--- OA_place: publisher OA_type: gold _id: '22004' abstract: - lang: eng 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." 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." alternative_title: - LIPIcs article_number: 29:1-29:15 article_processing_charge: Yes arxiv: 1 author: - first_name: Timothy M. full_name: Chan, 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 - first_name: Sándor full_name: Kisfaludi-Bak, Sándor last_name: Kisfaludi-Bak - first_name: Hung full_name: Le, Hung last_name: Le - first_name: Da Wei full_name: Zheng, Da Wei id: af77956b-e859-11ef-8dc9-d301b898e32f last_name: Zheng citation: 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' 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' 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. 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. 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.' 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. 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. conference: end_date: 2026-06-05 location: New Brunswick, NJ, United States name: 'SoCG: Symposium on Computational Geometry' start_date: 2026-06-02 corr_author: '1' das_tickbox: '0' date_created: 2026-06-14T22:01:44Z date_published: 2026-05-27T00:00:00Z date_updated: 2026-06-22T08:37:44Z day: '27' ddc: - '000' department: - _id: MoHe doi: 10.4230/LIPIcs.SoCG.2026.29 external_id: arxiv: - '2603.21790' file: - access_level: open_access checksum: ffff03934cc182757d6db82d88f896e6 content_type: application/pdf creator: dernst date_created: 2026-06-22T08:34:11Z date_updated: 2026-06-22T08:34:11Z file_id: '22114' file_name: 2026_LIPIcSSoCG_Chan.pdf file_size: 918197 relation: main_file success: 1 file_date_updated: 2026-06-22T08:34:11Z has_accepted_license: '1' intvolume: ' 367' keyword: - Graph Diameter - Geometric Intersection Graphs - Unit Ball Graphs language: - iso: eng month: '05' oa: 1 oa_version: Published Version project: - _id: bda196b2-d553-11ed-ba76-8e8ee6c21103 grant_number: I05982 name: Static and Dynamic Hierarchical Graph Decompositions publication: 42nd International Symposium on Computational Geometry publication_identifier: eissn: - 1868-8969 isbn: - '9783959774185' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: '1' status: public title: Charting the diameter computation landscape of intersection graphs in 3D and above tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 367 year: '2026' ... --- OA_place: publisher OA_type: hybrid PlanS_conform: '1' _id: '21159' 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." 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). article_number: '5' article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Matthew Alan full_name: Kwan, Matthew Alan id: 5fca0887-a1db-11eb-95d1-ca9d5e0453b3 last_name: Kwan orcid: 0000-0002-4003-7567 - first_name: Roodabeh full_name: Safavi Hemami, Roodabeh id: 72ed2640-8972-11ed-ae7b-f9c81ec75154 last_name: Safavi Hemami - first_name: Yiting full_name: Wang, Yiting id: 1917d194-076e-11ed-97cd-837255f88785 last_name: Wang orcid: 0000-0002-2856-767X 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 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 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. 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. short: M.A. Kwan, R. Safavi Hemami, Y. Wang, Combinatorica 46 (2026). corr_author: '1' date_created: 2026-02-08T23:02:49Z date_published: 2026-02-01T00:00:00Z date_updated: 2026-02-16T09:55:17Z day: '01' ddc: - '510' department: - _id: MaKw - _id: MoHe doi: 10.1007/s00493-025-00194-8 external_id: arxiv: - '2408.09589' file: - access_level: open_access checksum: 47b0031d90b0e6b9a843f422a1486089 content_type: application/pdf creator: dernst date_created: 2026-02-16T09:52:38Z date_updated: 2026-02-16T09:52:38Z file_id: '21228' file_name: 2026_Combinatorica_Kwan.pdf file_size: 539646 relation: main_file success: 1 file_date_updated: 2026-02-16T09:52:38Z has_accepted_license: '1' intvolume: ' 46' language: - iso: eng month: '02' oa: 1 oa_version: Published Version publication: Combinatorica publication_identifier: eissn: - 1439-6912 issn: - 0209-9683 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Counting perfect matchings in Dirac hypergraphs tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 46 year: '2026' ... --- OA_place: repository OA_type: green _id: '21719' 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 \U0001D457-tree decomposition of [Madry FOCS’10], achieving a poly-logarithmic approximation factor to the graph’s cut structure and supporting edge updates in \U0001D442⁡(\U0001D45B\U0001D700) amortized update time, for any arbitrarily small constant \U0001D700 ∈(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." 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." article_processing_charge: No arxiv: 1 author: - first_name: Gramoz full_name: Goranci, Gramoz last_name: Goranci - first_name: Monika H full_name: Henzinger, Monika H id: 540c9bbd-f2de-11ec-812d-d04a5be85630 last_name: Henzinger orcid: 0000-0002-5008-6530 - first_name: Peter full_name: Kiss, Peter last_name: Kiss - first_name: Ali full_name: Momeni, Ali last_name: Momeni - first_name: Gernot full_name: Zöcklein, Gernot id: 45d5e826-47af-11f1-84e5-ba87c23fe681 last_name: Zöcklein 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' 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 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.' 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. 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. conference: name: 'SODA: Symposium on Discrete Algorithms' date_created: 2026-04-12T22:01:51Z date_published: 2026-01-07T00:00:00Z date_updated: 2026-05-04T11:54:09Z day: '07' department: - _id: MoHe doi: 10.1137/1.9781611978971.45 ec_funded: 1 external_id: arxiv: - '2601.09139' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2601.09139 month: '01' oa: 1 oa_version: Preprint page: 1128-1180 project: - _id: bd9ca328-d553-11ed-ba76-dc4f890cfe62 call_identifier: H2020 grant_number: '101019564' 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 publication: Proceedings of the 2026 Annual ACM SIAM Symposium on Discrete Algorithms publication_identifier: eissn: - '15579468' isbn: - '9781611978971' issn: - '10719040' publication_status: published publisher: Society for Industrial and Applied Mathematics quality_controlled: '1' scopus_import: '1' status: public title: Dynamic hierarchical j-tree decomposition and its applications type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 2026-January year: '2026' ... --- OA_place: repository OA_type: green _id: '21720' abstract: - lang: eng text: "We present an exact fully-dynamic minimum cut algorithm that runs in \U0001D45B\U0001D45C⁡(1) deterministic update time when the minimum cut size is at most 2Θ⁡(log3/4−\U0001D450⁡\U0001D45B) for any \U0001D450 >0, improving on the previous algorithm of Jin, Sun, and Thorup (SODA 2024) whose minimum cut size limit is (log⁡\U0001D45B)\U0001D45C⁡(1). Combined with graph sparsification, we obtain the first (1 +\U0001D716)-approximate fully-dynamic minimum cut algorithm on weighted graphs, for any \U0001D716 ≥2−Θ⁡(log3/4−\U0001D450⁡\U0001D45B), in \U0001D45B\U0001D45C⁡(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)." 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. article_processing_charge: No arxiv: 1 author: - first_name: Antoine full_name: El-Hayek, Antoine id: 888a098e-fcac-11ee-aff7-d347be57b725 last_name: El-Hayek orcid: 0000-0003-4268-7368 - first_name: Monika H full_name: Henzinger, Monika H id: 540c9bbd-f2de-11ec-812d-d04a5be85630 last_name: Henzinger orcid: 0000-0002-5008-6530 - first_name: Jason full_name: Li, Jason last_name: Li 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' 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' 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. 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. 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.' 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. 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. conference: end_date: 2026-01-14 location: Vancouver, Canada name: 'SODA: Symposium on Discrete Algorithms' start_date: 2026-01-11 date_created: 2026-04-12T22:01:51Z date_published: 2026-01-07T00:00:00Z date_updated: 2026-05-04T11:36:47Z day: '07' department: - _id: MoHe - _id: GradSch doi: 10.1137/1.9781611978971.25 ec_funded: 1 external_id: arxiv: - '2512.13105' intvolume: ' 2026' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2512.13105 month: '01' oa: 1 oa_version: Preprint page: 613-663 project: - _id: bd9ca328-d553-11ed-ba76-dc4f890cfe62 call_identifier: H2020 grant_number: '101019564' 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 publication: Proceedings of the Annual ACM SIAM Symposium on Discrete Algorithms publication_identifier: eisbn: - '9781611978971' eissn: - 1557-9468 issn: - 1071-9040 publication_status: published publisher: Society for Industrial and Applied Mathematics quality_controlled: '1' scopus_import: '1' status: public title: Deterministic and exact fully-dynamic minimum cut of superpolylogarithmic size in subpolynomial time type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 2026 year: '2026' ... --- OA_place: publisher OA_type: gold _id: '21280' abstract: - lang: eng 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. 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." alternative_title: - LIPIcs article_processing_charge: No arxiv: 1 author: - first_name: Gramoz full_name: Goranci, Gramoz last_name: Goranci - first_name: Monika H full_name: Henzinger, Monika H id: 540c9bbd-f2de-11ec-812d-d04a5be85630 last_name: Henzinger orcid: 0000-0002-5008-6530 - first_name: Harald full_name: Räcke, Harald last_name: Räcke - first_name: A. full_name: Sricharan, A. last_name: Sricharan citation: 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' 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' 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. 