniform hypergraph G has minimum d-degree at least (1+γ )md (k, n)\r\n(for any constantγ > 0), then the number of perfect matchings in G is controlled by\r\nan entropy-like parameter of G. This strengthens cruder estimates arising from work\r\nof Kang–Kelly–Kühn–Osthus–Pfenninger and Pham–Sah–Sawhney–Simkin."}],"oa_version":"Published Version","arxiv":1,"PlanS_conform":"1","day":"01","publication_identifier":{"eissn":["1439-6912"],"issn":["0209-9683"]},"acknowledgement":"We would like to thank the referees for a number of helpful comments and suggestions, which have substantially improved the paper. Open access funding provided by Institute of Science and Technology (IST Austria).","scopus_import":"1","date_updated":"2026-02-16T09:55:17Z","file":[{"file_id":"21228","date_updated":"2026-02-16T09:52:38Z","content_type":"application/pdf","success":1,"file_size":539646,"creator":"dernst","checksum":"47b0031d90b0e6b9a843f422a1486089","access_level":"open_access","relation":"main_file","file_name":"2026_Combinatorica_Kwan.pdf","date_created":"2026-02-16T09:52:38Z"}],"file_date_updated":"2026-02-16T09:52:38Z","_id":"21159","type":"journal_article","OA_place":"publisher","date_published":"2026-02-01T00:00:00Z","oa":1,"article_number":"5","publication":"Combinatorica","publication_status":"published","citation":{"ama":"Kwan MA, Safavi Hemami R, Wang Y. Counting perfect matchings in Dirac hypergraphs. Combinatorica. 2026;46. doi:10.1007/s00493-025-00194-8","short":"M.A. Kwan, R. Safavi Hemami, Y. Wang, Combinatorica 46 (2026).","mla":"Kwan, Matthew Alan, et al. “Counting Perfect Matchings in Dirac Hypergraphs.” Combinatorica, vol. 46, 5, Springer Nature, 2026, doi:10.1007/s00493-025-00194-8.","chicago":"Kwan, Matthew Alan, Roodabeh Safavi Hemami, and Yiting Wang. “Counting Perfect Matchings in Dirac Hypergraphs.” Combinatorica. Springer Nature, 2026. https://doi.org/10.1007/s00493-025-00194-8.","ieee":"M. A. Kwan, R. Safavi Hemami, and Y. Wang, “Counting perfect matchings in Dirac hypergraphs,” Combinatorica, vol. 46. Springer Nature, 2026.","ista":"Kwan MA, Safavi Hemami R, Wang Y. 2026. Counting perfect matchings in Dirac hypergraphs. Combinatorica. 46, 5.","apa":"Kwan, M. A., Safavi Hemami, R., & Wang, Y. (2026). Counting perfect matchings in Dirac hypergraphs. Combinatorica. Springer Nature. https://doi.org/10.1007/s00493-025-00194-8"},"corr_author":"1","intvolume":" 46","quality_controlled":"1","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"status":"public","doi":"10.1007/s00493-025-00194-8","department":[{"_id":"MaKw"},{"_id":"MoHe"}],"title":"Counting perfect matchings in Dirac hypergraphs","language":[{"iso":"eng"}],"has_accepted_license":"1","month":"02","year":"2026","publisher":"Springer Nature","volume":46,"OA_type":"hybrid","author":[{"last_name":"Kwan","full_name":"Kwan, Matthew Alan","orcid":"0000-0002-4003-7567","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","first_name":"Matthew Alan"},{"full_name":"Safavi Hemami, Roodabeh","id":"72ed2640-8972-11ed-ae7b-f9c81ec75154","first_name":"Roodabeh","last_name":"Safavi Hemami"},{"last_name":"Wang","id":"1917d194-076e-11ed-97cd-837255f88785","first_name":"Yiting","full_name":"Wang, Yiting","orcid":"0000-0002-2856-767X"}],"article_processing_charge":"Yes (via OA deal)"},{"date_updated":"2026-05-04T11:54:09Z","_id":"21719","ec_funded":1,"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.","scopus_import":"1","oa_version":"Preprint","arxiv":1,"publication_identifier":{"issn":["10719040"],"eissn":["15579468"],"isbn":["9781611978971"]},"day":"07","external_id":{"arxiv":["2601.09139"]},"date_created":"2026-04-12T22:01:51Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","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."}],"conference":{"name":"SODA: Symposium on Discrete Algorithms"},"quality_controlled":"1","citation":{"ama":"Goranci G, Henzinger M, Kiss P, Momeni A, Zöcklein G. Dynamic hierarchical j-tree decomposition and its applications. In: Proceedings of the 2026 Annual ACM SIAM Symposium on Discrete Algorithms. Vol 2026-January. Society for Industrial and Applied Mathematics; 2026:1128-1180. doi:10.1137/1.9781611978971.45","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.","mla":"Goranci, Gramoz, et al. “Dynamic Hierarchical J-Tree Decomposition and Its Applications.” Proceedings of the 2026 Annual ACM SIAM Symposium on Discrete Algorithms, vol. 2026–January, Society for Industrial and Applied Mathematics, 2026, pp. 1128–80, doi:10.1137/1.9781611978971.45.","chicago":"Goranci, Gramoz, Monika Henzinger, Peter Kiss, Ali Momeni, and Gernot Zöcklein. “Dynamic Hierarchical J-Tree Decomposition and Its Applications.” In Proceedings of the 2026 Annual ACM SIAM Symposium on Discrete Algorithms, 2026–January:1128–80. Society for Industrial and Applied Mathematics, 2026. https://doi.org/10.1137/1.9781611978971.45.","ieee":"G. Goranci, M. Henzinger, P. Kiss, A. Momeni, and G. Zöcklein, “Dynamic hierarchical j-tree decomposition and its applications,” in Proceedings of the 2026 Annual ACM SIAM Symposium on Discrete Algorithms, 2026, vol. 2026–January, pp. 1128–1180.","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.","apa":"Goranci, G., Henzinger, M., Kiss, P., Momeni, A., & Zöcklein, G. (2026). Dynamic hierarchical j-tree decomposition and its applications. In Proceedings of the 2026 Annual ACM SIAM Symposium on Discrete Algorithms (Vol. 2026–January, pp. 1128–1180). Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611978971.45"},"publication":"Proceedings of the 2026 Annual ACM SIAM Symposium on Discrete Algorithms","publication_status":"published","page":"1128-1180","type":"conference","OA_place":"repository","date_published":"2026-01-07T00:00:00Z","oa":1,"volume":"2026-January","project":[{"grant_number":"101019564","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","call_identifier":"H2020","name":"The design and evaluation of modern fully dynamic data structures"},{"name":"Static and Dynamic Hierarchical Graph Decompositions","_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103","grant_number":"I05982"}],"publisher":"Society for Industrial and Applied Mathematics","year":"2026","language":[{"iso":"eng"}],"title":"Dynamic hierarchical j-tree decomposition and its applications","month":"01","status":"public","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2601.09139"}],"department":[{"_id":"MoHe"}],"doi":"10.1137/1.9781611978971.45","author":[{"first_name":"Gramoz","full_name":"Goranci, Gramoz","last_name":"Goranci"},{"orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","first_name":"Monika H","last_name":"Henzinger"},{"full_name":"Kiss, Peter","first_name":"Peter","last_name":"Kiss"},{"last_name":"Momeni","full_name":"Momeni, Ali","first_name":"Ali"},{"last_name":"Zöcklein","id":"45d5e826-47af-11f1-84e5-ba87c23fe681","first_name":"Gernot","full_name":"Zöcklein, Gernot"}],"article_processing_charge":"No","OA_type":"green"},{"OA_type":"gold","author":[{"last_name":"Kalinin","first_name":"Nikita","id":"4b14526e-14d2-11ed-ba64-c14c9553d137","full_name":"Kalinin, Nikita"},{"last_name":"Andersson","id":"4a893819-d954-11f0-89b1-e360bad9ccc5","first_name":"Joel D","full_name":"Andersson, Joel D"}],"article_processing_charge":"No","language":[{"iso":"eng"}],"title":"Learning rate scheduling with matrix factorization for private training","keyword":["differential privacy","machine learning","matrix factorization"],"has_accepted_license":"1","researchdata_availability":"no","month":"06","status":"public","doi":"10.4230/LIPIcs.FORC.2026.2","department":[{"_id":"ChLa"},{"_id":"GradSch"},{"_id":"MoHe"}],"volume":368,"project":[{"grant_number":"101019564","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","call_identifier":"H2020","name":"The design and evaluation of modern fully dynamic data structures"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","year":"2026","das_tickbox":"0","publication":"7th Symposium on Foundations of Responsible Computing","article_number":"2:1-2:21","publication_status":"published","type":"conference","OA_place":"publisher","date_published":"2026-06-01T00:00:00Z","oa":1,"tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"quality_controlled":"1","conference":{"location":"Cambridge, MA; United States","end_date":"2026-06-05","start_date":"2026-06-03","name":"FORC: Symposium on Foundations of Responsible Computing"},"citation":{"mla":"Kalinin, Nikita, and Joel D. Andersson. “Learning Rate Scheduling with Matrix Factorization for Private Training.” 7th Symposium on Foundations of Responsible Computing, vol. 368, 2:1-2:21, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026, doi:10.4230/LIPIcs.FORC.2026.2.","chicago":"Kalinin, Nikita, and Joel D Andersson. “Learning Rate Scheduling with Matrix Factorization for Private Training.” In 7th Symposium on Foundations of Responsible Computing, Vol. 368. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026. https://doi.org/10.4230/LIPIcs.FORC.2026.2.","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.","apa":"Kalinin, N., & Andersson, J. D. (2026). Learning rate scheduling with matrix factorization for private training. In 7th Symposium on Foundations of Responsible Computing (Vol. 368). Cambridge, MA; United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.FORC.2026.2","ieee":"N. Kalinin and J. D. Andersson, “Learning rate scheduling with matrix factorization for private training,” in 7th Symposium on Foundations of Responsible Computing, Cambridge, MA; United States, 2026, vol. 368.","ama":"Kalinin N, Andersson JD. Learning rate scheduling with matrix factorization for private training. In: 7th Symposium on Foundations of Responsible Computing. Vol 368. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2026. doi:10.4230/LIPIcs.FORC.2026.2","short":"N. Kalinin, J.D. Andersson, in:, 7th Symposium on Foundations of Responsible Computing, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026."},"corr_author":"1","alternative_title":["LIPIcs"],"intvolume":" 368","oa_version":"Published Version","arxiv":1,"day":"01","publication_identifier":{"isbn":["9783959774192"],"eissn":["1868-8969"]},"ddc":["000"],"date_created":"2026-06-28T22:01:34Z","external_id":{"arxiv":["2511.17994"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","supplementarymaterial":"no","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."