{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2311.01115"}],"doi":"10.1137/1.9781611977912.11","_id":"15093","type":"conference","quality_controlled":"1","title":"Dynamically maintaining the persistent homology of time series","article_processing_charge":"No","date_published":"2024-01-04T00:00:00Z","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.","status":"public","date_updated":"2024-03-20T09:36:56Z","page":"243 - 295","publication_status":"published","related_material":{"record":[{"relation":"dissertation_contains","id":"15094","status":"public"}]},"conference":{"end_date":"2024-01-10","location":"Alexandria, VA, USA","name":"SODA: Symposium on Discrete Algorigthms","start_date":"2024-01-07"},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","publication":"Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)","abstract":[{"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.","lang":"eng"}],"editor":[{"full_name":"Woodruff, David P.","last_name":"Woodruff","first_name":"David P."}],"oa_version":"Preprint","citation":{"ista":"Cultrera di Montesano S, Edelsbrunner H, Henzinger MH, 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 Algorigthms, 243–295.","ama":"Cultrera di Montesano S, Edelsbrunner H, Henzinger MH, Ost L. Dynamically maintaining the persistent homology of time series. In: Woodruff DP, ed. <i>Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)</i>. Society for Industrial and Applied Mathematics; 2024:243-295. doi:<a href=\"https://doi.org/10.1137/1.9781611977912.11\">10.1137/1.9781611977912.11</a>","apa":"Cultrera di Montesano, S., Edelsbrunner, H., Henzinger, M. H., &#38; Ost, L. (2024). Dynamically maintaining the persistent homology of time series. In D. P. Woodruff (Ed.), <i>Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)</i> (pp. 243–295). Alexandria, VA, USA: Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/1.9781611977912.11\">https://doi.org/10.1137/1.9781611977912.11</a>","chicago":"Cultrera di Montesano, Sebastiano, Herbert Edelsbrunner, Monika H Henzinger, and Lara Ost. “Dynamically Maintaining the Persistent Homology of Time Series.” In <i>Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)</i>, edited by David P. Woodruff, 243–95. Society for Industrial and Applied Mathematics, 2024. <a href=\"https://doi.org/10.1137/1.9781611977912.11\">https://doi.org/10.1137/1.9781611977912.11</a>.","short":"S. Cultrera di Montesano, H. Edelsbrunner, M.H. 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.","ieee":"S. Cultrera di Montesano, H. Edelsbrunner, M. H. Henzinger, and L. Ost, “Dynamically maintaining the persistent homology of time series,” in <i>Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)</i>, Alexandria, VA, USA, 2024, pp. 243–295.","mla":"Cultrera di Montesano, Sebastiano, et al. “Dynamically Maintaining the Persistent Homology of Time Series.” <i>Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)</i>, edited by David P. Woodruff, Society for Industrial and Applied Mathematics, 2024, pp. 243–95, doi:<a href=\"https://doi.org/10.1137/1.9781611977912.11\">10.1137/1.9781611977912.11</a>."},"publication_identifier":{"eisbn":["9781611977912"]},"ec_funded":1,"department":[{"_id":"HeEd"},{"_id":"MoHe"}],"project":[{"call_identifier":"H2020","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"The Wittgenstein Prize","call_identifier":"FWF","grant_number":"Z00342"},{"grant_number":"101019564","call_identifier":"H2020","name":"The design and evaluation of modern fully dynamic data structures","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62"},{"_id":"34def286-11ca-11ed-8bc3-da5948e1613c","name":"Wittgenstein Award - Monika Henzinger","grant_number":"Z00422"},{"grant_number":"P33775 ","name":"Fast Algorithms for a Reactive Network Layer","_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe"}],"month":"01","day":"04","year":"2024","author":[{"id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6249-0832","first_name":"Sebastiano","full_name":"Cultrera di Montesano, Sebastiano","last_name":"Cultrera di Montesano"},{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"id":"540c9bbd-f2de-11ec-812d-d04a5be85630","first_name":"Monika H","orcid":"0000-0002-5008-6530","last_name":"Henzinger","full_name":"Henzinger, Monika H"},{"last_name":"Ost","full_name":"Ost, Lara","first_name":"Lara"}],"language":[{"iso":"eng"}],"publisher":"Society for Industrial and Applied Mathematics","external_id":{"arxiv":["2311.01115"]},"date_created":"2024-03-08T10:27:39Z","oa":1}