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.' 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. 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. conference: end_date: 2025-07-11 location: Aarhus, Denmark name: 'ICALP: Automata, Languages and Programming' start_date: 2025-07-08 corr_author: '1' date_created: 2026-02-17T08:26:06Z date_published: 2025-06-30T00:00:00Z date_updated: 2026-02-18T09:06:12Z day: '30' ddc: - '000' department: - _id: MoHe doi: 10.4230/lipics.icalp.2025.91 ec_funded: 1 external_id: arxiv: - '2502.09105' file: - access_level: open_access checksum: c178cf554e44204b9f64ebd9b54cf7ba content_type: application/pdf creator: dernst date_created: 2026-02-18T09:02:33Z date_updated: 2026-02-18T09:02:33Z file_id: '21315' file_name: 2025_ICALP_Goranci.pdf file_size: 944824 relation: main_file success: 1 file_date_updated: 2026-02-18T09:02:33Z has_accepted_license: '1' intvolume: ' 334' language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 91:1-91:20 project: - _id: bd9ca328-d553-11ed-ba76-dc4f890cfe62 call_identifier: H2020 grant_number: '101019564' name: The design and evaluation of modern fully dynamic data structures - _id: 34def286-11ca-11ed-8bc3-da5948e1613c grant_number: Z00422 name: Efficient algorithms - _id: bda196b2-d553-11ed-ba76-8e8ee6c21103 grant_number: I05982 name: Static and Dynamic Hierarchical Graph Decompositions - _id: bd9e3a2e-d553-11ed-ba76-8aa684ce17fe grant_number: P33775 name: Fast Algorithms for a Reactive Network Layer publication: 52nd International Colloquium on Automata, Languages, and Programming publication_identifier: isbn: - '9783959773720' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: '1' status: public title: Incremental approximate maximum flow via residual graph sparsification tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 334 year: '2025' ... --- OA_place: repository OA_type: green _id: '15121' abstract: - lang: eng text: We present an auction algorithm using multiplicative instead of constant weight updates to compute a (1-E)-approximate maximum weight matching (MWM) in a bipartite graph with n vertices and m edges in time 0(mE-1), beating the running time of the fastest known approximation algorithm of Duan and Pettie [JACM ’14] that runs in 0(mE-1 log E-1). Our algorithm is very simple and it can be extended to give a dynamic data structure that maintains a (1-E)-approximate maximum weight matching under (1) one-sided vertex deletions (with incident edges) and (2) one-sided vertex insertions (with incident edges sorted by weight) to the other side. The total time time used is 0(mE-1), where m is the sum of the number of initially existing and inserted edges. 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. article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Da Wei full_name: Zheng, Da Wei last_name: Zheng - first_name: Monika H full_name: Henzinger, Monika H id: 540c9bbd-f2de-11ec-812d-d04a5be85630 last_name: Henzinger orcid: 0000-0002-5008-6530 citation: 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 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. 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. ista: Zheng DW, Henzinger M. 2025. Multiplicative auction algorithm for approximate maximum weight bipartite matching. Mathematical Programming. 210, 881–894. 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. short: D.W. Zheng, M. Henzinger, Mathematical Programming 210 (2025) 881–894. corr_author: '1' date_created: 2024-03-17T23:00:58Z date_published: 2025-03-01T00:00:00Z date_updated: 2025-09-09T12:39:58Z day: '01' department: - _id: MoHe doi: 10.1007/s10107-024-02066-3 ec_funded: 1 external_id: arxiv: - '2301.09217' isi: - '001176048100003' intvolume: ' 210' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2301.09217 month: '03' oa: 1 oa_version: Preprint page: 881-894 project: - _id: bd9ca328-d553-11ed-ba76-dc4f890cfe62 call_identifier: H2020 grant_number: '101019564' name: The design and evaluation of modern fully dynamic data structures - _id: bd9e3a2e-d553-11ed-ba76-8aa684ce17fe grant_number: P33775 name: Fast Algorithms for a Reactive Network Layer publication: Mathematical Programming publication_identifier: eissn: - 1436-4646 issn: - 0025-5610 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '13236' relation: earlier_version status: public scopus_import: '1' status: public title: Multiplicative auction algorithm for approximate maximum weight bipartite matching type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 210 year: '2025' ... --- OA_place: repository OA_type: green _id: '19038' 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. 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.' article_processing_charge: No arxiv: 1 author: - first_name: Monika H full_name: Henzinger, Monika H id: 540c9bbd-f2de-11ec-812d-d04a5be85630 last_name: Henzinger orcid: 0000-0002-5008-6530 - first_name: Jalaj full_name: Upadhyay, Jalaj last_name: Upadhyay citation: 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' 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' 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. 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. 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.' 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. conference: end_date: 2025-01-15 location: New Orleans, LA, United States name: 'SODA: Symposium on Discrete Algorithms' start_date: 2025-01-12 date_created: 2025-02-17T09:31:03Z date_published: 2025-01-20T00:00:00Z date_updated: 2025-04-14T13:50:49Z day: '20' department: - _id: MoHe doi: 10.1137/1.9781611978322.95 ec_funded: 1 external_id: arxiv: - '2412.02840' intvolume: ' 5' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2412.02840 month: '01' oa: 1 oa_version: Preprint page: 2951 - 2970 project: - _id: bd9ca328-d553-11ed-ba76-dc4f890cfe62 call_identifier: H2020 grant_number: '101019564' name: The design and evaluation of modern fully dynamic data structures - _id: 34def286-11ca-11ed-8bc3-da5948e1613c grant_number: Z00422 name: Efficient algorithms - _id: bda196b2-d553-11ed-ba76-8e8ee6c21103 grant_number: I05982 name: Static and Dynamic Hierarchical Graph Decompositions - _id: bd9e3a2e-d553-11ed-ba76-8aa684ce17fe grant_number: P33775 name: Fast Algorithms for a Reactive Network Layer publication: Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms publication_identifier: isbn: - 979-833131200-8 issn: - 1071-9040 publication_status: published publisher: Association for Computing Machinery quality_controlled: '1' scopus_import: '1' status: public title: Improved differentially private continual observation using group algebra type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 5 year: '2025' ... --- OA_place: publisher OA_type: gold _id: '19858' abstract: - lang: eng text: "Given a graph G that undergoes a sequence of edge insertions and deletions, we study the Maximum k-Edge Coloring problem (MkEC): Having access to k different colors, color as many edges of G as possible such that no two adjacent edges share the same color. While this problem is different from simply maintaining a b-matching with b = k, the two problems are related. However, maximum b-matching can be solved efficiently in the static setting, whereas MkEC is NP-hard and even APX-hard for k ≥ 2. \r\nWe present new results on both problems: For b-matching, we show a new integrality gap result and we adapt Wajc’s matching sparsification scheme [David Wajc, 2020] for the case where b is a constant.\r\nUsing these as basis, we give three new algorithms for the dynamic MkEC problem: Our MatchO algorithm builds on the dynamic (2+ε)-approximation algorithm of Bhattacharya, Gupta, and Mohan [Sayan Bhattacharya et al., 2017] for b-matching and achieves a (2+ε)(k+1)/k-approximation in O(poly(log n, ε^-1)) update time against an oblivious adversary. Our MatchA algorithm builds on the dynamic (7+ε)-approximation algorithm by Bhattacharya, Henzinger, and Italiano [Sayan Bhattacharya et al., 2015] for fractional b-matching and achieves a (7+ε)(3k+3)/(3k-1)-approximation in O(poly(log n, ε^-1)) update time against an adaptive adversary. Moreover, our reductions use the dynamic b-matching algorithm as a black box, so any future improvement in the approximation ratio for dynamic b-matching will automatically translate into a better approximation ratio for our algorithms. Finally, we present a greedy algorithm with O(Δ+k) update time, which guarantees a 2.16 approximation factor." 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." alternative_title: - LIPIcs article_number: '4' article_processing_charge: No arxiv: 1 author: - first_name: Antoine full_name: El-Hayek, Antoine id: 888a098e-fcac-11ee-aff7-d347be57b725 last_name: El-Hayek orcid: 0000-0003-4268-7368 - first_name: Kathrin full_name: Hanauer, Kathrin last_name: Hanauer - first_name: Monika H full_name: Henzinger, Monika H id: 540c9bbd-f2de-11ec-812d-d04a5be85630 last_name: Henzinger orcid: 0000-0002-5008-6530 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' 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' 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. 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.' 