}],"file":[{"file_size":1231914,"creator":"dernst","file_id":"22149","date_updated":"2026-06-29T06:55:23Z","success":1,"content_type":"application/pdf","file_name":"2026_LIPIcsFORC_Kalinin.pdf","relation":"main_file","date_created":"2026-06-29T06:55:23Z","checksum":"c661f016d3861a1c1b590b87a744d087","access_level":"open_access"}],"file_date_updated":"2026-06-29T06:55:23Z","date_updated":"2026-06-29T06:56:34Z","_id":"22146","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","ec_funded":1,"scopus_import":"1"},{"author":[{"orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H","first_name":"Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","last_name":"Henzinger"},{"first_name":"Robin","full_name":"Münk, Robin","last_name":"Münk"},{"first_name":"Harald","full_name":"Räcke, Harald","last_name":"Räcke"}],"article_processing_charge":"No","OA_type":"gold","project":[{"grant_number":"101019564","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","call_identifier":"H2020","name":"The design and evaluation of modern fully dynamic data structures"},{"grant_number":"I05982","_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103","name":"Static and Dynamic Hierarchical Graph Decompositions"}],"publisher":"Association for Computing Machinery","year":"2026","das_tickbox":"0","language":[{"iso":"eng"}],"title":"An improved quality hierarchical congestion approximator in near-linear time","has_accepted_license":"1","keyword":["Congestion Approximators","Hierarchical Graph Decompositions"],"researchdata_availability":"no","month":"06","status":"public","doi":"10.1145/3798129.3800851","department":[{"_id":"MoHe"}],"conference":{"location":"Salt Lake City, UT, United States","end_date":"2026-06-26","start_date":"2026-06-22","name":"STOC: Symposium on the Theory of Computing"},"tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"quality_controlled":"1","citation":{"chicago":"Henzinger, Monika, Robin Münk, and Harald Räcke. “An Improved Quality Hierarchical Congestion Approximator in Near-Linear Time.” In 58th Annual ACM Symposium on Theory of Computing, 1417–28. Association for Computing Machinery, 2026. https://doi.org/10.1145/3798129.3800851.","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.","ieee":"M. Henzinger, R. Münk, and H. Räcke, “An improved quality hierarchical congestion approximator in near-linear time,” in 58th Annual ACM Symposium on Theory of Computing, Salt Lake City, UT, United States, 2026, pp. 1417–1428.","apa":"Henzinger, M., Münk, R., & Räcke, H. (2026). An improved quality hierarchical congestion approximator in near-linear time. In 58th Annual ACM Symposium on Theory of Computing (pp. 1417–1428). Salt Lake City, UT, United States: Association for Computing Machinery. https://doi.org/10.1145/3798129.3800851","mla":"Henzinger, Monika, et al. “An Improved Quality Hierarchical Congestion Approximator in Near-Linear Time.” 58th Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, 2026, pp. 1417–28, doi:10.1145/3798129.3800851.","ama":"Henzinger M, Münk R, Räcke H. An improved quality hierarchical congestion approximator in near-linear time. In: 58th Annual ACM Symposium on Theory of Computing. Association for Computing Machinery; 2026:1417-1428. doi:10.1145/3798129.3800851","short":"M. Henzinger, R. Münk, H. Räcke, in:, 58th Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, 2026, pp. 1417–1428."},"corr_author":"1","publication":"58th Annual ACM Symposium on Theory of Computing","publication_status":"published","type":"conference","page":"1417-1428","OA_place":"publisher","date_published":"2026-06-09T00:00:00Z","oa":1,"file":[{"file_id":"22250","content_type":"application/pdf","success":1,"date_updated":"2026-07-06T06:57:16Z","file_size":919005,"creator":"dernst","access_level":"open_access","checksum":"2bef46be8da6d19a641697bb0d8ade65","file_name":"2026_STOC_HenzingerMo.pdf","relation":"main_file","date_created":"2026-07-06T06:57:16Z"}],"file_date_updated":"2026-07-06T06:57:16Z","date_updated":"2026-07-06T06:59:52Z","_id":"22245","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.","ec_funded":1,"scopus_import":"1","arxiv":1,"oa_version":"Published Version","publication_identifier":{"isbn":["9798400725364"],"issn":["0737-8017"]},"day":"09","ddc":["000"],"date_created":"2026-07-05T22:01:36Z","external_id":{"arxiv":["2511.03716"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","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"}],"supplementarymaterial":"no"},{"status":"public","department":[{"_id":"MoHe"}],"doi":"10.1145/3798129.3800917","language":[{"iso":"eng"}],"title":"Cutting planarians: Planar emulators for string graphs","has_accepted_license":"1","researchdata_availability":"no","month":"06","year":"2026","publisher":"Association for Computing Machinery","das_tickbox":"0","OA_type":"gold","author":[{"last_name":"Chang","full_name":"Chang, Hsien Chih","first_name":"Hsien Chih"},{"last_name":"Conroy","first_name":"Jonathan","full_name":"Conroy, Jonathan"},{"full_name":"Tan, Zihan","first_name":"Zihan","last_name":"Tan"},{"last_name":"Zheng","full_name":"Zheng, Da Wei","id":"af77956b-e859-11ef-8dc9-d301b898e32f","first_name":"Da Wei"}],"article_processing_charge":"No","ddc":["500","000"],"date_created":"2026-07-05T22:01:37Z","external_id":{"arxiv":["2510.21700"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"text":"In this paper we construct distance sketches for intersection graphs of arbitrary path-connected regions in the plane (known as the string graphs) in the constant and 1+ε distortion regimes. Furthermore, the distance sketches themselves are planar graphs. First, we show that every unweighted string graph G has an O(1)-distortion planar emulator: that is, there exists an edge-weighted planar graph H containing every vertex in G, such that every pair of vertices (u,v) satisfies δG(u,v) ≤ δH(u,v) ≤ O(1) · δG(u,v). Furthermore, we show that for any constant ε > 0, there is an edge-weighted planar graph H′ such that every pair of vertices (u,v) satisfies δG(u,v) ≤ δH′(u,v) ≤ (1+ε) · δG(u,v) + O(ε−4polylogn). No previous constructions of sparse distance sketches were known even for intersection graphs of simple shapes like axis-parallel rectangles or fat convex polygons.\r\nAs applications, we construct the first (1+ε, +O(1)) mixed-distortion tree cover and distance oracle for arbitrary string graphs, as well as the first additive +(εΔ+O(1))-distortion embedding of string graphs G with diameter Δ into graphs of constant treewidth O(ε−4).","lang":"eng"}],"supplementarymaterial":"no","arxiv":1,"oa_version":"Published Version","day":"09","publication_identifier":{"isbn":["9798400725364"],"issn":["0737-8017"]},"acknowledgement":"Hsien-Chih Chang and Jonathan Conroy are supported by the U.S.\r\nNational Science Foundation CAREER Award under the Grant No.\r\nCCF-2443017.","scopus_import":"1","file_date_updated":"2026-07-06T10:23:09Z","file":[{"content_type":"application/pdf","date_updated":"2026-07-06T10:23:09Z","success":1,"file_id":"22253","creator":"dernst","file_size":2015699,"checksum":"c184596a3e18fee912caef4c7751a96d","access_level":"open_access","date_created":"2026-07-06T10:23:09Z","file_name":"2026_STOC_Chang.pdf","relation":"main_file"}],"date_updated":"2026-07-06T10:25:23Z","_id":"22246","type":"conference","page":"2140-2151","OA_place":"publisher","date_published":"2026-06-09T00:00:00Z","oa":1,"publication":"58th Annual ACM Symposium on Theory of Computing","publication_status":"published","citation":{"short":"H.C. Chang, J. Conroy, Z. Tan, D.W. Zheng, in:, 58th Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, 2026, pp. 2140–2151.","ama":"Chang HC, Conroy J, Tan Z, Zheng DW. Cutting planarians: Planar emulators for string graphs. In: 58th Annual ACM Symposium on Theory of Computing. Association for Computing Machinery; 2026:2140-2151. doi:10.1145/3798129.3800917","mla":"Chang, Hsien Chih, et al. “Cutting Planarians: Planar Emulators for String Graphs.” 58th Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, 2026, pp. 2140–51, doi:10.1145/3798129.3800917.","apa":"Chang, H. C., Conroy, J., Tan, Z., & Zheng, D. W. (2026). Cutting planarians: Planar emulators for string graphs. In 58th Annual ACM Symposium on Theory of Computing (pp. 2140–2151). Salt Lake City, UT, United States: Association for Computing Machinery. https://doi.org/10.1145/3798129.3800917","ieee":"H. C. Chang, J. Conroy, Z. Tan, and D. W. Zheng, “Cutting planarians: Planar emulators for string graphs,” in 58th Annual ACM Symposium on Theory of Computing, Salt Lake City, UT, United States, 2026, pp. 2140–2151.","ista":"Chang HC, Conroy J, Tan Z, Zheng DW. 2026. Cutting planarians: Planar emulators for string graphs. 58th Annual ACM Symposium on Theory of Computing. STOC: Symposium on the Theory of Computing, 2140–2151.","chicago":"Chang, Hsien Chih, Jonathan Conroy, Zihan Tan, and Da Wei Zheng. “Cutting Planarians: Planar Emulators for String Graphs.” In 58th Annual ACM Symposium on Theory of Computing, 2140–51. Association for Computing Machinery, 2026. https://doi.org/10.1145/3798129.3800917."