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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.01115 |
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| _version_ | 1866929405205413888 |
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| author | di Montesano, Sebastiano Cultrera Edelsbrunner, Herbert Henzinger, Monika Ost, Lara |
| author_facet | di Montesano, Sebastiano Cultrera Edelsbrunner, Herbert Henzinger, Monika Ost, Lara |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_01115 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dynamically Maintaining the Persistent Homology of Time Series di Montesano, Sebastiano Cultrera Edelsbrunner, Herbert Henzinger, Monika Ost, Lara Data Structures and Algorithms Computational Geometry 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. |
| title | Dynamically Maintaining the Persistent Homology of Time Series |
| topic | Data Structures and Algorithms Computational Geometry |
| url | https://arxiv.org/abs/2311.01115 |