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. short: A. El-Hayek, K. Hanauer, M. Henzinger, in:, 4th Symposium on Algorithmic Foundations of Dynamic Networks, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. conference: end_date: 2025-06-11 location: Liverpool, United Kingdom name: 'SAND: Symposium on Algorithmic Foundations of Dynamic Networks' start_date: 2025-06-09 corr_author: '1' date_created: 2025-06-22T22:02:06Z date_published: 2025-06-02T00:00:00Z date_updated: 2025-09-30T13:37:28Z day: '02' ddc: - '000' department: - _id: MoHe doi: 10.4230/LIPIcs.SAND.2025.4 ec_funded: 1 external_id: arxiv: - '2310.01149' isi: - '001532136900004' file: - access_level: open_access checksum: ad93a1e052adb29d7bfe8bd551bab193 content_type: application/pdf creator: dernst date_created: 2025-06-23T11:23:29Z date_updated: 2025-06-23T11:23:29Z file_id: '19872' file_name: 2025_LIPIcs_ElHayek.pdf file_size: 995666 relation: main_file success: 1 file_date_updated: 2025-06-23T11:23:29Z has_accepted_license: '1' intvolume: ' 330' isi: 1 language: - iso: eng month: '06' oa: 1 oa_version: Published Version project: - _id: bd9ca328-d553-11ed-ba76-dc4f890cfe62 call_identifier: H2020 grant_number: '101019564' name: The design and evaluation of modern fully dynamic data structures - _id: 34def286-11ca-11ed-8bc3-da5948e1613c grant_number: Z00422 name: Efficient algorithms - _id: bda196b2-d553-11ed-ba76-8e8ee6c21103 grant_number: I05982 name: Static and Dynamic Hierarchical Graph Decompositions - _id: bd9e3a2e-d553-11ed-ba76-8aa684ce17fe grant_number: P33775 name: Fast Algorithms for a Reactive Network Layer publication: 4th Symposium on Algorithmic Foundations of Dynamic Networks publication_identifier: isbn: - '9783959773683' issn: - 1868-8969 publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: '1' status: public title: On b-matching and fully-dynamic maximum k-edge coloring tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 330 year: '2025' ... --- OA_place: repository OA_type: green _id: '19982' abstract: - lang: eng text: "Dynamically maintaining the minimum cut in a graph G under edge insertions and deletion is a fundamental problem in dynamic graph algorithms for which no conditional lower bound on the time per operation exists. In an n-node graph the best known (1 + o (1))-approximate algorithm takes update time [14]. If the minimum cut is guaranteed to be (log n )o (1), a deterministic exact algorithm with n o (1) update time exists [8].\r\nWe present the first fully dynamic algorithm for (1 + o (1))-approximate minimum cut with n o(1) update time. Our main technical contribution is to show that it suffices to consider small-volume cuts in suitably contracted graphs." acknowledgement: This project has received funding from the European Research Council (ERC) under the European Union’sHorizon 2020 research and innovation programme (MoDynStruct, No. 101019564) and the Austrian Science Fund(FWF) grant DOI 10.55776/Z422, grant DOI 10.55776/I5982, and grant DOI 10.55776/P33775 with additional funding from the netidee SCIENCE Stiftung, 2020–2024. article_processing_charge: No arxiv: 1 author: - first_name: Antoine full_name: El-Hayek, Antoine id: 888a098e-fcac-11ee-aff7-d347be57b725 last_name: El-Hayek orcid: 0000-0003-4268-7368 - first_name: Monika H full_name: Henzinger, Monika H id: 540c9bbd-f2de-11ec-812d-d04a5be85630 last_name: Henzinger orcid: 0000-0002-5008-6530 - first_name: Jason full_name: Li, Jason last_name: Li citation: ama: 'El-Hayek A, Henzinger M, Li J. Fully dynamic approximate minimum cut in subpolynomial time per operation. In: Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms. Society for Industrial and Applied Mathematics; 2025:750-784. doi:10.1137/1.9781611978322.22' apa: 'El-Hayek, A., Henzinger, M., & Li, J. (2025). Fully dynamic approximate minimum cut in subpolynomial time per operation. In Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 750–784). New Orleans, LA, United States: Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611978322.22' chicago: El-Hayek, Antoine, Monika Henzinger, and Jason Li. “Fully Dynamic Approximate Minimum Cut in Subpolynomial Time per Operation.” In Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms, 750–84. Society for Industrial and Applied Mathematics, 2025. https://doi.org/10.1137/1.9781611978322.22. ieee: A. El-Hayek, M. Henzinger, and J. Li, “Fully dynamic approximate minimum cut in subpolynomial time per operation,” in Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms, New Orleans, LA, United States, 2025, pp. 750–784. ista: 'El-Hayek A, Henzinger M, Li J. 2025. Fully dynamic approximate minimum cut in subpolynomial time per operation. Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms, 750–784.' mla: El-Hayek, Antoine, et al. “Fully Dynamic Approximate Minimum Cut in Subpolynomial Time per Operation.” Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, 2025, pp. 750–84, doi:10.1137/1.9781611978322.22. short: A. El-Hayek, M. Henzinger, J. Li, in:, Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, 2025, pp. 750–784. conference: end_date: 2025-01-15 location: New Orleans, LA, United States name: 'SODA: Symposium on Discrete Algorithms' start_date: 2025-01-12 corr_author: '1' date_created: 2025-07-10T13:08:57Z date_published: 2025-01-07T00:00:00Z date_updated: 2025-12-29T12:30:04Z day: '07' department: - _id: MoHe doi: 10.1137/1.9781611978322.22 ec_funded: 1 external_id: arxiv: - '2412.15069' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2412.15069 month: '01' oa: 1 oa_version: Preprint page: 750-784 project: - _id: bd9ca328-d553-11ed-ba76-dc4f890cfe62 call_identifier: H2020 grant_number: '101019564' name: The design and evaluation of modern fully dynamic data structures - _id: 34def286-11ca-11ed-8bc3-da5948e1613c grant_number: Z00422 name: Efficient algorithms - _id: bda196b2-d553-11ed-ba76-8e8ee6c21103 grant_number: I05982 name: Static and Dynamic Hierarchical Graph Decompositions - _id: bd9e3a2e-d553-11ed-ba76-8aa684ce17fe grant_number: P33775 name: Fast Algorithms for a Reactive Network Layer publication: Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms publication_identifier: eisbn: - '9781611978322' publication_status: published publisher: Society for Industrial and Applied Mathematics quality_controlled: '1' status: public title: Fully dynamic approximate minimum cut in subpolynomial time per operation type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2025' ... --- OA_place: publisher OA_type: hybrid _id: '20051' abstract: - lang: eng text: "We revisit the majority problem in the population protocol communication model, as first studied by Angluin et al. (Distributed Computing 2008). We consider a more general version of this problem known as plurality consensus, which has already been studied intensively in the literature. In this problem, each node in a system of n nodes, has initially one of k different opinions, and they need to agree on the (relative) majority opinion. In particular, we consider the important and intensively studied model of Undecided State Dynamics.\r\nOur main contribution is an almost tight lower bound on the stabilization time: we prove that there exists an initial configuration, even with bias \\Delta = \\omega(\\sqrt{n\\log n}), where stabilization requires \\Omega(kn\\log \\frac {\\sqrt n} {k \\log n}) interactions, or equivalently, \\Omega(k\\log \\frac {\\sqrt n} {k \\log n}) parallel time for any k = o\\left(\\frac {\\sqrt n}{\\log n}\\right). This bound is tight for any k \\le n^{\\frac 1 2 - \\epsilon}, where \\epsilon >0 can be any small constant, as Amir et al.~(PODC'23) gave a O(k\\log n) parallel time upper bound for k = O\\left(\\frac {\\sqrt n} {\\log ^2 n}\\right)." acknowledgement: "This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (MoDynStruct, No. 101019564) and the Austrian Science Fund (FWF) grant DOI 10.55776/I5862,grant DOI 10.55776/I5982, and grant DOI 10.55776/P33775 with\r\nadditional funding from the netidee SCIENCE Stiftung, 2020–2024\r\nand the German Research Foundation (DFG), grant 470029389\r\n(FlexNets)." article_processing_charge: Yes (via OA deal) arxiv: 1 author: - first_name: Antoine full_name: El-Hayek, Antoine id: 888a098e-fcac-11ee-aff7-d347be57b725 last_name: El-Hayek orcid: 0000-0003-4268-7368 - first_name: Robert full_name: Elsässer, Robert last_name: Elsässer - first_name: Stefan full_name: Schmid, Stefan last_name: Schmid citation: ama: 'El-Hayek A, Elsässer R, Schmid S. An almost tight lower bound for plurality consensus with undecided state dynamics in the population protocol model. In: Proceedings of the ACM Symposium on Principles of Distributed Computing. Association for Computing Machinery; 2025. doi:10.1145/3732772.3733505' apa: 'El-Hayek, A., Elsässer, R., & Schmid, S. (2025). An almost tight lower bound for plurality consensus with undecided state dynamics in the population protocol model. In Proceedings of the ACM Symposium on Principles of Distributed Computing. Huatulco, Mexico: Association for Computing Machinery. https://doi.org/10.1145/3732772.3733505' chicago: El-Hayek, Antoine, Robert Elsässer, and Stefan Schmid. “An Almost Tight Lower Bound for Plurality Consensus with Undecided State Dynamics in the Population Protocol Model.” In Proceedings of the ACM Symposium on Principles of Distributed Computing. Association for Computing Machinery, 2025. https://doi.org/10.1145/3732772.3733505. ieee: A. El-Hayek, R. Elsässer, and S. Schmid, “An almost tight lower bound for plurality consensus with undecided state dynamics in the population protocol model,” in Proceedings of the ACM Symposium on Principles of Distributed Computing, Huatulco, Mexico, 2025. ista: 'El-Hayek A, Elsässer R, Schmid S. 2025. An almost tight lower bound for plurality consensus with undecided state dynamics in the population protocol model. Proceedings of the ACM Symposium on Principles of Distributed Computing. PODC: Symposium on Principles of Distributed Computing.' mla: El-Hayek, Antoine, et al. “An Almost Tight Lower Bound for Plurality Consensus with Undecided State Dynamics in the Population Protocol Model.” Proceedings of the ACM Symposium on Principles of Distributed Computing, Association for Computing Machinery, 2025, doi:10.1145/3732772.3733505. short: A. El-Hayek, R. Elsässer, S. Schmid, in:, Proceedings of the ACM Symposium on Principles of Distributed Computing, Association for Computing Machinery, 2025. conference: end_date: 2025-06-20 