},"corr_author":"1","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"conference":{"end_date":"2026-06-26","location":"Salt Lake City, UT, United States","start_date":"2026-06-22","name":"STOC: Symposium on the Theory of Computing"},"quality_controlled":"1"},{"_id":"22318","date_updated":"2026-07-16T09:14:49Z","file_date_updated":"2026-07-16T09:09:53Z","file":[{"date_created":"2026-07-16T09:09:53Z","file_name":"2026_ACMMgmtData_Henzinger.pdf","relation":"main_file","access_level":"open_access","checksum":"c6c5e256d02b90682c0690c3bee94040","creator":"dernst","file_size":655405,"date_updated":"2026-07-16T09:09:53Z","content_type":"application/pdf","success":1,"file_id":"22345"}],"scopus_import":"1","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.","ec_funded":1,"day":"01","publication_identifier":{"issn":["2836-6573"]},"arxiv":1,"oa_version":"Published Version","PlanS_conform":"1","article_type":"original","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","supplementarymaterial":"no","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"}],"ddc":["000"],"date_created":"2026-07-13T14:59:14Z","external_id":{"arxiv":["2411.03299"]},"quality_controlled":"1","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"intvolume":" 4","citation":{"chicago":"Henzinger, Monika, Roodabeh Safavi Hemami, and Salil Vadhan. “Concurrent Composition for Differentially Private Continual Mechanisms.” Proceedings of the ACM on Management of Data. Association for Computing Machinery, 2026. https://doi.org/10.1145/3801895.","ieee":"M. Henzinger, R. Safavi Hemami, and S. Vadhan, “Concurrent composition for differentially private continual mechanisms,” Proceedings of the ACM on Management of Data, vol. 4, no. 2. Association for Computing Machinery, pp. 1–26, 2026.","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.","apa":"Henzinger, M., Safavi Hemami, R., & Vadhan, S. (2026). Concurrent composition for differentially private continual mechanisms. Proceedings of the ACM on Management of Data. Association for Computing Machinery. https://doi.org/10.1145/3801895","mla":"Henzinger, Monika, et al. “Concurrent Composition for Differentially Private Continual Mechanisms.” Proceedings of the ACM on Management of Data, vol. 4, no. 2, Association for Computing Machinery, 2026, pp. 1–26, doi:10.1145/3801895.","ama":"Henzinger M, Safavi Hemami R, Vadhan S. Concurrent composition for differentially private continual mechanisms. Proceedings of the ACM on Management of Data. 2026;4(2):1-26. doi:10.1145/3801895","short":"M. Henzinger, R. Safavi Hemami, S. Vadhan, Proceedings of the ACM on Management of Data 4 (2026) 1–26."},"corr_author":"1","publication_status":"published","publication":"Proceedings of the ACM on Management of Data","date_published":"2026-06-01T00:00:00Z","oa":1,"type":"journal_article","page":"1-26","OA_place":"publisher","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"},{"_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe","grant_number":"P33775","name":"Fast Algorithms for a Reactive Network Layer"},{"grant_number":"Z00422","_id":"34def286-11ca-11ed-8bc3-da5948e1613c","name":"Efficient algorithms"}],"volume":4,"das_tickbox":"0","publisher":"Association for Computing Machinery","year":"2026","researchdata_availability":"no","month":"06","title":"Concurrent composition for differentially private continual mechanisms","language":[{"iso":"eng"}],"has_accepted_license":"1","keyword":["differential privacy","concurrent composition","continual release","continual observation","data streaming","continual mechanisms","concurrent parallel composition","concurrent filter composition"],"doi":"10.1145/3801895","department":[{"_id":"MoHe"}],"status":"public","article_processing_charge":"Yes","author":[{"last_name":"Henzinger","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","first_name":"Monika H","full_name":"Henzinger, Monika H","orcid":"0000-0002-5008-6530"},{"full_name":"Safavi Hemami, Roodabeh","id":"72ed2640-8972-11ed-ae7b-f9c81ec75154","first_name":"Roodabeh","last_name":"Safavi Hemami"},{"full_name":"Vadhan, Salil","first_name":"Salil","last_name":"Vadhan"}],"issue":"2","OA_type":"gold"},{"external_id":{"arxiv":["2512.15981"]},"date_created":"2026-07-14T05:33:58Z","ddc":["000"],"supplementarymaterial":"no","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."}],"article_type":"original","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","PlanS_conform":"1","arxiv":1,"oa_version":"Published Version","day":"01","publication_identifier":{"issn":["2836-6573"]},"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","ec_funded":1,"scopus_import":"1","file":[{"checksum":"21a48a620e415a31a3874077c55bc6c3","access_level":"open_access","date_created":"2026-07-16T09:29:08Z","relation":"main_file","file_name":"2026_ACMMgmtData_Aryanfard.pdf","content_type":"application/pdf","date_updated":"2026-07-16T09:29:08Z","success":1,"file_id":"22349","file_size":934963,"creator":"dernst"}],"file_date_updated":"2026-07-16T09:29:08Z","date_updated":"2026-07-16T09:30:31Z","_id":"22322","OA_place":"publisher","page":"1-27","type":"journal_article","oa":1,"date_published":"2026-06-01T00:00:00Z","publication":"Proceedings of the ACM on Management of Data","publication_status":"published","corr_author":"1","citation":{"ama":"Aryanfard B, Henzinger M, Saulpic D, Sricharan AR. Improved lower bounds for privacy under continual release. Proceedings of the ACM on Management of Data. 2026;4(2):1-27. doi:10.1145/3801903","short":"B. Aryanfard, M. Henzinger, D. Saulpic, A.R. Sricharan, Proceedings of the ACM on Management of Data 4 (2026) 1–27.","chicago":"Aryanfard, Bardiya, Monika Henzinger, David Saulpic, and A. R. Sricharan. “Improved Lower Bounds for Privacy under Continual Release.” Proceedings of the ACM on Management of Data. Association for Computing Machinery, 2026. https://doi.org/10.1145/3801903.","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.","ieee":"B. Aryanfard, M. Henzinger, D. Saulpic, and A. R. Sricharan, “Improved lower bounds for privacy under continual release,” Proceedings of the ACM on Management of Data, vol. 4, no. 2. Association for Computing Machinery, pp. 1–27, 2026.","apa":"Aryanfard, B., Henzinger, M., Saulpic, D., & Sricharan, A. R. (2026). Improved lower bounds for privacy under continual release. Proceedings of the ACM on Management of Data. Association for Computing Machinery. https://doi.org/10.1145/3801903","mla":"Aryanfard, Bardiya, et al. “Improved Lower Bounds for Privacy under Continual Release.” Proceedings of the ACM on Management of Data, vol. 4, no. 2, Association for Computing Machinery, 2026, pp. 1–27, doi:10.1145/3801903."},"intvolume":" 4","quality_controlled":"1","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"status":"public","department":[{"_id":"MoHe"},{"_id":"GradSch"}],"doi":"10.1145/3801903","has_accepted_license":"1","language":[{"iso":"eng"}],"title":"Improved lower bounds for privacy under continual release","month":"06","researchdata_availability":"no","publisher":"Association for Computing Machinery","year":"2026","das_tickbox":"0","volume":4,"project":[{"_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","grant_number":"101019564","name":"The design and evaluation of modern fully dynamic data structures","call_identifier":"H2020"}],"OA_type":"gold","issue":"2","author":[{"last_name":"Aryanfard","first_name":"Bardiya","id":"1e8f4084-31df-11ee-b195-f706b4b77091","full_name":"Aryanfard, Bardiya"},{"first_name":"Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H","last_name":"Henzinger"},{"first_name":"David","id":"f8e48cf0-b0ff-11ed-b0e9-b4c35598f964","full_name":"Saulpic, David","last_name":"Saulpic"},{"full_name":"Sricharan, A. R.","first_name":"A. R.","last_name":"Sricharan"}],"article_processing_charge":"Yes"},{"day":"01","publication_identifier":{"isbn":["9798400725128"]},"oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","supplementarymaterial":"no","abstract":[{"lang":"eng","text":"We study simple dynamics in the population protocol model, in\r\nwhich 𝑛 agents start with totally ordered initial opinions 𝑥1, 𝑥2, . . . ,\r\n𝑥𝑛 and, in each round, a randomly chosen agent changes its opinion\r\nas a function of the opinion of other randomly chosen agents. Such\r\ndynamics often converge to consensus on a single fixation value 𝑋ˆ.\r\nThis paper asks how to control the distribution of 𝑋ˆ as a randomised\r\nchoice among the initial opinions by designing suitable simple\r\ndynamics. Writing the sorted initial values as 𝑥(1) ≤ · · · ≤ 𝑥(𝑛)\r\n,\r\nwe design two protocols that realise natural target laws over order\r\nstatistics.\r\nFirst, for a parameter 𝑝 ∈ (0, 1), our geometric protocol biases\r\ntoward larger opinions and satisfies P\r\n\r\n𝑋ˆ = 𝑥(𝑘)\r\n\r\n∝ 𝑝\r\n𝑛−𝑘\r\n, for\r\n𝑘 = 1, . . . , 𝑛. Equivalently, P\r\n\r\n𝑋ˆ = 𝑥(𝑘)\r\n\r\n= (1 − 𝑝)𝑝\r\n𝑛−𝑘\r\n/(1 − 𝑝\r\n𝑛\r\n).\r\nSecond, our binomial protocol assigns a shifted binomial law to the\r\nranks in ascending order: if 𝐾 −1 ∼ Bin(𝑛−1, 1−𝑝), then 𝑋ˆ = 𝑥(𝐾)\r\n,\r\ni.e., P\r\n\r\n𝑋ˆ = 𝑥(𝑘)\r\n\r\n=\r\n𝑛−1\r\n𝑘−1\r\n\u0001\r\n𝑝\r\n𝑛−𝑘\r\n(1 − 𝑝)\r\n𝑘−1\r\n, for 𝑘 = 1, . . . , 𝑛.\r\nApplications of this include computing the Top-𝑘 values for\r\nsmall 𝑘 on general interaction graphs. A central contribution of\r\nthis work is that, in contrast to most population protocols, we can\r\ncharacterise the fixation distribution in closed form. This is enabled\r\nby a novel analysis technique, which also yields applications: we\r\nderive new results for the Median protocol that extend the state of\r\nthe art."}],"ddc":["000"],"date_created":"2026-07-19T22:01:47Z","_id":"22368","file_date_updated":"2026-07-21T07:31:29Z","file":[{"content_type":"application/pdf","success":1,"date_updated":"2026-07-21T07:31:29Z","file_id":"22379","file_size":824239,"creator":"dernst","checksum":"e8208393a016d8e71d7b26c402045488","access_level":"open_access","date_created":"2026-07-21T07:31:29Z","relation":"main_file","file_name":"2026_ACMPODC_dArchivio.pdf"}],"date_updated":"2026-07-21T07:34:49Z","scopus_import":"1","acknowledgement":"This work has been supported by the AID INRIA-DGA project\r\nn°2023000872 “BioSwarm”, the French government National Research Agency (ANR) through the UCA JEDI (ANR-15-IDEX-01),\r\nthe EUR DS4H (ANR-17-EURE-004) and the 3IA Cote d’Azur Investments ANR-23-IACL-0001, and EPSRC grant EP/W005573/1","publication_status":"published","publication":"Proceedings of the Annual ACM Symposium on Principles of Distributed Computing","date_published":"2026-07-01T00:00:00Z","oa":1,"page":"425-436","type":"conference","OA_place":"publisher","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"quality_controlled":"1","conference":{"start_date":"2026-07-06","end_date":"2026-07-10","location":"Egham, United Kingdom","name":"PODC: Symposium on Principles of Distributed Computing"},"citation":{"short":"N. D’Archivio, H. Almahmoud, E. Natale, F. Mallmann-Trenn, in:, Proceedings of the Annual ACM Symposium on Principles of Distributed Computing, Association for Computing Machinery, 2026, pp. 425–436.","ama":"D’Archivio N, Almahmoud H, Natale