[{"publisher":"Society for Industrial & Applied Mathematics","page":"220-233","quality_controlled":"1","ec_funded":1,"publication_status":"published","department":[{"_id":"MoHe"}],"article_processing_charge":"No","date_created":"2024-01-09T16:22:47Z","title":"Experimental evaluation of fully dynamic k-means via coresets","_id":"14769","scopus_import":"1","author":[{"last_name":"Henzinger","first_name":"Monika H","full_name":"Henzinger, Monika H","orcid":"0000-0002-5008-6530","id":"540c9bbd-f2de-11ec-812d-d04a5be85630"},{"first_name":"David","last_name":"Saulpic","full_name":"Saulpic, David","id":"f8e48cf0-b0ff-11ed-b0e9-b4c35598f964"},{"id":"8b563fd0-b441-11ee-9101-a3891c61efa6","full_name":"Sidl, Leonhard","last_name":"Sidl","first_name":"Leonhard"}],"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.","doi":"10.1137/1.9781611977929.17","arxiv":1,"day":"04","abstract":[{"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.","lang":"eng"}],"date_updated":"2025-07-15T12:51:52Z","year":"2024","citation":{"chicago":"Henzinger, Monika H, David Saulpic, and Leonhard Sidl. “Experimental Evaluation of Fully Dynamic K-Means via Coresets.” In <i>2024 Proceedings of the Symposium on Algorithm Engineering and Experiments</i>, 220–33. Society for Industrial &#38; Applied Mathematics, 2024. <a href=\"https://doi.org/10.1137/1.9781611977929.17\">https://doi.org/10.1137/1.9781611977929.17</a>.","ieee":"M. H. Henzinger, D. Saulpic, and L. Sidl, “Experimental evaluation of fully dynamic k-means via coresets,” in <i>2024 Proceedings of the Symposium on Algorithm Engineering and Experiments</i>, Alexandria, VA, United States, 2024, pp. 220–233.","apa":"Henzinger, M. H., Saulpic, D., &#38; Sidl, L. (2024). Experimental evaluation of fully dynamic k-means via coresets. In <i>2024 Proceedings of the Symposium on Algorithm Engineering and Experiments</i> (pp. 220–233). Alexandria, VA, United States: Society for Industrial &#38; Applied Mathematics. <a href=\"https://doi.org/10.1137/1.9781611977929.17\">https://doi.org/10.1137/1.9781611977929.17</a>","ama":"Henzinger MH, Saulpic D, Sidl L. Experimental evaluation of fully dynamic k-means via coresets. In: <i>2024 Proceedings of the Symposium on Algorithm Engineering and Experiments</i>. Society for Industrial &#38; Applied Mathematics; 2024:220-233. doi:<a href=\"https://doi.org/10.1137/1.9781611977929.17\">10.1137/1.9781611977929.17</a>","ista":"Henzinger MH, 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.","short":"M.H. Henzinger, D. Saulpic, L. Sidl, in:, 2024 Proceedings of the Symposium on Algorithm Engineering and Experiments, Society for Industrial &#38; Applied Mathematics, 2024, pp. 220–233.","mla":"Henzinger, Monika H., et al. “Experimental Evaluation of Fully Dynamic K-Means via Coresets.” <i>2024 Proceedings of the Symposium on Algorithm Engineering and Experiments</i>, Society for Industrial &#38; Applied Mathematics, 2024, pp. 220–33, doi:<a href=\"https://doi.org/10.1137/1.9781611977929.17\">10.1137/1.9781611977929.17</a>."},"external_id":{"arxiv":["2310.18034"]},"conference":{"end_date":"2024-01-08","location":"Alexandria, VA, United States","start_date":"2024-01-07","name":"ALENEX: Workshop on Algorithm Engineering and Experiments"},"language":[{"iso":"eng"}],"oa_version":"Preprint","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":"Wittgenstein Award - Monika Henzinger"},{"_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103","name":"Static and Dynamic Hierarchical Graph Decompositions","grant_number":"I05982"},{"grant_number":"P33775 ","name":"Fast Algorithms for a Reactive Network Layer","_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe"},{"name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"month":"01","publication":"2024 Proceedings of the Symposium on Algorithm Engineering and Experiments","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2310.18034"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","publication_identifier":{"eisbn":["9781611977929"]},"oa":1,"date_published":"2024-01-04T00:00:00Z","type":"conference"},{"author":[{"last_name":"Goranci","first_name":"Gramoz","full_name":"Goranci, Gramoz"},{"id":"540c9bbd-f2de-11ec-812d-d04a5be85630","orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H","first_name":"Monika H","last_name":"Henzinger"},{"full_name":"Räcke, Harald","last_name":"Räcke","first_name":"Harald"},{"last_name":"Sachdeva","first_name":"Sushant","full_name":"Sachdeva, Sushant"},{"first_name":"A. R.","last_name":"Sricharan","full_name":"Sricharan, A. R."