location: Huatulco, Mexico name: 'PODC: Symposium on Principles of Distributed Computing' start_date: 2025-06-16 corr_author: '1' date_created: 2025-07-21T08:16:15Z date_published: 2025-06-13T00:00:00Z date_updated: 2025-10-16T13:08:45Z day: '13' ddc: - '000' department: - _id: MoHe doi: 10.1145/3732772.3733505 ec_funded: 1 external_id: arxiv: - '2505.02765' isi: - '001525534800066' file: - access_level: open_access checksum: 52976d226f3f691aa519d71c1c718fa5 content_type: application/pdf creator: dernst date_created: 2025-08-04T09:10:55Z date_updated: 2025-08-04T09:10:55Z file_id: '20115' file_name: 2025_PODC_ElHayek.pdf file_size: 2200347 relation: main_file success: 1 file_date_updated: 2025-08-04T09:10:55Z has_accepted_license: '1' isi: 1 language: - iso: eng month: '06' oa: 1 oa_version: Published Version project: - _id: bd9ca328-d553-11ed-ba76-dc4f890cfe62 call_identifier: H2020 grant_number: '101019564' 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 - _id: bd9e3a2e-d553-11ed-ba76-8aa684ce17fe grant_number: P33775 name: Fast Algorithms for a Reactive Network Layer publication: Proceedings of the ACM Symposium on Principles of Distributed Computing publication_identifier: isbn: - ' 9798400718854' publication_status: published publisher: Association for Computing Machinery quality_controlled: '1' status: public title: An almost tight lower bound for plurality consensus with undecided state dynamics in the population protocol model tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2025' ... --- OA_place: publisher OA_type: hybrid _id: '20052' abstract: - lang: eng 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." 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). ' article_processing_charge: No author: - first_name: Tom-Lukas full_name: Breitkopf, Tom-Lukas last_name: Breitkopf - first_name: Julien full_name: Dallot, Julien last_name: Dallot - first_name: Antoine full_name: El-Hayek, Antoine id: 888a098e-fcac-11ee-aff7-d347be57b725 last_name: El-Hayek orcid: 0000-0003-4268-7368 - first_name: Stefan full_name: Schmid, Stefan last_name: Schmid citation: 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' 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' 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.' 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.' 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.' 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.' 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. conference: end_date: 2025-06-20 location: Huatulco, Mexico name: 'PODC: Symposium on Principles of Distributed Computing' start_date: 2025-06-16 corr_author: '1' date_created: 2025-07-21T08:17:04Z date_published: 2025-06-13T00:00:00Z date_updated: 2026-02-16T11:46:37Z day: '13' ddc: - '000' department: - _id: MoHe doi: 10.1145/3732772.3733512 ec_funded: 1 external_id: isi: - '001525534800069' file: - access_level: open_access checksum: e99679ffb28877b7cea4d54860302790 content_type: application/pdf creator: dernst date_created: 2025-08-05T07:32:01Z date_updated: 2025-08-05T07:32:01Z file_id: '20123' file_name: 2025_PODC_Breitkopf.pdf file_size: 549706 relation: main_file success: 1 file_date_updated: 2025-08-05T07:32:01Z has_accepted_license: '1' isi: 1 language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 549-552 project: - _id: bd9ca328-d553-11ed-ba76-dc4f890cfe62 call_identifier: H2020 grant_number: '101019564' 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 - _id: bd9e3a2e-d553-11ed-ba76-8aa684ce17fe grant_number: P33775 name: Fast Algorithms for a Reactive Network Layer publication: Proceedings of the ACM Symposium on Principles of Distributed Computing publication_identifier: isbn: - '9798400718854' publication_status: published publisher: Association for Computing Machinery quality_controlled: '1' status: public title: 'Brief announcement: Minimizing energy solves relative majority with a cubic number of states in population protocols' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2025' ... --- OA_place: repository OA_type: green _id: '20301' 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}). " 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." alternative_title: - PMLR article_processing_charge: No arxiv: 1 author: - first_name: Monika H full_name: Henzinger, Monika H id: 540c9bbd-f2de-11ec-812d-d04a5be85630 last_name: Henzinger orcid: 0000-0002-5008-6530 - first_name: A. R. full_name: Sricharan, A. R. last_name: Sricharan - first_name: Teresa Anna full_name: Steiner, Teresa Anna last_name: Steiner 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.' 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.' 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. 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. 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.' 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. 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. conference: end_date: 2025-05-05 location: Mai Khao, Thailand name: 'AISTATS: Conference on Artificial Intelligence and Statistics' start_date: 2025-05-03 date_created: 2025-09-07T22:01:35Z date_published: 2025-05-01T00:00:00Z date_updated: 2025-09-09T07:09:22Z day: '01' department: - _id: MoHe ec_funded: 1 external_id: arxiv: - '2302.11341' intvolume: ' 258' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2302.11341 month: '05' oa: 1 oa_version: Preprint page: 1990-1998 project: - _id: bd9ca328-d553-11ed-ba76-dc4f890cfe62 call_identifier: H2020 grant_number: '101019564' name: The design and evaluation of modern fully dynamic data structures - _id: 34def286-11ca-11ed-8bc3-da5948e1613c grant_number: Z00422 name: Efficient algorithms - _id: bda196b2-d553-11ed-ba76-8e8ee6c21103 grant_number: I05982 name: Static and Dynamic Hierarchical Graph Decompositions - _id: bd9e3a2e-d553-11ed-ba76-8aa684ce17fe grant_number: P33775 name: Fast Algorithms for a Reactive Network Layer publication: The 28th International Conference on Artificial Intelligence and Statistics publication_identifier: eissn: - 2640-3498 publication_status: published publisher: ML Research Press quality_controlled: '1' scopus_import: '1' status: public title: Differentially private continual release of histograms and related queries type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 258 year: '2025' ... --- OA_place: publisher OA_type: gold _id: '20533' abstract: - lang: eng text: We give an introduction into differential privacy in the dynamic setting, called the continual observation setting. alternative_title: - LIPIcs article_number: '2' article_processing_charge: No author: - first_name: Monika H full_name: Henzinger, Monika H id: 540c9bbd-f2de-11ec-812d-d04a5be85630 last_name: Henzinger orcid: 0000-0002-5008-6530 - first_name: Roodabeh full_name: Safavi Hemami, Roodabeh id: 72ed2640-8972-11ed-ae7b-f9c81ec75154 last_name: Safavi Hemami citation: ama: 'Henzinger M, Safavi Hemami R. Securing dynamic data: A primer on differentially private data structures. In: 33rd Annual European Symposium on Algorithms. Vol 351. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2025. doi:10.4230/LIPIcs.ESA.2025.2' apa: 'Henzinger, M., & Safavi Hemami, R. (2025). Securing dynamic data: A primer on differentially private data structures. In 33rd Annual European Symposium on Algorithms (Vol. 351). Warsaw, Poland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.ESA.2025.2' chicago: 'Henzinger, Monika, and Roodabeh Safavi Hemami. “Securing Dynamic Data: A Primer on Differentially Private Data Structures.” In 33rd Annual European Symposium on Algorithms, Vol. 351. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. https://doi.org/10.4230/LIPIcs.ESA.2025.2.' ieee: 'M. Henzinger and R. Safavi Hemami, “Securing dynamic data: A primer on differentially private data structures,” in 33rd Annual European Symposium on Algorithms, Warsaw, Poland, 2025, vol. 351.' ista: 'Henzinger M, Safavi Hemami R. 2025. Securing dynamic data: A primer on differentially private data structures. 33rd Annual European Symposium on Algorithms. ESA: European Symposium on Algorithms, LIPIcs, vol. 351, 2.' mla: 'Henzinger, Monika, and Roodabeh Safavi Hemami. “Securing Dynamic Data: A Primer on Differentially Private Data Structures.” 33rd Annual European Symposium on Algorithms, vol. 351, 2, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025, doi:10.4230/LIPIcs.ESA.2025.2.' short: M. Henzinger, R. Safavi Hemami, in:, 33rd Annual European Symposium on Algorithms, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. conference: end_date: 2025-09-17 location: Warsaw, Poland name: 'ESA: European Symposium on Algorithms' start_date: 2025-09-15 corr_author: '1' date_created: 2025-10-26T23:01:34Z date_published: 2025-10-01T00:00:00Z date_updated: 2025-10-27T08:00:13Z day: '01' ddc: - '000' department: - _id: MoHe doi: 10.4230/LIPIcs.ESA.2025.2 file: - access_level: open_access checksum: 094e0466d90664fbea397b469a60acbb content_type: application/pdf creator: dernst date_created: 2025-10-27T07:57:00Z date_updated: 2025-10-27T07:57:00Z file_id: '20541' file_name: 2025_LIPIcs.ESA_Henzinger.pdf file_size: 770227 relation: main_file success: 1 file_date_updated: 2025-10-27T07:57:00Z has_accepted_license: '1' intvolume: ' 351' language: - iso: eng month: '10' oa: 1 oa_version: Published Version publication: 33rd Annual European Symposium on Algorithms publication_identifier: isbn: - '9783959773959' issn: - 1868-8969 publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: '1' status: public title: 'Securing dynamic data: A primer on differentially private data structures' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 351 year: '2025' ... --- OA_place: publisher OA_type: gold _id: '20534' abstract: - lang: eng text: "A non-trivial minimum cut (NMC) sparsifier is a multigraph Ĝ that preserves all non-trivial minimum cuts of a given undirected graph G. We introduce a flexible data structure for fully dynamic graphs that can efficiently provide an NMC sparsifier upon request at any point during the sequence of updates. We employ simple dynamic forest data structures to achieve a fast from-scratch construction of the sparsifier at query time. Based on the strength of the adversary and desired type of time bounds, the data structure comes with different guarantees. Specifically, let G be a fully dynamic simple graph with n vertices and minimum degree δ. Then our data structure supports an insertion/deletion of an edge to/from G in n^o(1) worst-case time. Furthermore, upon request, it can return w.h.p. an NMC sparsifier of G that has O(n/δ) vertices and O(n) edges, in Ô(n) time. The probabilistic guarantees hold against an adaptive adversary. Alternatively, the update and query times can be improved to Õ(1) and Õ(n) respectively, if amortized-time guarantees are sufficient, or if the adversary is oblivious. Throughout the paper, we use Õ to hide polylogarithmic factors and Ô to hide subpolynomial (i.e., n^o(1)) factors.