E, Mallmann-Trenn F. Order statistics in population protocols via simple dynamics. In: Proceedings of the Annual ACM Symposium on Principles of Distributed Computing. Association for Computing Machinery; 2026:425-436. doi:10.1145/3796701.3815922","mla":"D’Archivio, Niccolò, et al. “Order Statistics in Population Protocols via Simple Dynamics.” Proceedings of the Annual ACM Symposium on Principles of Distributed Computing, Association for Computing Machinery, 2026, pp. 425–36, doi:10.1145/3796701.3815922.","ieee":"N. D’Archivio, H. Almahmoud, E. Natale, and F. Mallmann-Trenn, “Order statistics in population protocols via simple dynamics,” in Proceedings of the Annual ACM Symposium on Principles of Distributed Computing, Egham, United Kingdom, 2026, pp. 425–436.","apa":"D’Archivio, N., Almahmoud, H., Natale, E., & Mallmann-Trenn, F. (2026). Order statistics in population protocols via simple dynamics. In Proceedings of the Annual ACM Symposium on Principles of Distributed Computing (pp. 425–436). Egham, United Kingdom: Association for Computing Machinery. https://doi.org/10.1145/3796701.3815922","ista":"D’Archivio N, Almahmoud H, Natale E, Mallmann-Trenn F. 2026. Order statistics in population protocols via simple dynamics. Proceedings of the Annual ACM Symposium on Principles of Distributed Computing. PODC: Symposium on Principles of Distributed Computing, 425–436.","chicago":"D’Archivio, Niccolò, Hind Almahmoud, Emanuele Natale, and Frederik Mallmann-Trenn. “Order Statistics in Population Protocols via Simple Dynamics.” In Proceedings of the Annual ACM Symposium on Principles of Distributed Computing, 425–36. Association for Computing Machinery, 2026. https://doi.org/10.1145/3796701.3815922."},"corr_author":"1","researchdata_availability":"no","month":"07","language":[{"iso":"eng"}],"title":"Order statistics in population protocols via simple dynamics","has_accepted_license":"1","department":[{"_id":"MoHe"}],"doi":"10.1145/3796701.3815922","status":"public","das_tickbox":"0","year":"2026","publisher":"Association for Computing Machinery","OA_type":"gold","article_processing_charge":"No","author":[{"last_name":"D'Archivio","full_name":"D'Archivio, Niccolò","first_name":"Niccolò"},{"full_name":"Almahmoud, Hind","first_name":"Hind","last_name":"Almahmoud"},{"first_name":"Emanuele","full_name":"Natale, Emanuele","last_name":"Natale"},{"full_name":"Mallmann-Trenn, Frederik","first_name":"Frederik","id":"68748c44-84d5-11f1-b4f6-ca083374e553","last_name":"Mallmann-Trenn"}]},{"supplementarymaterial":"no","abstract":[{"lang":"eng","text":"We study the Undecided-State Dynamics (USD), a fundamental consensus process in which each vertex holds one of k decided opinions or the undecided state. We consider both the gossip model and the population protocol model. Prior work established tight bounds on the consensus time of this process only for the regime \r\nk\r\n=\r\nO\r\n(\r\nn\r\n/\r\n(\r\nlog\r\n\r\nn\r\n)\r\n2\r\n)\r\n (for the population protocol model) and k = O((n/log n)1/3) (for the gossip model), often under restrictive assumptions on the initial configuration.\r\nIn this paper, we obtain the first consensus-time guarantees for USD that hold for arbitrary 2 ≤ k ≤ n and for arbitrary initial configurations in both the gossip model and the population protocol model. In the gossip model, USD reaches consensus within \r\nO\r\n~\r\n(\r\nmin\r\n{\r\nk\r\n,\r\nn\r\n}\r\n)\r\n synchronous rounds with probability 1 - p⊥ - n-c, where p⊥ is the gossip-specific probability of collapsing to the all-undecided state in the first round. In the population protocol model, USD reaches consensus within \r\nO\r\n~\r\n(\r\nmin\r\n{\r\nk\r\nn\r\n,\r\nn\r\n3\r\n/\r\n2\r\n}\r\n)\r\n asynchronous interactions with high probability. We also present lower bounds that match the upper bounds up to polylogarithmic factors for a specific initial configuration and show that our upper bounds are essentially optimal."}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2026-07-19T22:01:47Z","external_id":{"arxiv":["2603.02636"]},"ddc":["000"],"day":"01","publication_identifier":{"isbn":["9798400725128"]},"arxiv":1,"oa_version":"Published Version","scopus_import":"1","acknowledgement":"Nobutaka Shimizu is supported by JSPS KAKENHI Grant Number\r\n23K16837. Takeharu Shiraga is supported by JSPS KAKENHI Grant\r\nNumber 23K16840, and JST CRONOS Grant Number JPMJCS24K2.\r\nColin Cooper is supported by a Mercator Fellowship from DFG\r\nProject 491453517 at the University of Hamburg. We thank the\r\nanonymous reviewers for their helpful comments and suggestions.","_id":"22367","date_updated":"2026-07-21T07:54:01Z","file_date_updated":"2026-07-21T07:51:58Z","file":[{"checksum":"9ada61feba1e93fd72867a5ba4ee8bb8","access_level":"open_access","date_created":"2026-07-21T07:51:58Z","file_name":"2026_ACMPODC_Cooper.pdf","relation":"main_file","date_updated":"2026-07-21T07:51:58Z","success":1,"content_type":"application/pdf","file_id":"22380","file_size":709077,"creator":"dernst"}],"oa":1,"date_published":"2026-07-01T00:00:00Z","OA_place":"publisher","type":"conference","page":"77-87","publication_status":"published","publication":"Proceedings of the Annual ACM Symposium on Principles of Distributed Computing","corr_author":"1","citation":{"ama":"Cooper C, Mallmann-Trenn F, Radzik T, Shimizu N, Shiraga T. Undecided state dynamics with many opinions. In: Proceedings of the Annual ACM Symposium on Principles of Distributed Computing. Association for Computing Machinery; 2026:77-87. doi:10.1145/3796701.3815920","short":"C. Cooper, F. Mallmann-Trenn, T. Radzik, N. Shimizu, T. Shiraga, in:, Proceedings of the Annual ACM Symposium on Principles of Distributed Computing, Association for Computing Machinery, 2026, pp. 77–87.","mla":"Cooper, Colin, et al. “Undecided State Dynamics with Many Opinions.” Proceedings of the Annual ACM Symposium on Principles of Distributed Computing, Association for Computing Machinery, 2026, pp. 77–87, doi:10.1145/3796701.3815920.","chicago":"Cooper, Colin, Frederik Mallmann-Trenn, Tomasz Radzik, Nobutaka Shimizu, and Takeharu Shiraga. “Undecided State Dynamics with Many Opinions.” In Proceedings of the Annual ACM Symposium on Principles of Distributed Computing, 77–87. Association for Computing Machinery, 2026. https://doi.org/10.1145/3796701.3815920.","ieee":"C. Cooper, F. Mallmann-Trenn, T. Radzik, N. Shimizu, and T. Shiraga, “Undecided state dynamics with many opinions,” in Proceedings of the Annual ACM Symposium on Principles of Distributed Computing, Egham, United Kingdom, 2026, pp. 77–87.","apa":"Cooper, C., Mallmann-Trenn, F., Radzik, T., Shimizu, N., & Shiraga, T. (2026). Undecided state dynamics with many opinions. In Proceedings of the Annual ACM Symposium on Principles of Distributed Computing (pp. 77–87). Egham, United Kingdom: Association for Computing Machinery. https://doi.org/10.1145/3796701.3815920","ista":"Cooper C, Mallmann-Trenn F, Radzik T, Shimizu N, Shiraga T. 2026. Undecided state dynamics with many opinions. Proceedings of the Annual ACM Symposium on Principles of Distributed Computing. PODC: Symposium on Principles of Distributed Computing, 77–87."},"quality_controlled":"1","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"conference":{"start_date":"2026-07-06","end_date":"2026-07-10","location":"Egham, United Kingdom","name":"PODC: Symposium on Principles of Distributed Computing"},"doi":"10.1145/3796701.3815920","department":[{"_id":"MoHe"}],"status":"public","month":"07","researchdata_availability":"no","has_accepted_license":"1","keyword":["consensus dynamics","undecided state dynamics","gossip model","population protocol model"],"language":[{"iso":"eng"}],"title":"Undecided state dynamics with many opinions","das_tickbox":"1","year":"2026","publisher":"Association for Computing Machinery","OA_type":"gold","article_processing_charge":"No","author":[{"full_name":"Cooper, Colin","first_name":"Colin","last_name":"Cooper"},{"last_name":"Mallmann-Trenn","first_name":"Frederik","id":"68748c44-84d5-11f1-b4f6-ca083374e553","full_name":"Mallmann-Trenn, Frederik"},{"last_name":"Radzik","full_name":"Radzik, Tomasz","first_name":"Tomasz"},{"last_name":"Shimizu","full_name":"Shimizu, Nobutaka","first_name":"Nobutaka"},{"full_name":"Shiraga, Takeharu","first_name":"Takeharu","last_name":"Shiraga"}]},{"status":"public","department":[{"_id":"MoHe"},{"_id":"GradSch"}],"doi":"10.1145/3796701.3815913","has_accepted_license":"1","language":[{"iso":"eng"}],"title":"Ranking opinions with few states in population protocols","month":"07","researchdata_availability":"no","publisher":"Association for Computing Machinery","year":"2026","das_tickbox":"0","project":[{"grant_number":"101019564","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","call_identifier":"H2020","name":"The design and evaluation of modern fully dynamic data structures"},{"_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103","grant_number":"I05982","name":"Static and Dynamic Hierarchical Graph Decompositions"}],"OA_type":"gold","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","first_name":"Antoine","id":"888a098e-fcac-11ee-aff7-d347be57b725","orcid":"0000-0003-4268-7368","full_name":"El-Hayek, Antoine"},{"last_name":"Schmid","first_name":"Stefan","full_name":"Schmid, Stefan"}],"article_processing_charge":"Yes","date_created":"2026-07-14T05:40:17Z","external_id":{"arxiv":["2605.18707"]},"ddc":["000"],"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."