}],"scopus_import":"1","_id":"15008","intvolume":"       287","alternative_title":["LIPIcs"],"title":"Electrical flows for polylogarithmic competitive oblivious routing","article_processing_charge":"No","date_created":"2024-02-18T23:01:02Z","department":[{"_id":"MoHe"}],"publication_status":"published","file_date_updated":"2024-02-26T10:10:48Z","quality_controlled":"1","ec_funded":1,"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","external_id":{"arxiv":["2303.02491"]},"citation":{"chicago":"Goranci, Gramoz, Monika H Henzinger, Harald Räcke, Sushant Sachdeva, and A. R. Sricharan. “Electrical Flows for Polylogarithmic Competitive Oblivious Routing.” In <i>15th Innovations in Theoretical Computer Science Conference</i>, Vol. 287. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. <a href=\"https://doi.org/10.4230/LIPIcs.ITCS.2024.55\">https://doi.org/10.4230/LIPIcs.ITCS.2024.55</a>.","ieee":"G. Goranci, M. H. Henzinger, H. Räcke, S. Sachdeva, and A. R. Sricharan, “Electrical flows for polylogarithmic competitive oblivious routing,” in <i>15th Innovations in Theoretical Computer Science Conference</i>, Berkeley, CA, United States, 2024, vol. 287.","ama":"Goranci G, Henzinger MH, Räcke H, Sachdeva S, Sricharan AR. Electrical flows for polylogarithmic competitive oblivious routing. In: <i>15th Innovations in Theoretical Computer Science Conference</i>. Vol 287. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:<a href=\"https://doi.org/10.4230/LIPIcs.ITCS.2024.55\">10.4230/LIPIcs.ITCS.2024.55</a>","apa":"Goranci, G., Henzinger, M. H., Räcke, H., Sachdeva, S., &#38; Sricharan, A. R. (2024). Electrical flows for polylogarithmic competitive oblivious routing. In <i>15th Innovations in Theoretical Computer Science Conference</i> (Vol. 287). Berkeley, CA, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.ITCS.2024.55\">https://doi.org/10.4230/LIPIcs.ITCS.2024.55</a>","ista":"Goranci G, Henzinger MH, 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 Conference, LIPIcs, vol. 287, 55.","short":"G. Goranci, M.H. Henzinger, H. Räcke, S. Sachdeva, A.R. Sricharan, in:, 15th Innovations in Theoretical Computer Science Conference, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.","mla":"Goranci, Gramoz, et al. “Electrical Flows for Polylogarithmic Competitive Oblivious Routing.” <i>15th Innovations in Theoretical Computer Science Conference</i>, vol. 287, 55, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:<a href=\"https://doi.org/10.4230/LIPIcs.ITCS.2024.55\">10.4230/LIPIcs.ITCS.2024.55</a>."},"year":"2024","date_updated":"2025-07-15T12:51:53Z","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."}],"day":"24","arxiv":1,"doi":"10.4230/LIPIcs.ITCS.2024.55","ddc":["000"],"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.","volume":287,"has_accepted_license":"1","publication":"15th Innovations in Theoretical Computer Science Conference","article_number":"55","month":"01","project":[{"call_identifier":"H2020","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","name":"The design and evaluation of modern fully dynamic data structures","grant_number":"101019564"},{"grant_number":"Z00422","name":"Wittgenstein Award - Monika Henzinger","_id":"34def286-11ca-11ed-8bc3-da5948e1613c"},{"_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103","grant_number":"I05982","name":"Static and Dynamic Hierarchical Graph Decompositions"},{"name":"Fast Algorithms for a Reactive Network Layer","grant_number":"P33775 ","_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe"}],"oa_version":"Published Version","language":[{"iso":"eng"}],"conference":{"location":"Berkeley, CA, United States","end_date":"2024-02-02","name":"ITCS: Innovations in Theoretical Computer Science Conference","start_date":"2024-01-30"},"type":"conference","date_published":"2024-01-24T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"publication_identifier":{"issn":["1868-8969"],"isbn":["9783959773096"]},"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"date_updated":"2024-02-26T10:10:48Z","file_name":"2024_LIPICs_Goranci.pdf","content_type":"application/pdf","date_created":"2024-02-26T10:10:48Z","file_size":1054754,"checksum":"b89716aae6a5599f187897e39de1e53a","file_id":"15030","creator":"dernst","relation":"main_file","access_level":"open_access","success":1}]},{"conference":{"start_date":"2023-07-23","name":"ICML: International Conference on Machine Learning","location":"Honolulu, Hawaii, HI, United States","end_date":"2023-07-29"},"language":[{"iso":"eng"}],"oa_version":"Published Version","project":[{"name":"The design and evaluation of modern fully dynamic data structures","grant_number":"101019564","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","call_identifier":"H2020"},{"_id":"34def286-11ca-11ed-8bc3-da5948e1613c","name":"Wittgenstein Award - Monika Henzinger","grant_number":"Z00422"},{"name":"Fast Algorithms for a Reactive Network Layer","grant_number":"P33775 ","_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe"}],"month":"07","publication":"Proceedings of the 40th International Conference on Machine Learning","main_file_link":[{"open_access":"1","url":"https://proceedings.mlr.press/v202/fichtenberger23a/fichtenberger23a.pdf"}],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"eissn":["2640-3498"]},"oa":1,"date_published":"2023-07-30T00:00:00Z","type":"conference","publisher":"ML Research Press","page":"10072-10092","ec_funded":1,"quality_controlled":"1","publication_status":"published","date_created":"2023-10-29T23:01:17Z","article_processing_charge":"No","department":[{"_id":"MoHe"}],"title":"Constant matters: Fine-grained error bound on differentially private continual observation","alternative_title":["PMLR"],"intvolume":"       202","_id":"14462","scopus_import":"1","author":[{"full_name":"Fichtenberger, Hendrik","last_name":"Fichtenberger","first_name":"Hendrik"},{"id":"540c9bbd-f2de-11ec-812d-d04a5be85630","first_name":"Monika H","last_name":"Henzinger","orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H"},{"full_name":"Upadhyay, Jalaj","last_name":"Upadhyay","first_name":"Jalaj"}],"acknowledgement":"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.\r\n101019564 “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. 2020–2024. JU’s research was funded by Decanal Research Grant. A part of this work was done when JU was visiting Indian Statistical Institute, Delhi. The authors would like to thank Rajat Bhatia, Aleksandar Nikolov, Shanta Laisharam, Vern Paulsen, Ryan Rogers, Abhradeep Thakurta, and Sarvagya Upadhyay for useful discussions.","volume":202,"day":"30","abstract":[{"text":"We study fine-grained error bounds for differentially private algorithms for counting under continual observation. Our main insight is that the matrix mechanism when using lower-triangular matrices can be used in the continual observation model. More specifically, we give an explicit factorization for the counting matrix Mcount and upper bound the error explicitly. We also give a fine-grained analysis, specifying the exact constant in the upper bound. Our analysis is based on upper and lower bounds of the completely bounded norm (cb-norm) of Mcount\r\n. Along the way, we improve the best-known bound of 28 years by Mathias (SIAM Journal on Matrix Analysis and Applications, 1993) on the cb-norm of Mcount for a large range of the dimension of Mcount. Furthermore, we are the first to give concrete error bounds for various problems under continual observation such as binary counting, maintaining a histogram, releasing an approximately cut-preserving synthetic graph, many graph-based statistics, and substring and episode counting. Finally, we note that our result can be used to get a fine-grained error bound for non-interactive local learning and the first lower bounds on the additive error for (ϵ,δ)-differentially-private counting under continual observation. Subsequent to this work, Henzinger et al. (SODA, 2023) showed that our factorization also achieves fine-grained mean-squared error.","lang":"eng"}],"date_updated":"2025-07-15T12:51:52Z","year":"2023","citation":{"ista":"Fichtenberger H, Henzinger MH, Upadhyay J. 2023. Constant matters: Fine-grained error bound on differentially private continual observation. Proceedings of the 40th International Conference on Machine Learning. ICML: International Conference on Machine Learning, PMLR, vol. 202, 10072–10092.","mla":"Fichtenberger, Hendrik, et al. “Constant Matters: Fine-Grained Error Bound on Differentially Private Continual Observation.” <i>Proceedings of the 40th International Conference on Machine Learning</i>, vol. 202, ML Research Press, 2023, pp. 