\r\nWe discuss two applications of our new data structure. First, it can be used to efficiently report a cactus representation of all minimum cuts of a fully dynamic simple graph. Building this cactus for the NMC sparsifier instead of the original graph allows for a construction time that is sublinear in the number of edges. Against an adaptive adversary, we can with high probability output the cactus representation in worst-case Ô(n) time. Second, our data structure allows us to efficiently compute the maximal k-edge-connected subgraphs of undirected simple graphs, by repeatedly applying a minimum cut algorithm on the NMC sparsifier. Specifically, we can compute with high probability the maximal k-edge-connected subgraphs of a simple graph with n vertices and m edges in Õ(m+n²/k) time. This improves the best known time bounds for k = Ω(n^{1/8}) and naturally extends to the case of fully dynamic graphs." acknowledgement: 'Monika Henzinger and Evangelos Kosinas: This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (MoDynStruct, No. 101019564) and the Austrian Science Fund (FWF) grant https://www.doi.org/10.55776/Z422 and grant https://www.doi.org/10.55776/I5982. Harald Räcke and Robin Münk: This project has received funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 498605858.' article_number: '36' article_processing_charge: No arxiv: 1 author: - first_name: Monika H full_name: Henzinger, Monika H id: 540c9bbd-f2de-11ec-812d-d04a5be85630 last_name: Henzinger orcid: 0000-0002-5008-6530 - first_name: Evangelos full_name: Kosinas, Evangelos id: 4c7f9625-dbbc-11ee-9d86-bdcc2db5a949 last_name: Kosinas - first_name: Robin full_name: Münk, Robin last_name: Münk - first_name: Harald full_name: Räcke, Harald last_name: Räcke citation: ama: 'Henzinger M, Kosinas E, Münk R, Räcke H. Efficient contractions of dynamic graphs - with applications. In: 33rd Annual European Symposium on Algorithms. Vol 351. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2025. doi:10.4230/LIPIcs.ESA.2025.36' apa: 'Henzinger, M., Kosinas, E., Münk, R., & Räcke, H. (2025). Efficient contractions of dynamic graphs - with applications. In 33rd Annual European Symposium on Algorithms (Vol. 351). Warsaw, Poland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.ESA.2025.36' chicago: Henzinger, Monika, Evangelos Kosinas, Robin Münk, and Harald Räcke. “Efficient Contractions of Dynamic Graphs - with Applications.” In 33rd Annual European Symposium on Algorithms, Vol. 351. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. https://doi.org/10.4230/LIPIcs.ESA.2025.36. ieee: M. Henzinger, E. Kosinas, R. Münk, and H. Räcke, “Efficient contractions of dynamic graphs - with applications,” in 33rd Annual European Symposium on Algorithms, Warsaw, Poland, 2025, vol. 351. ista: 'Henzinger M, Kosinas E, Münk R, Räcke H. 2025. Efficient contractions of dynamic graphs - with applications. 33rd Annual European Symposium on Algorithms. ESA: European Symposium on Algorithms vol. 351, 36.' mla: Henzinger, Monika, et al. “Efficient Contractions of Dynamic Graphs - with Applications.” 33rd Annual European Symposium on Algorithms, vol. 351, 36, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025, doi:10.4230/LIPIcs.ESA.2025.36. short: M. Henzinger, E. Kosinas, R. Münk, H. Räcke, in:, 33rd Annual European Symposium on Algorithms, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. conference: end_date: 2025-09-17 location: Warsaw, Poland name: 'ESA: European Symposium on Algorithms' start_date: 2025-09-15 corr_author: '1' date_created: 2025-10-26T23:01:34Z date_published: 2025-10-01T00:00:00Z date_updated: 2025-10-27T08:05:46Z day: '01' ddc: - '000' department: - _id: MoHe doi: 10.4230/LIPIcs.ESA.2025.36 ec_funded: 1 external_id: arxiv: - '2509.05157' file: - access_level: open_access checksum: d2daf9a467e96fb5e7084a8a85321776 content_type: application/pdf creator: dernst date_created: 2025-10-27T08:03:36Z date_updated: 2025-10-27T08:03:36Z file_id: '20542' file_name: 2025_LIPIcs.ESA_HenzingerM.pdf file_size: 934846 relation: main_file success: 1 file_date_updated: 2025-10-27T08:03:36Z has_accepted_license: '1' intvolume: ' 351' language: - iso: eng month: '10' oa: 1 oa_version: Published Version project: - _id: bd9ca328-d553-11ed-ba76-dc4f890cfe62 call_identifier: H2020 grant_number: '101019564' name: The design and evaluation of modern fully dynamic data structures - _id: 34def286-11ca-11ed-8bc3-da5948e1613c grant_number: Z00422 name: Efficient algorithms - _id: bda196b2-d553-11ed-ba76-8e8ee6c21103 grant_number: I05982 name: Static and Dynamic Hierarchical Graph Decompositions publication: 33rd Annual European Symposium on Algorithms publication_identifier: isbn: - '9783959773959' issn: - 1868-8969 publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: '1' status: public title: Efficient contractions of dynamic graphs - with applications tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 351 year: '2025' ... --- OA_place: publisher OA_type: gold _id: '20535' abstract: - lang: eng text: "Many differentially private and classical non-private graph algorithms rely crucially on determining whether some property of each vertex meets a threshold. For example, for the k-core decomposition problem, the classic peeling algorithm iteratively removes a vertex if its induced degree falls below a threshold. The sparse vector technique (SVT) is generally used to transform non-private threshold queries into private ones with only a small additive loss in accuracy. However, a naive application of SVT in the graph setting leads to an amplification of the error by a factor of n due to composition, as SVT is applied to every vertex. In this paper, we resolve this problem by formulating a novel generalized sparse vector technique which we call the Multidimensional AboveThreshold (MAT) Mechanism which generalizes SVT (applied to vectors with one dimension) to vectors with multiple dimensions. When applied to vectors with n dimensions, we solve a number of important graph problems with better bounds than previous work.\r\nSpecifically, we apply our MAT mechanism to obtain a set of improved bounds for a variety of problems including k-core decomposition, densest subgraph, low out-degree ordering, and vertex coloring. We give a tight local edge differentially private (LEDP) algorithm for k-core decomposition that results in an approximation with O(ε^{-1} log n) additive error and no multiplicative error in O(n) rounds. We also give a new (2+η)-factor multiplicative, O(ε^{-1} log n) additive error algorithm in O(log² n) rounds for any constant η > 0. Both of these results are asymptotically tight against our new lower bound of Ω(log n) for any constant-factor approximation algorithm for k-core decomposition. Our new algorithms for k-core decomposition also directly lead to new algorithms for the related problems of densest subgraph and low out-degree ordering. Finally, we give novel LEDP differentially private defective coloring algorithms that use number of colors given in terms of the arboricity of the graph." acknowledgement: "Monika Henzinger and A. R. Sricharan: This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation\r\nprogramme (MoDynStruct, No. 101019564) and the Austrian Science Fund (FWF) grant DOI\r\n10.55776/Z422 and grant DOI 10.55776/I5982. Laxman Dhulipala and George Z. Li: supported by NSF award number CNS-2317194. Quanquan C. Liu: supported by a Google Academic Research Award and by an NSF award number CCF-2453323." alternative_title: - LIPIcs article_number: '91' article_processing_charge: No arxiv: 1 author: - first_name: Laxman full_name: Dhulipala, Laxman last_name: Dhulipala - first_name: Monika H full_name: Henzinger, Monika H id: 540c9bbd-f2de-11ec-812d-d04a5be85630 last_name: Henzinger orcid: 0000-0002-5008-6530 - first_name: George Z. full_name: Li, George Z. last_name: Li - first_name: Quanquan C. full_name: Liu, Quanquan C. last_name: Liu - first_name: A. R. full_name: Sricharan, A. R. last_name: Sricharan - first_name: Leqi full_name: Zhu, Leqi id: a2117c59-cee4-11ed-b9d0-874ecf0f8ac5 last_name: Zhu citation: ama: 'Dhulipala L, Henzinger M, Li GZ, Liu QC, Sricharan AR, Zhu L. Near-optimal differentially private graph algorithms via the Multidimensional AboveThreshold Mechanism. In: 33rd Annual European Symposium on Algorithms. Vol 351. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2025. doi:10.4230/LIPIcs.ESA.2025.91' apa: 'Dhulipala, L., Henzinger, M., Li, G. Z., Liu, Q. C., Sricharan, A. R., & Zhu, L. (2025). Near-optimal differentially private graph algorithms via the Multidimensional AboveThreshold Mechanism. In 33rd Annual European Symposium on Algorithms (Vol. 351). Warsaw, Poland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.ESA.2025.91' chicago: Dhulipala, Laxman, Monika Henzinger, George Z. Li, Quanquan C. Liu, A. R. Sricharan, and Leqi Zhu. “Near-Optimal Differentially Private Graph Algorithms via the Multidimensional AboveThreshold Mechanism.” In 33rd Annual European Symposium on Algorithms, Vol. 351. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. https://doi.org/10.4230/LIPIcs.ESA.2025.91. ieee: L. Dhulipala, M. Henzinger, G. Z. Li, Q. C. Liu, A. R. Sricharan, and L. Zhu, “Near-optimal differentially private graph algorithms via the Multidimensional AboveThreshold Mechanism,” in 33rd Annual European Symposium on Algorithms, Warsaw, Poland, 2025, vol. 351. ista: 'Dhulipala L, Henzinger M, Li GZ, Liu QC, Sricharan AR, Zhu L. 2025. Near-optimal differentially private graph algorithms via the Multidimensional AboveThreshold Mechanism. 33rd Annual European Symposium on Algorithms. ESA: European Symposium on Algorithms, LIPIcs, vol. 351, 91.' mla: Dhulipala, Laxman, et al. “Near-Optimal Differentially Private Graph Algorithms via the Multidimensional AboveThreshold Mechanism.” 33rd Annual European Symposium on Algorithms, vol. 351, 91, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025, doi:10.4230/LIPIcs.ESA.2025.91. short: L. Dhulipala, M. Henzinger, G.Z. Li, Q.C. Liu, A.R. Sricharan, L. Zhu, in:, 33rd Annual European Symposium on Algorithms, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. conference: end_date: 2025-09-17 location: Warsaw, Poland name: 'ESA: European Symposium on Algorithms' start_date: 2025-09-15 corr_author: '1' date_created: 2025-10-26T23:01:35Z date_published: 2025-10-01T00:00:00Z date_updated: 2025-10-27T07:02:06Z day: '01' ddc: - '000' department: - _id: MoHe doi: 10.4230/LIPIcs.ESA.2025.91 ec_funded: 1 external_id: arxiv: - '2508.02182' file: - access_level: open_access checksum: 19146e935b5b6ad5d33c8d08280ad8e7 content_type: application/pdf creator: dernst date_created: 2025-10-27T06:58:43Z date_updated: 2025-10-27T06:58:43Z file_id: '20539' file_name: 2025_LIPIcs.ESA_Dhulipala.pdf file_size: 870317 relation: main_file success: 1 file_date_updated: 2025-10-27T06:58:43Z has_accepted_license: '1' intvolume: ' 351' language: - iso: eng month: '10' oa: 1 oa_version: Published Version project: - _id: bd9ca328-d553-11ed-ba76-dc4f890cfe62 call_identifier: H2020 grant_number: '101019564' name: The design and evaluation of modern fully dynamic data structures - _id: 34def286-11ca-11ed-8bc3-da5948e1613c grant_number: Z00422 name: Efficient algorithms - _id: bda196b2-d553-11ed-ba76-8e8ee6c21103 grant_number: I05982 name: Static and Dynamic Hierarchical Graph Decompositions publication: 33rd Annual European Symposium on Algorithms publication_identifier: isbn: - '9783959773959' issn: - 1868-8969 publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: '1' status: public title: Near-optimal differentially private graph algorithms via the Multidimensional AboveThreshold Mechanism tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 351 year: '2025' ... --- OA_place: publisher OA_type: gold _id: '20536' abstract: - lang: eng text: "Uniquely represented (UR) data structures represent each logical state with a unique storage state. We study the problem of maintaining a dynamic set of n keys from a totally ordered universe in this context. UR structures are also called \"strongly history independent\" structures in the literature.\r\nWe introduce a two-layer data structure called (α,ε)-Randomized Block Search Tree (RBST) that is uniquely represented and suitable for external memory (EM). Though RBSTs naturally generalize the well-known binary Treaps, several new ideas are needed to analyze the expected search, update, and storage efficiency in terms of block-reads, block-writes, and blocks stored. We prove that searches have O(ε^{-1} + log_α n) block-reads, that dynamic updates perform O(ε^{-1} + log_α(n)/α) block-writes and O(ε^{-2}+(1+(ε^{-1}+log n)/α)log_α n) block-reads, and that (α, ε)-RBSTs have an asymptotic load-factor of at least (1-ε) for every ε ∈ (0,1/2].\r\nThus (α, ε)-RBSTs improve on the known, uniquely represented B-Treap [Golovin; ICALP'09]. Compared with non-UR structures, the RBST is also, to the best of our knowledge, the first external memory structure that is storage-efficient and has a non-amortized, write-efficient update bound." acknowledgement: "This work was supported under the Australian Research Council Discovery Projects\r\nfunding scheme (project number DP180102870). This project has received funding from the\r\nEuropean Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No. 101019564) “The Design of Modern Fully Dynamic Data Structures (MoDynStruct)” and from the Austrian Science Fund (FWF) project Z 422-N and project “Fast Algorithms for a Reactive Network Layer (ReactNet)” P 33775-N, with additional funding from the netidee SCIENCE Stiftung, 2020–2024." alternative_title: - LIPIcs article_number: '47' article_processing_charge: No arxiv: 1 author: - first_name: Roodabeh full_name: Safavi Hemami, Roodabeh id: 72ed2640-8972-11ed-ae7b-f9c81ec75154 last_name: Safavi Hemami - first_name: Martin P. full_name: Seybold, Martin P. last_name: Seybold citation: ama: 'Safavi Hemami R, Seybold MP. B-Treaps revised: Write efficient randomized block search trees with high load. In: 19th International Symposium on Algorithms and Data Structures. Vol 349. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2025. doi:10.4230/LIPIcs.WADS.2025.47' apa: 'Safavi Hemami, R., & Seybold, M. P. (2025). B-Treaps revised: Write efficient randomized block search trees with high load. In 19th International Symposium on Algorithms and Data Structures (Vol. 349). Toronto, Canada: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.WADS.2025.47' chicago: 'Safavi Hemami, Roodabeh, and Martin P. Seybold. “B-Treaps Revised: Write Efficient Randomized Block Search Trees with High Load.” In 19th International Symposium on Algorithms and Data Structures, Vol. 349. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. https://doi.org/10.4230/LIPIcs.WADS.2025.47.' ieee: 'R. Safavi Hemami and M. P. Seybold, “B-Treaps revised: Write efficient randomized block search trees with high load,” in 19th International Symposium on Algorithms and Data Structures, Toronto, Canada, 2025, vol. 349.' ista: 'Safavi Hemami R, Seybold MP. 2025. B-Treaps revised: Write efficient randomized block search trees with high load. 19th International Symposium on Algorithms and Data Structures. WADS: Algorithms and Data Structures Symposium, LIPIcs, vol. 349, 47.' mla: 'Safavi Hemami, Roodabeh, and Martin P. Seybold. “B-Treaps Revised: Write Efficient Randomized Block Search Trees with High Load.” 19th International Symposium on Algorithms and Data Structures, vol. 349, 47, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025, doi:10.4230/LIPIcs.WADS.2025.47.' short: R. Safavi Hemami, M.P. Seybold, in:, 19th International Symposium on Algorithms and Data Structures, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. conference: end_date: 2025-08-15 location: Toronto, Canada name: 'WADS: Algorithms and Data Structures Symposium' start_date: 2025-08-11 corr_author: '1' date_created: 2025-10-26T23:01:35Z date_published: 2025-08-29T00:00:00Z date_updated: 2025-10-27T07:10:49Z day: '29' ddc: - '000' department: - _id: MoHe doi: 10.4230/LIPIcs.WADS.2025.47 ec_funded: 1 external_id: arxiv: - '2303.04722' file: - access_level: open_access checksum: 196af33762831a78e87f4f95ecd8677b content_type: application/pdf creator: dernst date_created: 2025-10-27T07:09:41Z date_updated: 2025-10-27T07:09:41Z file_id: '20540' file_name: 2025_LIPIcs.WADS_Safavi.pdf file_size: 1081870 relation: main_file success: 1 file_date_updated: 2025-10-27T07:09:41Z has_accepted_license: '1' intvolume: ' 349' language: - iso: eng month: '08' oa: 1 oa_version: Published Version project: - _id: bd9ca328-d553-11ed-ba76-dc4f890cfe62 call_identifier: H2020 grant_number: '101019564' name: The design and evaluation of modern fully dynamic data structures - _id: 34def286-11ca-11ed-8bc3-da5948e1613c grant_number: Z00422 name: Efficient algorithms - _id: bd9e3a2e-d553-11ed-ba76-8aa684ce17fe grant_number: P33775 name: Fast Algorithms for a Reactive Network Layer publication: 19th International Symposium on Algorithms and Data Structures publication_identifier: isbn: - '9783959773980' issn: - 1868-8969 publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: '1' status: public title: 'B-Treaps revised: Write efficient randomized block search trees with high load' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 349 year: '2025' ... --- OA_place: publisher OA_type: gold _id: '20819' abstract: - lang: eng text: "Clustering is a cornerstone of data analysis that is particularly suited to identifying coherent subgroups or substructures in unlabeled data, as are generated continuously in large amounts these days. However, in many cases traditional clustering methods are not applicable, because data are increasingly being produced and stored in a distributed way, e.g. on edge devices, and privacy concerns prevent it from being transferred to a central server. To address this challenge, we present FedDP-KMeans, a new algorithm for \r\n-means clustering that is fully-federated as well as differentially private. Our approach leverages (potentially small and out-of-distribution) server-side data to overcome the primary challenge of differentially private clustering methods: the need for a good initialization. Combining our initialization with a simple federated DP-Lloyds algorithm we obtain an algorithm that achieves excellent results on synthetic and real-world benchmark tasks. We also provide a theoretical analysis of our method that provides bounds on the convergence speed and cluster identification success." acknowledged_ssus: - _id: ScienComp acknowledgement: "This research was funded in part by the Austrian Science Fund (FWF) [10.55776/COE12] and supported by the Scientific Service Units (SSU) of ISTA through resources provided by Scientific Computing (SciComp).