}],"supplementarymaterial":"no","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","oa_version":"Published Version","arxiv":1,"day":"01","publication_identifier":{"isbn":["9798400725128"]},"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.","ec_funded":1,"scopus_import":"1","file":[{"date_created":"2026-07-16T11:18:44Z","relation":"main_file","file_name":"2026_ACMPODC_Breitkopf.pdf","access_level":"open_access","checksum":"e56da70c1b2e7e663d2d8106cf07a30a","file_size":702140,"creator":"dernst","content_type":"application/pdf","date_updated":"2026-07-16T11:18:44Z","success":1,"file_id":"22353"}],"file_date_updated":"2026-07-16T11:18:44Z","date_updated":"2026-07-22T07:49:22Z","_id":"22327","OA_place":"publisher","type":"conference","page":"414 - 424","oa":1,"date_published":"2026-07-01T00:00:00Z","publication":"Proceedings of the ACM Symposium on Principles of Distributed Computing","publication_status":"published","corr_author":"1","citation":{"mla":"Breitkopf, Tom-Lukas, et al. “Ranking Opinions with Few States in Population Protocols.” Proceedings of the ACM Symposium on Principles of Distributed Computing, Association for Computing Machinery, 2026, pp. 414–24, doi:10.1145/3796701.3815913.","chicago":"Breitkopf, Tom-Lukas, Julien Dallot, Antoine El-Hayek, and Stefan Schmid. “Ranking Opinions with Few States in Population Protocols.” In Proceedings of the ACM Symposium on Principles of Distributed Computing, 414–24. Association for Computing Machinery, 2026. https://doi.org/10.1145/3796701.3815913.","apa":"Breitkopf, T.-L., Dallot, J., El-Hayek, A., & Schmid, S. (2026). Ranking opinions with few states in population protocols. In Proceedings of the ACM Symposium on Principles of Distributed Computing (pp. 414–424). Egham, United Kingdom: Association for Computing Machinery. https://doi.org/10.1145/3796701.3815913","ieee":"T.-L. Breitkopf, J. Dallot, A. El-Hayek, and S. Schmid, “Ranking opinions with few states in population protocols,” in Proceedings of the ACM Symposium on Principles of Distributed Computing, Egham, United Kingdom, 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.","ama":"Breitkopf T-L, Dallot J, El-Hayek A, Schmid S. Ranking opinions with few states in population protocols. In: Proceedings of the ACM Symposium on Principles of Distributed Computing. Association for Computing Machinery; 2026:414-424. doi:10.1145/3796701.3815913","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."},"quality_controlled":"1","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"conference":{"location":"Egham, United Kingdom","end_date":"2026-07-10","start_date":"2026-07-06","name":"PODC: Symposium on Principles of Distributed Computing"}},{"author":[{"last_name":"El-Hayek","id":"888a098e-fcac-11ee-aff7-d347be57b725","first_name":"Antoine","orcid":"0000-0003-4268-7368","full_name":"El-Hayek, Antoine"}],"article_processing_charge":"No","publisher":"Institute of Science and Technology Austria","year":"2026","doi_confirm":"1","project":[{"name":"The design and evaluation of modern fully dynamic data structures","call_identifier":"H2020","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","grant_number":"101019564"},{"name":"Static and Dynamic Hierarchical Graph Decompositions","grant_number":"I05982","_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103"},{"grant_number":"P33775","_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe","name":"Fast Algorithms for a Reactive Network Layer"}],"status":"public","doi":"10.15479/AT-ISTA-22281","department":[{"_id":"GradSch"},{"_id":"MoHe"}],"language":[{"iso":"eng"}],"title":"Handling updates and failures: Dynamic graph algorithms and distributed computing on dynamic networks","has_accepted_license":"1","month":"07","citation":{"ama":"El-Hayek A. Handling updates and failures: Dynamic graph algorithms and distributed computing on dynamic networks. 2026. doi:10.15479/AT-ISTA-22281","short":"A. El-Hayek, Handling Updates and Failures: Dynamic Graph Algorithms and Distributed Computing on Dynamic Networks, Institute of Science and Technology Austria, 2026.","mla":"El-Hayek, Antoine. Handling Updates and Failures: Dynamic Graph Algorithms and Distributed Computing on Dynamic Networks. Institute of Science and Technology Austria, 2026, doi:10.15479/AT-ISTA-22281.","chicago":"El-Hayek, Antoine. “Handling Updates and Failures: Dynamic Graph Algorithms and Distributed Computing on Dynamic Networks.” Institute of Science and Technology Austria, 2026. https://doi.org/10.15479/AT-ISTA-22281.","ieee":"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). Handling updates and failures: Dynamic graph algorithms and distributed computing on dynamic networks. Institute of Science and Technology Austria. https://doi.org/10.15479/AT-ISTA-22281","ista":"El-Hayek A. 2026. Handling updates and failures: Dynamic graph algorithms and distributed computing on dynamic networks. Institute of Science and Technology Austria."},"corr_author":"1","supervisor":[{"last_name":"Henzinger","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","first_name":"Monika H","orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H"}],"alternative_title":["ISTA Thesis"],"tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"type":"dissertation","page":"244","OA_place":"publisher","date_published":"2026-07-13T00:00:00Z","oa":1,"publication_status":"published","ec_funded":1,"related_material":{"record":[{"relation":"part_of_dissertation","id":"20051","status":"public"},{"id":"18557","relation":"part_of_dissertation","status":"public"},{"status":"public","id":"19982","relation":"part_of_dissertation"},{"status":"public","relation":"part_of_dissertation","id":"21720"},{"relation":"part_of_dissertation","id":"22374","status":"public"},{"status":"public","id":"22373","relation":"part_of_dissertation"}]},"degree_awarded":"PhD","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","date_updated":"2026-07-24T12:48:29Z","file":[{"relation":"main_file","file_name":"2026_El-Hayek_Antoine_Thesis.pdf","date_created":"2026-07-17T11:39:47Z","access_level":"open_access","checksum":"923e4ca769c9ef2f6b0b005444faf462","file_size":5465973,"creator":"aelhayek","file_id":"22356","content_type":"application/pdf","date_updated":"2026-07-17T11:39:47Z","success":1},{"file_size":9116107,"creator":"aelhayek","date_updated":"2026-07-20T11:29:38Z","content_type":"application/x-zip-compressed","file_id":"22357","date_created":"2026-07-17T11:40:34Z","relation":"source_file","file_name":"2026_El-Hayek_Antoine_Thesis.zip","access_level":"closed","checksum":"262689f9df27dd6c2c7c7861f1de7329"}],"file_date_updated":"2026-07-20T11:29:38Z","publisher_comment":"Sections 2.4 and 7.1 and chapter 6 are not CC-BY 4.0, they are All Rights Reserved.","_id":"22281","ddc":["000"],"date_created":"2026-07-13T09:39:59Z","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","abstract":[{"lang":"eng","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."}],"oa_version":"Published Version","day":"13","publication_identifier":{"issn":["2663-337X"]}},{"day":"07","publication_identifier":{"eissn":["1557-9468"],"issn":["1071-9040"],"eisbn":["9781611978971"]},"arxiv":1,"oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","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−𝑐𝑛) for any 𝑐 >0, improving on the previous algorithm of Jin, Sun, and Thorup (SODA 2024) whose minimum cut size limit is (log𝑛)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−𝑐𝑛), 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)."}],"external_id":{"arxiv":["2512.13105"]},"date_created":"2026-04-12T22:01:51Z","_id":"21720","date_updated":"2026-07-24T12:48:29Z","scopus_import":"1","ec_funded":1,"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"22281"}]},"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.","publication_status":"published","publication":"Proceedings of the Annual ACM SIAM Symposium on Discrete Algorithms","date_published":"2026-01-07T00:00:00Z","oa":1,"page":"613-663","type":"conference","OA_place":"repository","quality_controlled":"1","conference":{"location":"Vancouver, Canada","end_date":"2026-01-14","start_date":"2026-01-11","name":"SODA: Symposium on Discrete Algorithms"},"intvolume":" 2026","citation":{"ama":"El-Hayek A, Henzinger M, Li J. Deterministic and exact fully-dynamic minimum cut of superpolylogarithmic size in subpolynomial time. In: Proceedings of the Annual ACM SIAM Symposium on Discrete Algorithms. Vol 2026. Society for Industrial and Applied Mathematics; 2026:613-663. doi:10.1137/1.9781611978971.25","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.","mla":"El-Hayek, Antoine, et al. “Deterministic and Exact Fully-Dynamic Minimum Cut of Superpolylogarithmic Size in Subpolynomial Time.” Proceedings of the Annual ACM SIAM Symposium on Discrete Algorithms, vol. 2026, Society for Industrial and Applied Mathematics, 2026, pp. 613–63, doi:10.1137/1.9781611978971.25.","chicago":"El-Hayek, Antoine, Monika Henzinger, and Jason Li. “Deterministic and Exact Fully-Dynamic Minimum Cut of Superpolylogarithmic Size in Subpolynomial Time.” In Proceedings of the Annual ACM SIAM Symposium on Discrete Algorithms, 2026:613–63. Society for Industrial and Applied Mathematics, 2026. https://doi.org/10.1137/1.9781611978971.25.","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.","apa":"El-Hayek, A., Henzinger, M., & Li, J. (2026). Deterministic and exact fully-dynamic minimum cut of superpolylogarithmic size in subpolynomial time. In Proceedings of the Annual ACM SIAM Symposium on Discrete Algorithms (Vol. 2026, pp. 613–663). Vancouver, Canada: Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611978971.25","ieee":"A. El-Hayek, M. Henzinger, and J. Li, “Deterministic and exact fully-dynamic minimum cut of superpolylogarithmic size in subpolynomial time,” in Proceedings of the Annual ACM SIAM Symposium on Discrete Algorithms, Vancouver, Canada, 2026, vol. 2026, pp. 613–663."},"month":"01","title":"Deterministic and exact fully-dynamic minimum cut of superpolylogarithmic size in subpolynomial time","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2512.13105"}],"department":[{"_id":"MoHe"},{"_id":"GradSch"}],"doi":"10.1137/1.9781611978971.25","status":"public","project":[{"name":"The design and evaluation of modern fully dynamic data structures","call_identifier":"H2020","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","grant_number":"101019564"},{"name":"Static and Dynamic Hierarchical Graph Decompositions","grant_number":"I05982","_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103"}],"volume":2026,"publisher":"Society for Industrial and Applied Mathematics","year":"2026","OA_type":"green","article_processing_charge":"No","author":[{"last_name":"El-Hayek","full_name":"El-Hayek, Antoine","orcid":"0000-0003-4268-7368","first_name":"Antoine","id":"888a098e-fcac-11ee-aff7-d347be57b725"},{"last_name":"Henzinger","first_name":"Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H"},{"last_name":"Li","first_name":"Jason","full_name":"Li, Jason"}]},{"author":[{"last_name":"Chan","full_name":"Chan, Timothy M.","orcid":"0000-0002-8093-0675","first_name":"Timothy M."