10072–92.","short":"H. Fichtenberger, M.H. Henzinger, J. Upadhyay, in:, Proceedings of the 40th International Conference on Machine Learning, ML Research Press, 2023, pp. 10072–10092.","ieee":"H. Fichtenberger, M. H. Henzinger, and J. Upadhyay, “Constant matters: Fine-grained error bound on differentially private continual observation,” in <i>Proceedings of the 40th International Conference on Machine Learning</i>, Honolulu, Hawaii, HI, United States, 2023, vol. 202, pp. 10072–10092.","chicago":"Fichtenberger, Hendrik, Monika H Henzinger, and Jalaj Upadhyay. “Constant Matters: Fine-Grained Error Bound on Differentially Private Continual Observation.” In <i>Proceedings of the 40th International Conference on Machine Learning</i>, 202:10072–92. ML Research Press, 2023.","apa":"Fichtenberger, H., Henzinger, M. H., &#38; Upadhyay, J. (2023). Constant matters: Fine-grained error bound on differentially private continual observation. In <i>Proceedings of the 40th International Conference on Machine Learning</i> (Vol. 202, pp. 10072–10092). Honolulu, Hawaii, HI, United States: ML Research Press.","ama":"Fichtenberger H, Henzinger MH, Upadhyay J. Constant matters: Fine-grained error bound on differentially private continual observation. In: <i>Proceedings of the 40th International Conference on Machine Learning</i>. Vol 202. ML Research Press; 2023:10072-10092."}},{"language":[{"iso":"eng"}],"month":"10","oa_version":"None","project":[{"_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","call_identifier":"H2020","name":"The design and evaluation of modern fully dynamic data structures","grant_number":"101019564"},{"_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe","name":"Fast Algorithms for a Reactive Network Layer","grant_number":"P33775 "},{"_id":"34def286-11ca-11ed-8bc3-da5948e1613c","name":"Wittgenstein Award - Monika Henzinger","grant_number":"Z00422"},{"_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103","grant_number":"I05982","name":"Static and Dynamic Hierarchical Graph Decompositions"}],"publication":"SIAM Journal on Computing","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"eissn":["1095-7111"],"issn":["0097-5397"]},"date_published":"2023-10-01T00:00:00Z","type":"journal_article","article_type":"original","publisher":"Society for Industrial and Applied Mathematics","page":"1132-1192","ec_funded":1,"quality_controlled":"1","title":"Deterministic near-optimal approximation algorithms for dynamic set cover","intvolume":"        52","publication_status":"published","department":[{"_id":"MoHe"}],"date_created":"2023-11-19T23:00:56Z","article_processing_charge":"No","author":[{"first_name":"Sayan","last_name":"Bhattacharya","full_name":"Bhattacharya, Sayan"},{"orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H","first_name":"Monika H","last_name":"Henzinger","id":"540c9bbd-f2de-11ec-812d-d04a5be85630"},{"first_name":"Danupon","last_name":"Nanongkai","full_name":"Nanongkai, Danupon"},{"last_name":"Wu","first_name":"Xiaowei","full_name":"Wu, Xiaowei"}],"issue":"5","_id":"14558","scopus_import":"1","acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grants 715672 and\r\n101019564 ``The Design of Modern Fully Dynamic Data Structures (MoDynStruct)\"\") and from the Engineering and Physical Sciences Research Council, UK (EPSRC) under grant EP/S03353X/1. The second author was also supported by 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, project ``Static and Dynamic Hierarchical Graph Decompositions,\"\"I 5982-N, and project Z 422-N. The third author was also supported by the Swedish Research Council (Reg. No. 2015-04659). The fourth author was also supported by the Science and Technology Development Fund (FDCT), Macau SAR (file 0014/2022/AFJ, 0085/2022/A, 0143/2020/A3, and SKL-IOTSC-2021-2023).","volume":52,"abstract":[{"lang":"eng","text":"n the dynamic minimum set cover problem, the challenge is to minimize the update time while guaranteeing a close-to-optimal min{O(log n), f} approximation factor. (Throughout, n, m, f , and C are parameters denoting the maximum number of elements, the number of sets, the frequency, and the cost range.) In the high-frequency range, when f = Ω(log n) , this was achieved by a deterministic O(log n) -approximation algorithm with O(f log n) amortized update time by Gupta et al. [Online and dynamic algorithms for set cover, in Proceedings STOC 2017, ACM, pp. 537–550]. In this paper we consider