\r\n" alternative_title: - PMLR article_processing_charge: No arxiv: 1 author: - first_name: Jonathan A full_name: Scott, Jonathan A id: e499926b-f6e0-11ea-865d-9c63db0031e8 last_name: Scott - first_name: Christoph full_name: Lampert, Christoph id: 40C20FD2-F248-11E8-B48F-1D18A9856A87 last_name: Lampert orcid: 0000-0001-8622-7887 - first_name: David full_name: Saulpic, David id: f8e48cf0-b0ff-11ed-b0e9-b4c35598f964 last_name: Saulpic citation: ama: 'Scott JA, Lampert C, Saulpic D. Differentially private federated k-means clustering with server-side data. In: 42nd International Conference on Machine Learning. Vol 267. ML Research Press; 2025:53757-53790.' apa: 'Scott, J. A., Lampert, C., & Saulpic, D. (2025). Differentially private federated k-means clustering with server-side data. In 42nd International Conference on Machine Learning (Vol. 267, pp. 53757–53790). Vancouver, Canada: ML Research Press.' chicago: Scott, Jonathan A, Christoph Lampert, and David Saulpic. “Differentially Private Federated K-Means Clustering with Server-Side Data.” In 42nd International Conference on Machine Learning, 267:53757–90. ML Research Press, 2025. ieee: J. A. Scott, C. Lampert, and D. Saulpic, “Differentially private federated k-means clustering with server-side data,” in 42nd International Conference on Machine Learning, Vancouver, Canada, 2025, vol. 267, pp. 53757–53790. ista: 'Scott JA, Lampert C, Saulpic D. 2025. Differentially private federated k-means clustering with server-side data. 42nd International Conference on Machine Learning. ICML: International Conference on Machine Learning, PMLR, vol. 267, 53757–53790.' mla: Scott, Jonathan A., et al. “Differentially Private Federated K-Means Clustering with Server-Side Data.” 42nd International Conference on Machine Learning, vol. 267, ML Research Press, 2025, pp. 53757–90. short: J.A. Scott, C. Lampert, D. Saulpic, in:, 42nd International Conference on Machine Learning, ML Research Press, 2025, pp. 53757–53790. conference: end_date: 2025-07-19 location: Vancouver, Canada name: 'ICML: International Conference on Machine Learning' start_date: 2025-07-13 corr_author: '1' date_created: 2025-12-14T23:02:05Z date_published: 2025-05-01T00:00:00Z date_updated: 2026-04-07T11:46:11Z day: '01' ddc: - '000' department: - _id: ChLa - _id: MoHe external_id: arxiv: - '2506.05408' file: - access_level: open_access checksum: 815b32b463023ca21e569c2158745c15 content_type: application/pdf creator: dernst date_created: 2025-12-16T12:38:29Z date_updated: 2025-12-16T12:38:29Z file_id: '20829' file_name: 2025_ICML_Scott.pdf file_size: 746612 relation: main_file success: 1 file_date_updated: 2025-12-16T12:38:29Z has_accepted_license: '1' intvolume: ' 267' language: - iso: eng month: '05' oa: 1 oa_version: Published Version page: 53757-53790 publication: 42nd International Conference on Machine Learning publication_identifier: eissn: - 2640-3498 publication_status: published publisher: ML Research Press quality_controlled: '1' related_material: record: - id: '21198' relation: dissertation_contains status: public scopus_import: '1' status: public title: Differentially private federated k-means clustering with server-side data tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 267 year: '2025' ... --- _id: '14769' abstract: - lang: eng text: 'For a set of points in Rd, the Euclidean k-means problems consists of finding k centers such that the sum of distances squared from each data point to its closest center is minimized. Coresets are one the main tools developed recently to solve this problem in a big data context. They allow to compress the initial dataset while preserving its structure: running any algorithm on the coreset provides a guarantee almost equivalent to running it on the full data. In this work, we study coresets in a fully-dynamic setting: points are added and deleted with the goal to efficiently maintain a coreset with which a k-means solution can be computed. Based on an algorithm from Henzinger and Kale [ESA''20], we present an efficient and practical implementation of a fully dynamic coreset algorithm, that improves the running time by up to a factor of 20 compared to our non-optimized implementation of the algorithm by Henzinger and Kale, without sacrificing more than 7% on the quality of the k-means solution.' acknowledgement: This project has received funding from the Euro-pean Research Council (ERC) under the EuropeanUnion’s Horizon 2020 research and innovation programme (Grant agreement No. 101019564 “The De-sign of Modern Fully Dynamic Data Structures (Mo-DynStruct)” and the Austrian Science Fund (FWF)project Z 422-N, project “Static and Dynamic Hierar-chical Graph Decompositions”, I 5982-N, and project“Fast Algorithms for a Reactive Network Layer (Re-actNet)”, P 33775-N, with additional funding from thenetidee SCIENCE Stiftung, 2020–2024.D. Sauplic has received funding from the Euro-pean Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreementNo 101034413. article_processing_charge: No arxiv: 1 author: - first_name: Monika H full_name: Henzinger, Monika H id: 540c9bbd-f2de-11ec-812d-d04a5be85630 last_name: Henzinger orcid: 0000-0002-5008-6530 - first_name: David full_name: Saulpic, David id: f8e48cf0-b0ff-11ed-b0e9-b4c35598f964 last_name: Saulpic - first_name: Leonhard full_name: Sidl, Leonhard id: 8b563fd0-b441-11ee-9101-a3891c61efa6 last_name: Sidl citation: ama: 'Henzinger M, Saulpic D, Sidl L. Experimental evaluation of fully dynamic k-means via coresets. In: 2024 Proceedings of the Symposium on Algorithm Engineering and Experiments. Society for Industrial and Applied Mathematics; 2024:220-233. doi:10.1137/1.9781611977929.17' apa: 'Henzinger, M., Saulpic, D., & Sidl, L. (2024). Experimental evaluation of fully dynamic k-means via coresets. In 2024 Proceedings of the Symposium on Algorithm Engineering and Experiments (pp. 220–233). Alexandria, VA, United States: Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611977929.17' chicago: Henzinger, Monika, David Saulpic, and Leonhard Sidl. “Experimental Evaluation of Fully Dynamic K-Means via Coresets.” In 2024 Proceedings of the Symposium on Algorithm Engineering and Experiments, 220–33. Society for Industrial and Applied Mathematics, 2024. https://doi.org/10.1137/1.9781611977929.17. ieee: M. Henzinger, D. Saulpic, and L. Sidl, “Experimental evaluation of fully dynamic k-means via coresets,” in 2024 Proceedings of the Symposium on Algorithm Engineering and Experiments, Alexandria, VA, United States, 2024, pp. 220–233. ista: 'Henzinger M, Saulpic D, Sidl L. 2024. Experimental evaluation of fully dynamic k-means via coresets. 2024 Proceedings of the Symposium on Algorithm Engineering and Experiments. ALENEX: Workshop on Algorithm Engineering and Experiments, 220–233.' mla: Henzinger, Monika, et al. “Experimental Evaluation of Fully Dynamic K-Means via Coresets.” 2024 Proceedings of the Symposium on Algorithm Engineering and Experiments, Society for Industrial and Applied Mathematics, 2024, pp. 220–33, doi:10.1137/1.9781611977929.17. short: M. Henzinger, D. Saulpic, L. Sidl, in:, 2024 Proceedings of the Symposium on Algorithm Engineering and Experiments, Society for Industrial and Applied Mathematics, 2024, pp. 220–233. conference: end_date: 2024-01-08 location: Alexandria, VA, United States name: 'ALENEX: Workshop on Algorithm Engineering and Experiments' start_date: 2024-01-07 corr_author: '1' date_created: 2024-01-09T16:22:47Z date_published: 2024-01-04T00:00:00Z date_updated: 2025-04-14T13:50:50Z day: '04' department: - _id: MoHe doi: 10.1137/1.9781611977929.17 ec_funded: 1 external_id: arxiv: - '2310.18034' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2310.18034 month: '01' oa: 1 oa_version: Preprint page: 220-233 project: - _id: bd9ca328-d553-11ed-ba76-dc4f890cfe62 call_identifier: H2020 grant_number: '101019564' name: The design and evaluation of modern fully dynamic data structures - _id: 34def286-11ca-11ed-8bc3-da5948e1613c grant_number: Z00422 name: Efficient algorithms - _id: bda196b2-d553-11ed-ba76-8e8ee6c21103 grant_number: I05982 name: Static and Dynamic Hierarchical Graph Decompositions - _id: bd9e3a2e-d553-11ed-ba76-8aa684ce17fe grant_number: P33775 name: Fast Algorithms for a Reactive Network Layer - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: 2024 Proceedings of the Symposium on Algorithm Engineering and Experiments publication_identifier: eisbn: - '9781611977929' publication_status: published publisher: Society for Industrial and Applied Mathematics quality_controlled: '1' scopus_import: '1' status: public title: Experimental evaluation of fully dynamic k-means via coresets type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2024' ... --- _id: '15008' abstract: - lang: eng text: "Oblivious routing is a well-studied paradigm that uses static precomputed routing tables for selecting routing paths within a network. Existing oblivious routing schemes with polylogarithmic competitive ratio for general networks are tree-based, in the sense that routing is performed according to a convex combination of trees. However, this restriction to trees leads to a construction that has time quadratic in the size of the network and does not parallelize well. \r\nIn this paper we study oblivious routing schemes based on electrical routing. In particular, we show that general networks with n vertices and m edges admit a routing scheme that has competitive ratio O(log² n) and consists of a convex combination of only O(√m) electrical routings. This immediately leads to an improved construction algorithm with time Õ(m^{3/2}) that can also be implemented in parallel with Õ(√m) depth." 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 (Grant agreement No. 101019564) and the Austrian Science Fund (FWF) project Z\r\n422-N, project I 5982-N, and project P 33775-N, with additional funding from the netidee SCIENCE Stiftung, 2020–2024.