},{"orcid":"0000-0001-6714-7988","full_name":"Chang, Hsien-Chih","first_name":"Hsien-Chih","last_name":"Chang"},{"last_name":"Gao","full_name":"Gao, Jie","orcid":"0000-0001-5083-6082","first_name":"Jie"},{"last_name":"Kisfaludi-Bak","first_name":"Sándor","full_name":"Kisfaludi-Bak, Sándor","orcid":"0000-0002-6856-2902"},{"last_name":"Le","orcid":"0000-0001-8223-9944","full_name":"Le, Hung","first_name":"Hung"},{"full_name":"Zheng, Da Wei","id":"af77956b-e859-11ef-8dc9-d301b898e32f","first_name":"Da Wei","last_name":"Zheng"}],"article_processing_charge":"No","OA_type":"gold","volume":374,"project":[{"_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103","grant_number":"I05982","name":"Static and Dynamic Hierarchical Graph Decompositions"}],"year":"2026","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","das_tickbox":"0","keyword":["String graphs","Fine-grained complexity","Theory of computation → Computational geometry"],"has_accepted_license":"1","language":[{"iso":"eng"}],"title":"Charting the landscape of diameter computation on geometric intersection graphs in the plane","researchdata_availability":"no","month":"07","status":"public","department":[{"_id":"MoHe"}],"doi":"10.4230/LIPICS.ICALP.2026.54","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"conference":{"start_date":"2026-07-07","end_date":"2026-07-10","location":"Egham, United Kingdom","name":"ICALP: Automata, Languages and Programming"},"quality_controlled":"1","corr_author":"1","citation":{"ama":"Chan TM, Chang H-C, Gao J, Kisfaludi-Bak S, Le H, Zheng DW. Charting the landscape of diameter computation on geometric intersection graphs in the plane. In: 53rd International Colloquium on Automata, Languages, and Programming. Vol 374. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2026. doi:10.4230/LIPICS.ICALP.2026.54","short":"T.M. Chan, H.-C. Chang, J. Gao, S. Kisfaludi-Bak, H. Le, D.W. Zheng, in:, 53rd International Colloquium on Automata, Languages, and Programming, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026.","mla":"Chan, Timothy M., et al. “Charting the Landscape of Diameter Computation on Geometric Intersection Graphs in the Plane.” 53rd International Colloquium on Automata, Languages, and Programming, vol. 374, 54:1-54:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026, doi:10.4230/LIPICS.ICALP.2026.54.","chicago":"Chan, Timothy M., Hsien-Chih Chang, Jie Gao, Sándor Kisfaludi-Bak, Hung Le, and Da Wei Zheng. “Charting the Landscape of Diameter Computation on Geometric Intersection Graphs in the Plane.” In 53rd International Colloquium on Automata, Languages, and Programming, Vol. 374. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026. https://doi.org/10.4230/LIPICS.ICALP.2026.54.","ista":"Chan TM, Chang H-C, Gao J, Kisfaludi-Bak S, Le H, Zheng DW. 2026. Charting the landscape of diameter computation on geometric intersection graphs in the plane. 53rd International Colloquium on Automata, Languages, and Programming. ICALP: Automata, Languages and Programming vol. 374, 54:1-54:22.","ieee":"T. M. Chan, H.-C. Chang, J. Gao, S. Kisfaludi-Bak, H. Le, and D. W. Zheng, “Charting the landscape of diameter computation on geometric intersection graphs in the plane,” in 53rd International Colloquium on Automata, Languages, and Programming, Egham, United Kingdom, 2026, vol. 374.","apa":"Chan, T. M., Chang, H.-C., Gao, J., Kisfaludi-Bak, S., Le, H., & Zheng, D. W. (2026). Charting the landscape of diameter computation on geometric intersection graphs in the plane. In 53rd International Colloquium on Automata, Languages, and Programming (Vol. 374). Egham, United Kingdom: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.ICALP.2026.54"},"intvolume":" 374","article_number":"54:1-54:22","publication":"53rd International Colloquium on Automata, Languages, and Programming","publication_status":"published","OA_place":"publisher","type":"conference","oa":1,"date_published":"2026-07-01T00:00:00Z","file_date_updated":"2026-07-27T06:20:41Z","file":[{"content_type":"application/pdf","success":1,"date_updated":"2026-07-27T06:20:41Z","file_id":"22407","creator":"dernst","file_size":1440497,"access_level":"open_access","checksum":"1e66eba4cfe4e74ab28108b1ca0bb956","date_created":"2026-07-27T06:20:41Z","relation":"main_file","file_name":"2026_LIPIcSICALP_Chan.pdf"}],"date_updated":"2026-08-12T09:03:26Z","_id":"22405","acknowledgement":"Timothy M. Chan: Supported by NSF grant CCF-2224271.\r\nHsien-Chih Chang: Supported by NSF CAREER award CCF-2443017.\r\nJie Gao: Supported by NSF DMS-2220271, DMS-2311064, IIS-2229876, CCF-2118953, CNS-2515159.\r\nSándor Kisfaludi-Bak: Supported by the Research Council of Finland, Grant 363444.\r\nHung Le: Supported by an NSF grant CCF-2517033 and an NSF CAREER Award CCF-2237288.\r\nDa Wei Zheng: This project has received funding from the Austrian Science Fund (FWF) grant\r\nDOI 10.55776/I5982. 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.\r\n","scopus_import":"1","arxiv":1,"oa_version":"Published Version","publication_identifier":{"eissn":["1868-8969","9783959774284"]},"day":"01","date_created":"2026-07-27T05:53:08Z","external_id":{"arxiv":["2605.10692"]},"ddc":["000"],"supplementarymaterial":"no","abstract":[{"lang":"eng","text":"Computing the diameter of the intersection graphs of objects is a basic problem in computational geometry. Previous works showed that the complexity of computing the diameter mainly depends on the object types: for unit disks and squares in 2D, the problem is solvable in truly subquadratic time [Chan et al., 2025], while for other objects, including unit segments and equilateral triangles in 2D or unit balls and axis-parallel unit cubes in 3D, there is no truly subquadratic time algorithm under the Orthogonal Vector (OV) hypothesis [Bringmann et al., 2022]. \r\nWe undertake a comprehensive study of computing the diameter of geometric intersection graphs for various types of objects. We discover many new irregularities, showing that the landscape is extremely nuanced: the source of hardness is a combination of the object type, the true diameter value, and how the objects intersect with each other. Our highlighted results for the 2D case include: \r\n1) The diameter of non-degenerate, axis-aligned line segments can be computed in truly subquadratic time. Previous hardness result [Bringmann et al., 2022] for line segments applies only to degenerate instances. On the other hand, for the degenerate case, we show that a truly subquadratic time algorithm exists when the true diameter is constant. \r\n2) An almost-linear-time algorithm for unit-square graphs of constant diameter. Previous algorithms [Duraj et al., 2024; Chan et al., 2025] rely on succinct representation assuming bounded VC-dimension; for such a strategy Ω(n^{7/4}) time is an inherent barrier. \r\n3) An Õ(n^{4/3})-time algorithm to decide if the diameter of a unit-disk graph is at most 2. This improves upon the recent algorithm with running time Õ(n^{2-1/9}) [Chan et al., 2025]. \r\n4) Deciding if the diameter of intersection graphs of fat triangles or line segments is at most 2 is truly subquadratic-hard under fine-grained complexity assumptions. Previous lower bounds [Bringmann et al., 2022] only hold when deciding if diameter is at most 3. Our findings are presented in a pair of papers. This paper focuses solely on the 2D case, while the companion paper is devoted to higher-dimensional cases."}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"OA_type":"gold","article_processing_charge":"No","author":[{"last_name":"Goranci","first_name":"Gramoz","full_name":"Goranci, Gramoz"},{"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":"Räcke, Harald","first_name":"Harald","last_name":"Räcke"},{"last_name":"Sricharan","first_name":"A.","full_name":"Sricharan, A."}],"department":[{"_id":"MoHe"}],"doi":"10.4230/lipics.icalp.2025.91","status":"public","month":"06","title":"Incremental approximate maximum flow via residual graph sparsification","language":[{"iso":"eng"}],"has_accepted_license":"1","year":"2025","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","project":[{"call_identifier":"H2020","name":"The design and evaluation of modern fully dynamic data structures","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","grant_number":"101019564"},{"name":"Efficient algorithms","grant_number":"Z00422","_id":"34def286-11ca-11ed-8bc3-da5948e1613c"},{"grant_number":"I05982","_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103","name":"Static and Dynamic Hierarchical Graph Decompositions"},{"name":"Fast Algorithms for a Reactive Network Layer","_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe","grant_number":"P33775"}],"volume":334,"date_published":"2025-06-30T00:00:00Z","oa":1,"type":"conference","page":"91:1-91:20","OA_place":"publisher","publication_status":"published","publication":"52nd International Colloquium on Automata, Languages, and Programming","alternative_title":["LIPIcs"],"intvolume":" 334","citation":{"mla":"Goranci, Gramoz, et al. “Incremental Approximate Maximum Flow via Residual Graph Sparsification.” 52nd International Colloquium on Automata, Languages, and Programming, vol. 334, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025, p. 91:1-91:20, doi:10.4230/lipics.icalp.2025.91.","chicago":"Goranci, Gramoz, Monika Henzinger, Harald Räcke, and A. Sricharan. “Incremental Approximate Maximum Flow via Residual Graph Sparsification.” In 52nd International Colloquium on Automata, Languages, and Programming, 334:91:1-91:20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. https://doi.org/10.4230/lipics.icalp.2025.91.","apa":"Goranci, G., Henzinger, M., Räcke, H., & Sricharan, A. (2025). Incremental approximate maximum flow via residual graph sparsification. In 52nd International Colloquium on Automata, Languages, and Programming (Vol. 334, p. 91:1-91:20). Aarhus, Denmark: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/lipics.icalp.2025.91","ieee":"G. Goranci, M. Henzinger, H. Räcke, and A. Sricharan, “Incremental approximate maximum flow via residual graph sparsification,” in 52nd International Colloquium on Automata, Languages, and Programming, Aarhus, Denmark, 2025, vol. 334, p. 91:1-91:20.","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.","ama":"Goranci G, Henzinger M, Räcke H, Sricharan A. Incremental approximate maximum flow via residual graph sparsification. In: 52nd International Colloquium on Automata, Languages, and Programming. Vol 334. