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Banana Trees for the Persistence in Time Series Experimentally

Authors Lara Ost , Sebastiano Cultrera di Montesano , Herbert Edelsbrunner

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ACM Subject Classification
  • Theory of computation → Computational geometry
  • Mathematics of computing → Topology
Keywords
  • persistent homology
  • time series
  • data structures
  • computational experiments

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Abstract

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 the multi-scale topological descriptor commonly known as persistent homology 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.

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Lara Ost, Sebastiano Cultrera di Montesano, and Herbert Edelsbrunner. Banana Trees for the Persistence in Time Series Experimentally. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 71:1-71:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SoCG.2025.71

Author Details

Lara Ost
  • Faculty of Computer Science, Doctoral School Computer Science, University of Vienna, Austria
Sebastiano Cultrera di Montesano
  • Eric and Wendy Schmidt Center, Broad Institute of MIT, Cambridge, MA, USA
  • Harvard, Cambridge, MS, USA
Herbert Edelsbrunner
  • IST Austria (Institute of Science and Technology Austria), Klosterneuburg, Austria

Funding

  • Ost, Lara: Supported by the Vienna Graduate School on Computational Optimization (VGSCO), FWF project no. W1260-N35.
  • Cultrera di Montesano, Sebastiano: Supported by the Eric and Wendy Schmidt Center at the Broad Institute of MIT and Harvard.
  • Edelsbrunner, Herbert: Partially supported 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.

Supplementary Materials

References

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