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arXiv · 2505.04048

The Kinetic Hourglass Data Structure for Computing the Bottleneck Distance of Dynamic Data

Elizabeth Munch·Elena Xinyi Wang·Carola Wenk
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Abstract

The kinetic data structure (KDS) framework is a powerful tool for maintaining various geometric configurations of continuously moving objects. In this work, we introduce the kinetic hourglass, a novel KDS implementation designed to compute the bottleneck distance for geometric matching problems. We detail the events and updates required for handling general graphs, accompanied by a complexity analysis. Furthermore, we demonstrate the utility of the kinetic hourglass by applying it to compute the bottleneck distance between two persistent homology transforms (PHTs) derived from shapes in $\mathbb{R}^2$, which are topological summaries obtained by computing persistent homology from every direction in $\mathbb{S}^1$.

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Elizabeth Munch, Elena Xinyi Wang, Carola Wenk. 2025-05-07. The Kinetic Hourglass Data Structure for Computing the Bottleneck Distance of Dynamic Data. https://arxiv.org/abs/2505.04048

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