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2025:91:1-91:20. doi:10.4230/lipics.icalp.2025.91","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."},"corr_author":"1","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"conference":{"name":"ICALP: Automata, Languages and Programming","start_date":"2025-07-08","location":"Aarhus, Denmark","end_date":"2025-07-11"},"quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"text":"We give an algorithm that, with high probability, maintains a (1-ε)-approximate s-t maximum flow in undirected, uncapacitated n-vertex graphs undergoing m edge insertions in Õ(m+ n F^*/ε) total update time, where F^{*} is the maximum flow on the final graph. This is the first algorithm to achieve polylogarithmic amortized update time for dense graphs (m = Ω(n²)), and more generally, for graphs where F^* = Õ(m/n). At the heart of our incremental algorithm is the residual graph sparsification technique of Karger and Levine [SICOMP '15], originally designed for computing exact maximum flows in the static setting. Our main contributions are (i) showing how to maintain such sparsifiers for approximate maximum flows in the incremental setting and (ii) generalizing the cut sparsification framework of Fung et al. [SICOMP '19] from undirected graphs to balanced directed graphs.","lang":"eng"}],"ddc":["000"],"external_id":{"arxiv":["2502.09105"]},"date_created":"2026-02-17T08:26:06Z","publication_identifier":{"isbn":["9783959773720"]},"day":"30","oa_version":"Published Version","arxiv":1,"scopus_import":"1","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.","ec_funded":1,"_id":"21280","file":[{"content_type":"application/pdf","success":1,"date_updated":"2026-02-18T09:02:33Z","file_id":"21315","creator":"dernst","file_size":944824,"access_level":"open_access","checksum":"c178cf554e44204b9f64ebd9b54cf7ba","date_created":"2026-02-18T09:02:33Z","file_name":"2025_ICALP_Goranci.pdf","relation":"main_file"}],"file_date_updated":"2026-02-18T09:02:33Z","date_updated":"2026-02-18T09:06:12Z"},{"oa":1,"date_published":"2025-03-01T00:00:00Z","OA_place":"repository","type":"journal_article","page":"881-894","publication_status":"published","publication":"Mathematical Programming","intvolume":" 210","corr_author":"1","citation":{"mla":"Zheng, Da Wei, and Monika Henzinger. “Multiplicative Auction Algorithm for Approximate Maximum Weight Bipartite Matching.” Mathematical Programming, vol. 210, Springer Nature, 2025, pp. 881–94, doi:10.1007/s10107-024-02066-3.","ista":"Zheng DW, Henzinger M. 2025. Multiplicative auction algorithm for approximate maximum weight bipartite matching. Mathematical Programming. 210, 881–894.","ieee":"D. W. Zheng and M. Henzinger, “Multiplicative auction algorithm for approximate maximum weight bipartite matching,” Mathematical Programming, vol. 210. Springer Nature, pp. 881–894, 2025.","apa":"Zheng, D. W., & Henzinger, M. (2025). Multiplicative auction algorithm for approximate maximum weight bipartite matching. Mathematical Programming. Springer Nature. https://doi.org/10.1007/s10107-024-02066-3","chicago":"Zheng, Da Wei, and Monika Henzinger. “Multiplicative Auction Algorithm for Approximate Maximum Weight Bipartite Matching.” Mathematical Programming. Springer Nature, 2025. https://doi.org/10.1007/s10107-024-02066-3.","short":"D.W. Zheng, M. Henzinger, Mathematical Programming 210 (2025) 881–894.","ama":"Zheng DW, Henzinger M. Multiplicative auction algorithm for approximate maximum weight bipartite matching. Mathematical Programming. 2025;210:881-894. doi:10.1007/s10107-024-02066-3"},"isi":1,"quality_controlled":"1","abstract":[{"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.","lang":"eng"}],"article_type":"original","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"isi":["001176048100003"],"arxiv":["2301.09217"]},"date_created":"2024-03-17T23:00:58Z","day":"01","publication_identifier":{"issn":["0025-5610"],"eissn":["1436-4646"]},"oa_version":"Preprint","arxiv":1,"scopus_import":"1","related_material":{"record":[{"status":"public","id":"13236","relation":"earlier_version"}]},"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.","ec_funded":1,"_id":"15121","date_updated":"2025-09-09T12:39:58Z","OA_type":"green","article_processing_charge":"No","author":[{"first_name":"Da Wei","full_name":"Zheng, Da Wei","last_name":"Zheng"},{"last_name":"Henzinger","full_name":"Henzinger, Monika H","orcid":"0000-0002-5008-6530","first_name":"Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630"}],"department":[{"_id":"MoHe"}],"doi":"10.1007/s10107-024-02066-3","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2301.09217"}],"status":"public","month":"03","language":[{"iso":"eng"}],"title":"Multiplicative auction algorithm for approximate maximum weight bipartite matching","publisher":"Springer Nature","year":"2025","project":[{"grant_number":"101019564","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","name":"The design and evaluation of modern fully dynamic data structures","call_identifier":"H2020"},{"name":"Fast Algorithms for a Reactive Network Layer","grant_number":"P33775","_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe"}],"volume":210},{"author":[{"full_name":"Henzinger, Monika H","orcid":"0000-0002-5008-6530","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","first_name":"Monika H","last_name":"Henzinger"},{"first_name":"Jalaj","full_name":"Upadhyay, Jalaj","last_name":"Upadhyay"}],"article_processing_charge":"No","OA_type":"green","year":"2025","publisher":"Association for Computing Machinery","volume":5,"project":[{"grant_number":"101019564","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","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"},{"grant_number":"I05982","_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103","name":"Static and Dynamic Hierarchical Graph Decompositions"},{"_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe","grant_number":"P33775","name":"Fast Algorithms for a Reactive Network Layer"}],"status":"public","department":[{"_id":"MoHe"}],"doi":"10.1137/1.9781611978322.95","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2412.02840"}],"title":"Improved differentially private continual observation using group algebra","language":[{"iso":"eng"}],"month":"01","citation":{"apa":"Henzinger, M., & Upadhyay, J. (2025). Improved differentially private continual observation using group algebra. In Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms (Vol. 5, pp. 2951–2970). New Orleans, LA, United States: Association for Computing Machinery. https://doi.org/10.1137/1.9781611978322.95","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.","ieee":"M. Henzinger and J. Upadhyay, “Improved differentially private continual observation using group algebra,” in Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms, New Orleans, LA, United States, 2025, vol. 5, pp. 2951–2970.","chicago":"Henzinger, Monika, and Jalaj Upadhyay. “Improved Differentially Private Continual Observation Using Group Algebra.” In Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms, 5:2951–70. Association for Computing Machinery, 2025. https://doi.org/10.1137/1.9781611978322.95.","mla":"Henzinger, Monika, and Jalaj Upadhyay. “Improved Differentially Private Continual Observation Using Group Algebra.” Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 5, Association for Computing Machinery, 2025, pp. 2951–70, doi:10.1137/1.9781611978322.95.","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.","ama":"Henzinger M, Upadhyay J. Improved differentially private continual observation using group algebra. In: Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms. Vol 5. Association for Computing Machinery; 2025:2951-2970. doi:10.1137/1.9781611978322.95"},"intvolume":" 5","conference":{"name":"SODA: Symposium on Discrete Algorithms","start_date":"2025-01-12","location":"New Orleans, LA, United States","end_date":"2025-01-15"},"quality_controlled":"1","OA_place":"repository","page":"2951 - 2970","type":"conference","oa":1,"date_published":"2025-01-20T00:00:00Z","publication":"Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms","publication_status":"published","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.","ec_funded":1,"scopus_import":"1","date_updated":"2025-04-14T13:50:49Z","_id":"19038","date_created":"2025-02-17T09:31:03Z","external_id":{"arxiv":["2412.02840"]},"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."