\r\nHarald Räcke: Research supported by German Research Foundation (DFG), grant 470029389\r\n(FlexNets), 2021-2024.\r\nSushant Sachdeva: SS’s work is supported by an Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant RGPIN-2018-06398 and a Sloan Research Fellowship." alternative_title: - LIPIcs article_number: '55' article_processing_charge: No arxiv: 1 author: - first_name: Gramoz full_name: Goranci, Gramoz last_name: Goranci - first_name: Monika H full_name: Henzinger, Monika H id: 540c9bbd-f2de-11ec-812d-d04a5be85630 last_name: Henzinger orcid: 0000-0002-5008-6530 - first_name: Harald full_name: Räcke, Harald last_name: Räcke - first_name: Sushant full_name: Sachdeva, Sushant last_name: Sachdeva - first_name: A. R. full_name: Sricharan, A. R. last_name: Sricharan citation: ama: 'Goranci G, Henzinger M, Räcke H, Sachdeva S, Sricharan AR. Electrical flows for polylogarithmic competitive oblivious routing. In: 15th Innovations in Theoretical Computer Science Conference. Vol 287. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:10.4230/LIPIcs.ITCS.2024.55' apa: 'Goranci, G., Henzinger, M., Räcke, H., Sachdeva, S., & Sricharan, A. R. (2024). Electrical flows for polylogarithmic competitive oblivious routing. In 15th Innovations in Theoretical Computer Science Conference (Vol. 287). Berkeley, CA, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.ITCS.2024.55' chicago: Goranci, Gramoz, Monika Henzinger, Harald Räcke, Sushant Sachdeva, and A. R. Sricharan. “Electrical Flows for Polylogarithmic Competitive Oblivious Routing.” In 15th Innovations in Theoretical Computer Science Conference, Vol. 287. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. https://doi.org/10.4230/LIPIcs.ITCS.2024.55. ieee: G. Goranci, M. Henzinger, H. Räcke, S. Sachdeva, and A. R. Sricharan, “Electrical flows for polylogarithmic competitive oblivious routing,” in 15th Innovations in Theoretical Computer Science Conference, Berkeley, CA, United States, 2024, vol. 287. ista: 'Goranci G, Henzinger M, Räcke H, Sachdeva S, Sricharan AR. 2024. Electrical flows for polylogarithmic competitive oblivious routing. 15th Innovations in Theoretical Computer Science Conference. ITCS: Innovations in Theoretical Computer Science, LIPIcs, vol. 287, 55.' mla: Goranci, Gramoz, et al. “Electrical Flows for Polylogarithmic Competitive Oblivious Routing.” 15th Innovations in Theoretical Computer Science Conference, vol. 287, 55, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:10.4230/LIPIcs.ITCS.2024.55. short: G. Goranci, M. Henzinger, H. Räcke, S. Sachdeva, A.R. Sricharan, in:, 15th Innovations in Theoretical Computer Science Conference, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. conference: end_date: 2024-02-02 location: Berkeley, CA, United States name: 'ITCS: Innovations in Theoretical Computer Science' start_date: 2024-01-30 corr_author: '1' date_created: 2024-02-18T23:01:02Z date_published: 2024-01-24T00:00:00Z date_updated: 2025-09-04T12:06:25Z day: '24' ddc: - '000' department: - _id: MoHe doi: 10.4230/LIPIcs.ITCS.2024.55 ec_funded: 1 external_id: arxiv: - '2303.02491' isi: - '001300389400055' file: - access_level: open_access checksum: b89716aae6a5599f187897e39de1e53a content_type: application/pdf creator: dernst date_created: 2024-02-26T10:10:48Z date_updated: 2024-02-26T10:10:48Z file_id: '15030' file_name: 2024_LIPICs_Goranci.pdf file_size: 1054754 relation: main_file success: 1 file_date_updated: 2024-02-26T10:10:48Z has_accepted_license: '1' intvolume: ' 287' isi: 1 language: - iso: eng month: '01' oa: 1 oa_version: Published Version project: - _id: bd9ca328-d553-11ed-ba76-dc4f890cfe62 call_identifier: H2020 grant_number: '101019564' name: The design and evaluation of modern fully dynamic data structures - _id: 34def286-11ca-11ed-8bc3-da5948e1613c grant_number: Z00422 name: Efficient algorithms - _id: bda196b2-d553-11ed-ba76-8e8ee6c21103 grant_number: I05982 name: Static and Dynamic Hierarchical Graph Decompositions - _id: bd9e3a2e-d553-11ed-ba76-8aa684ce17fe grant_number: P33775 name: Fast Algorithms for a Reactive Network Layer publication: 15th Innovations in Theoretical Computer Science Conference publication_identifier: isbn: - '9783959773096' issn: - 1868-8969 publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: '1' status: public title: Electrical flows for polylogarithmic competitive oblivious routing tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 287 year: '2024' ... --- _id: '15093' abstract: - lang: eng text: We present a dynamic data structure for maintaining the persistent homology of a time series of real numbers. The data structure supports local operations, including the insertion and deletion of an item and the cutting and concatenating of lists, each in time O(log n + k), in which n counts the critical items and k the changes in the augmented persistence diagram. To achieve this, we design a tailor-made tree structure with an unconventional representation, referred to as banana tree, which may be useful in its own right. acknowledgement: The first and second authors are funded by the European Research Council under the European Union’s Horizon 2020 research and innovation programme, ERC grant no. 788183,“Alpha Shape Theory Extended (Alpha)”, by the Wittgenstein Prize, FWF grant no. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, FWF grant no. I 02979-N35.The third author received funding by the European Research Council under the European Union’s Horizon 2020research and innovation programme, ERC grant no. 101019564, “The Design of Modern Fully Dynamic DataStructures (MoDynStruct)”, and by the Austrian Science Fund through the Wittgenstein Prize with FWF grant no. Z 422-N, and also by FWF grant no. I 5982-N, and by FWF grant no. P 33775-N, with additional funding from the netidee SCIENCE Stiftung, 2020–2024. The fourth author is funded by the Vienna Graduate School on Computational Optimization, FWF project no. W1260-N35. article_processing_charge: No arxiv: 1 author: - first_name: Sebastiano full_name: Cultrera di Montesano, Sebastiano id: 34D2A09C-F248-11E8-B48F-1D18A9856A87 last_name: Cultrera di Montesano orcid: 0000-0001-6249-0832 - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Monika H full_name: Henzinger, Monika H id: 540c9bbd-f2de-11ec-812d-d04a5be85630 last_name: Henzinger orcid: 0000-0002-5008-6530 - first_name: Lara full_name: Ost, Lara last_name: Ost citation: ama: 'Cultrera di Montesano S, Edelsbrunner H, Henzinger M, Ost L. Dynamically maintaining the persistent homology of time series. In: Woodruff DP, ed. Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). Society for Industrial and Applied Mathematics; 2024:243-295. doi:10.1137/1.9781611977912.11' apa: 'Cultrera di Montesano, S., Edelsbrunner, H., Henzinger, M., & Ost, L. (2024). Dynamically maintaining the persistent homology of time series. In D. P. Woodruff (Ed.), Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) (pp. 243–295). Alexandria, VA, USA: Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611977912.11' chicago: Cultrera di Montesano, Sebastiano, Herbert Edelsbrunner, Monika Henzinger, and Lara Ost. “Dynamically Maintaining the Persistent Homology of Time Series.” In Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), edited by David P. Woodruff, 243–95. Society for Industrial and Applied Mathematics, 2024. https://doi.org/10.1137/1.9781611977912.11. ieee: S. Cultrera di Montesano, H. Edelsbrunner, M. Henzinger, and L. Ost, “Dynamically maintaining the persistent homology of time series,” in Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Alexandria, VA, USA, 2024, pp. 243–295. ista: 'Cultrera di Montesano S, Edelsbrunner H, Henzinger M, Ost L. 2024. Dynamically maintaining the persistent homology of time series. Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). SODA: Symposium on Discrete Algorithms, 243–295.' mla: Cultrera di Montesano, Sebastiano, et al. “Dynamically Maintaining the Persistent Homology of Time Series.” Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), edited by David P. Woodruff, Society for Industrial and Applied Mathematics, 2024, pp. 243–95, doi:10.1137/1.9781611977912.11. short: S. Cultrera di Montesano, H. Edelsbrunner, M. Henzinger, L. Ost, in:, D.P. Woodruff (Ed.), Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Society for Industrial and Applied Mathematics, 2024, pp. 243–295. conference: end_date: 2024-01-10 location: Alexandria, VA, USA name: 'SODA: Symposium on Discrete Algorithms' start_date: 2024-01-07 corr_author: '1' date_created: 2024-03-08T10:27:39Z date_published: 2024-01-04T00:00:00Z date_updated: 2026-04-07T12:58:47Z day: '04' department: - _id: HeEd - _id: MoHe doi: 10.1137/1.9781611977912.11 ec_funded: 1 editor: - first_name: David P. full_name: Woodruff, David P. last_name: Woodruff external_id: arxiv: - '2311.01115' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2311.01115 month: '01' oa: 1 oa_version: Preprint page: 243 - 295 project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: Mathematics, Computer Science - _id: bd9ca328-d553-11ed-ba76-dc4f890cfe62 call_identifier: H2020 grant_number: '101019564' name: The design and evaluation of modern fully dynamic data structures - _id: 34def286-11ca-11ed-8bc3-da5948e1613c grant_number: Z00422 name: Efficient algorithms - _id: bd9e3a2e-d553-11ed-ba76-8aa684ce17fe grant_number: P33775 name: Fast Algorithms for a Reactive Network Layer publication: Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) publication_identifier: eisbn: - '9781611977912' publication_status: published publisher: Society for Industrial and Applied Mathematics quality_controlled: '1' related_material: record: - id: '15094' relation: dissertation_contains status: public scopus_import: '1' status: public title: Dynamically maintaining the persistent homology of time series type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2024' ...