conference paper published yes Sebastiano Cultrera di Montesano author 34D2A09C-F248-11E8-B48F-1D18A9856A870000-0001-6249-0832 Herbert Edelsbrunner author 3FB178DA-F248-11E8-B48F-1D18A9856A870000-0002-9823-6833 Monika H Henzinger author 540c9bbd-f2de-11ec-812d-d04a5be856300000-0002-5008-6530 Lara Ost author David P.Woodruff editor HeEd department MoHe department SODA: Symposium on Discrete Algorithms Alpha Shape Theory Extended project Mathematics, Computer Science project The design and evaluation of modern fully dynamic data structures project Efficient algorithms project Fast Algorithms for a Reactive Network Layer project 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. Society for Industrial and Applied Mathematics2024Alexandria, VA, USA eng 2311.0111510.1137/1.9781611977912.11 243 - 295 https://research-explorer.ista.ac.at/record/15094 Cultrera di Montesano, S., Edelsbrunner, H., Henzinger, M., &#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> 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. Cultrera di Montesano S, Edelsbrunner H, Henzinger M, 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> 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. S. Cultrera di Montesano, H. Edelsbrunner, M. 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. Cultrera di Montesano, Sebastiano, Herbert Edelsbrunner, Monika 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>. 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>. 150932024-03-08T10:27:39Z2026-04-07T12:58:47Z