}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","arxiv":1,"day":"20","publication_identifier":{"issn":["1071-9040"],"isbn":["979-833131200-8"]}},{"doi":"10.4230/LIPIcs.SAND.2025.4","department":[{"_id":"MoHe"}],"status":"public","month":"06","has_accepted_license":"1","language":[{"iso":"eng"}],"title":"On b-matching and fully-dynamic maximum k-edge coloring","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","year":"2025","project":[{"name":"The design and evaluation of modern fully dynamic data structures","call_identifier":"H2020","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","grant_number":"101019564"},{"name":"Efficient algorithms","_id":"34def286-11ca-11ed-8bc3-da5948e1613c","grant_number":"Z00422"},{"_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103","grant_number":"I05982","name":"Static and Dynamic Hierarchical Graph Decompositions"},{"grant_number":"P33775","_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe","name":"Fast Algorithms for a Reactive Network Layer"}],"volume":330,"OA_type":"gold","article_processing_charge":"No","author":[{"last_name":"El-Hayek","orcid":"0000-0003-4268-7368","full_name":"El-Hayek, Antoine","id":"888a098e-fcac-11ee-aff7-d347be57b725","first_name":"Antoine"},{"last_name":"Hanauer","full_name":"Hanauer, Kathrin","first_name":"Kathrin"},{"id":"540c9bbd-f2de-11ec-812d-d04a5be85630","first_name":"Monika H","orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H","last_name":"Henzinger"}],"abstract":[{"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.","lang":"eng"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","external_id":{"arxiv":["2310.01149"],"isi":["001532136900004"]},"date_created":"2025-06-22T22:02:06Z","ddc":["000"],"day":"02","publication_identifier":{"isbn":["9783959773683"],"issn":["1868-8969"]},"arxiv":1,"oa_version":"Published Version","scopus_import":"1","ec_funded":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.","_id":"19858","date_updated":"2025-09-30T13:37:28Z","file":[{"creator":"dernst","file_size":995666,"file_id":"19872","date_updated":"2025-06-23T11:23:29Z","success":1,"content_type":"application/pdf","file_name":"2025_LIPIcs_ElHayek.pdf","relation":"main_file","date_created":"2025-06-23T11:23:29Z","access_level":"open_access","checksum":"ad93a1e052adb29d7bfe8bd551bab193"}],"file_date_updated":"2025-06-23T11:23:29Z","oa":1,"date_published":"2025-06-02T00:00:00Z","OA_place":"publisher","type":"conference","publication_status":"published","publication":"4th Symposium on Algorithmic Foundations of Dynamic Networks","article_number":"4","intvolume":" 330","alternative_title":["LIPIcs"],"corr_author":"1","isi":1,"citation":{"ama":"El-Hayek A, Hanauer K, Henzinger M. On b-matching and fully-dynamic maximum k-edge coloring. In: 4th Symposium on Algorithmic Foundations of Dynamic Networks. Vol 330. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2025. doi:10.4230/LIPIcs.SAND.2025.4","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.” 4th Symposium on Algorithmic Foundations of Dynamic Networks, vol. 330, 4, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025, doi:10.4230/LIPIcs.SAND.2025.4.","chicago":"El-Hayek, Antoine, Kathrin Hanauer, and Monika Henzinger. “On B-Matching and Fully-Dynamic Maximum k-Edge Coloring.” In 4th Symposium on Algorithmic Foundations of Dynamic Networks, Vol. 330. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. https://doi.org/10.4230/LIPIcs.SAND.2025.4.","ieee":"A. El-Hayek, K. Hanauer, and M. Henzinger, “On b-matching and fully-dynamic maximum k-edge coloring,” in 4th Symposium on Algorithmic Foundations of Dynamic Networks, Liverpool, United Kingdom, 2025, vol. 330.","apa":"El-Hayek, A., Hanauer, K., & Henzinger, M. (2025). On b-matching and fully-dynamic maximum k-edge coloring. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (Vol. 330). Liverpool, United Kingdom: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SAND.2025.4","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."},"tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"conference":{"name":"SAND: Symposium on Algorithmic Foundations of Dynamic Networks","location":"Liverpool, United Kingdom","end_date":"2025-06-11","start_date":"2025-06-09"},"quality_controlled":"1"},{"article_processing_charge":"No","author":[{"last_name":"Breitkopf","full_name":"Breitkopf, Tom-Lukas","first_name":"Tom-Lukas"},{"full_name":"Dallot, Julien","first_name":"Julien","last_name":"Dallot"},{"last_name":"El-Hayek","orcid":"0000-0003-4268-7368","full_name":"El-Hayek, Antoine","id":"888a098e-fcac-11ee-aff7-d347be57b725","first_name":"Antoine"},{"first_name":"Stefan","full_name":"Schmid, Stefan","last_name":"Schmid"}],"OA_type":"hybrid","project":[{"grant_number":"101019564","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","name":"The design and evaluation of modern fully dynamic data structures","call_identifier":"H2020"},{"name":"Static and Dynamic Hierarchical Graph Decompositions","_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103","grant_number":"I05982"},{"grant_number":"P33775","_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe","name":"Fast Algorithms for a Reactive Network Layer"}],"year":"2025","publisher":"Association for Computing Machinery","month":"06","has_accepted_license":"1","title":"Brief announcement: Minimizing energy solves relative majority with a cubic number of states in population protocols","language":[{"iso":"eng"}],"department":[{"_id":"MoHe"}],"doi":"10.1145/3732772.3733512","status":"public","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"quality_controlled":"1","conference":{"name":"PODC: Symposium on Principles of Distributed Computing","end_date":"2025-06-20","location":"Huatulco, Mexico","start_date":"2025-06-16"},"corr_author":"1","isi":1,"citation":{"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.","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: Proceedings of the ACM Symposium on Principles of Distributed Computing. Association for Computing Machinery; 2025:549-552. doi:10.1145/3732772.3733512","mla":"Breitkopf, Tom-Lukas, et al. “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, Association for Computing Machinery, 2025, pp. 549–52, doi:10.1145/3732772.3733512.","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.","apa":"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. In Proceedings of the ACM Symposium on Principles of Distributed Computing (pp. 549–552). Huatulco, Mexico: Association for Computing Machinery. https://doi.org/10.1145/3732772.3733512","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 Proceedings of the ACM Symposium on Principles of Distributed Computing, Huatulco, Mexico, 2025, pp. 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 Proceedings of the ACM Symposium on Principles of Distributed Computing, 549–52. Association for Computing Machinery, 2025. https://doi.org/10.1145/3732772.3733512."},"publication_status":"published","publication":"Proceedings of the ACM Symposium on Principles of Distributed Computing","oa":1,"date_published":"2025-06-13T00:00:00Z","OA_place":"publisher","page":"549-552","type":"conference","_id":"20052","date_updated":"2026-02-16T11:46:37Z","file":[{"file_id":"20123","content_type":"application/pdf","success":1,"date_updated":"2025-08-05T07:32:01Z","file_size":549706,"creator":"dernst","access_level":"open_access","checksum":"e99679ffb28877b7cea4d54860302790","relation":"main_file","file_name":"2025_PODC_Breitkopf.pdf","date_created":"2025-08-05T07:32:01Z"}],"file_date_updated":"2025-08-05T07:32:01Z","ec_funded":1,"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). ","publication_identifier":{"isbn":["9798400718854"]},"day":"13","oa_version":"Published Version","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"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"isi":["001525534800069"]},"date_created":"2025-07-21T08:17:04Z","ddc":["000"]},{"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2302.11341"}],"department":[{"_id":"MoHe"}],"status":"public","month":"05","title":"Differentially private continual release of histograms and related queries","language":[{"iso":"eng"}],"publisher":"ML Research Press","year":"2025","project":[{"grant_number":"101019564","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","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"},{"name":"Static and Dynamic Hierarchical Graph Decompositions","grant_number":"I05982","_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103"},{"_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe","grant_number":"P33775","name":"Fast Algorithms for a Reactive Network Layer"}],"volume":258,"OA_type":"green","article_processing_charge":"No","author":[{"full_name":"Henzinger, Monika H","orcid":"0000-0002-5008-6530","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","first_name":"Monika H","last_name":"Henzinger"},{"last_name":"Sricharan","full_name":"Sricharan, A. R.","first_name":"A. R."},{"last_name":"Steiner","full_name":"Steiner, Teresa Anna","first_name":"Teresa Anna"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"lang":"eng","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}). "}],"external_id":{"arxiv":["2302.11341"]},"date_created":"2025-09-07T22:01:35Z","publication_identifier":{"eissn":["2640-3498"]},"day":"01","oa_version":"Preprint","arxiv":1,"scopus_import":"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.","ec_funded":1,"_id":"20301","date_updated":"2025-09-09T07:09:22Z","date_published":"2025-05-01T00:00:00Z","oa":1,"page":"1990-1998","type":"conference","OA_place":"repository","publication_status":"published","publication":"The 28th International Conference on Artificial Intelligence and Statistics","alternative_title":["PMLR"],"intvolume":" 258","citation":{"ama":"Henzinger M, Sricharan AR, Steiner TA. Differentially private continual release of histograms and related queries. In: The 28th International Conference on Artificial Intelligence and Statistics. Vol 258. ML Research Press; 2025:1990-1998.","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.","chicago":"Henzinger, Monika, A. R. Sricharan, and Teresa Anna Steiner. “Differentially Private Continual Release of Histograms and Related Queries.” In The 28th International Conference on Artificial Intelligence and Statistics, 258:1990–98. ML Research Press, 2025.","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.","ieee":"M. Henzinger, A. R. Sricharan, and T. A. Steiner, “Differentially private continual release of histograms and related queries,” in The 28th International Conference on Artificial Intelligence and Statistics, Mai Khao, Thailand, 2025, vol. 258, pp. 1990–1998.","apa":"Henzinger, M., Sricharan, A. R., & Steiner, T. A. (2025). Differentially private continual release of histograms and related queries. In The 28th International Conference on Artificial Intelligence and Statistics (Vol. 258, pp. 1990–1998). Mai Khao, Thailand: ML Research Press.","mla":"Henzinger, Monika, et al. “Differentially Private Continual Release of Histograms and Related Queries.” The 28th International Conference on Artificial Intelligence and Statistics, vol. 258, ML Research Press, 2025, pp. 1990–98."},"conference":{"end_date":"2025-05-05","location":"Mai Khao, Thailand","start_date":"2025-05-03","name":"AISTATS: Conference on Artificial Intelligence and Statistics"},"quality_controlled":"1"}]