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arXiv · 2311.01115

Dynamically Maintaining the Persistent Homology of Time Series

Sebastiano Cultrera di Montesano·Herbert Edelsbrunner·Monika Henzinger·Lara Ost
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Abstract

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.

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Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, Monika Henzinger, Lara Ost. 2023-11-02. Dynamically Maintaining the Persistent Homology of Time Series. https://arxiv.org/abs/2311.01115

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