In numerous fields, dynamic time series data require continuous updates, necessitating efficient data processing techniques for accurate analysis. This paper examines the banana tree data structure, specifically designed to efficiently maintain persistent homology -- a multi-scale topological descriptor -- for dynamically changing time series data. We implement this data structure and conduct an experimental study to assess its properties and runtime for update operations. Our findings indicate that banana trees are highly effective with unbiased random data, outperforming state-of-the-art static algorithms in these scenarios. Additionally, our results show that real-world time series share structural properties with unbiased random walks, suggesting potential practical utility for our implementation.

翻译：在许多领域中，动态时间序列数据需要持续更新，这要求采用高效的数据处理技术以进行精确分析。本文研究了香蕉树数据结构，该结构专门设计用于高效维护动态变化时间序列数据的持续性同调——一种多尺度拓扑描述符。我们实现了该数据结构，并通过实验研究评估了其更新操作的特性和运行时间。研究结果表明，香蕉树在处理无偏随机数据时表现出色，在这些场景中优于最先进的静态算法。此外，我们的结果显示真实世界时间序列具有与无偏随机游走相似的结构特性，这表明我们的实现具有潜在的实际应用价值。