the low-frequency range, when f = O(log n) , and obtain deterministic algorithms with a (1 + ∈)f -approximation ratio and the following guarantees on the update time. (1)  O ((f/∈)-log(Cn)) amortized update time: Prior to our work, the best approximation ratio guaranteed by deterministic algorithms was O(f2) of Bhattacharya, Henzinger, and Italiano [Design of dynamic algorithms via primal-dual method, in Proceedings ICALP 2015, Springer, pp. 206–218]. In contrast, the only result with O(f) -approximation was that of Abboud et al. [Dynamic set cover: Improved algorithms and lower bounds, in Proceedings STOC 2019, ACM, pp. 114–125], who designed a randomized (1+∈)f -approximation algorithm with  amortized update time. (2) O(f2/∈3 + (f/∈2).logC) amortized update time: This result improves the above update time bound for most values of f\r\n in the low-frequency range, i.e., f=o(log n) . It is also the first result that is independent of m\r\n and n. It subsumes the constant amortized update time of Bhattacharya and Kulkarni [Deterministically maintaining a (2 + ∈) -approximate minimum vertex cover in O(1/∈2) amortized update time, in Proceedings SODA 2019, SIAM, pp. 1872–1885] for unweighted dynamic vertex cover (i.e., when f = 2 and C = 1). (3) O((f/∈3).log2(Cn)) worst-case update time: No nontrivial worst-case update time was previously known for the dynamic set cover problem. Our bound subsumes and improves by a logarithmic factor the O(log3n/poly (∈)) \r\n worst-case update time for the unweighted dynamic vertex cover problem (i.e., when f = 2\r\n and C =1) of Bhattacharya, Henzinger, and Nanongkai [Fully dynamic approximate maximum matching and minimum vertex cover in O(log3)n worst case update time, in Proceedings SODA 2017, SIAM, pp. 470–489]. We achieve our results via the primal-dual approach, by maintaining a fractional packing solution as a dual certificate. Prior work in dynamic algorithms that employs the primal-dual approach uses a local update scheme that maintains relaxed complementary slackness conditions for every set. For our first result we use instead a global update scheme that does not always maintain complementary slackness conditions. For our second result we combine the global and the local update schema. To achieve our third result we use a hierarchy of background schedulers. It is an interesting open question whether this background scheduler technique can also be used to transform algorithms with amortized running time bounds into algorithms with worst-case running time bounds."}],"doi":"10.1137/21M1428649","day":"01","date_updated":"2025-07-15T12:51:52Z","citation":{"ieee":"S. Bhattacharya, M. H. Henzinger, D. Nanongkai, and X. Wu, “Deterministic near-optimal approximation algorithms for dynamic set cover,” <i>SIAM Journal on Computing</i>, vol. 52, no. 5. Society for Industrial and Applied Mathematics, pp. 1132–1192, 2023.","chicago":"Bhattacharya, Sayan, Monika H Henzinger, Danupon Nanongkai, and Xiaowei Wu. “Deterministic Near-Optimal Approximation Algorithms for Dynamic Set Cover.” <i>SIAM Journal on Computing</i>. Society for Industrial and Applied Mathematics, 2023. <a href=\"https://doi.org/10.1137/21M1428649\">https://doi.org/10.1137/21M1428649</a>.","apa":"Bhattacharya, S., Henzinger, M. H., Nanongkai, D., &#38; Wu, X. (2023). Deterministic near-optimal approximation algorithms for dynamic set cover. <i>SIAM Journal on Computing</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/21M1428649\">https://doi.org/10.1137/21M1428649</a>","ama":"Bhattacharya S, Henzinger MH, Nanongkai D, Wu X. Deterministic near-optimal approximation algorithms for dynamic set cover. <i>SIAM Journal on Computing</i>. 2023;52(5):1132-1192. doi:<a href=\"https://doi.org/10.1137/21M1428649\">10.1137/21M1428649</a>","ista":"Bhattacharya S, Henzinger MH, Nanongkai D, Wu X. 2023. Deterministic near-optimal approximation algorithms for dynamic set cover. SIAM Journal on Computing. 52(5), 1132–1192.","short":"S. Bhattacharya, M.H. Henzinger, D. Nanongkai, X. Wu, SIAM Journal on Computing 52 (2023) 1132–1192.","mla":"Bhattacharya, Sayan, et al. “Deterministic Near-Optimal Approximation Algorithms for Dynamic Set Cover.” <i>SIAM Journal on Computing</i>, vol. 52, no. 5, Society for Industrial and Applied Mathematics, 2023, pp. 1132–92, doi:<a href=\"https://doi.org/10.1137/21M1428649\">10.1137/21M1428649</a>."},"year":"2023"}]