Merge trees of periodic filtrations
Edelsbrunner H, Heiss T. Merge trees of periodic filtrations. arXiv, 10.48550/arXiv.2408.16575.
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Abstract
Motivated by applications to crystalline materials, we generalize the merge tree and the related barcode of a filtered complex to the periodic setting in Euclidean space. They are invariant under isometries, changing bases, and indeed changing lattices. In addition, we prove stability under perturbations and provide an algorithm that under mild geometric conditions typically satisfied by crystalline materials takes O((n+m)logn) time, in which n and m are the numbers of vertices and edges in the quotient complex, respectively.
Publishing Year
Date Published
2024-08-29
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arXiv
Acknowledgement
Both authors are partially supported by the European Research Council (ERC) Horizon 2020 project
‘Alpha Shape Theory Extended’, grant no. 788183. The first author is also partially supported by the DFG
Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund
(FWF), grant no. I 02979-N35.
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Cite this
Edelsbrunner H, Heiss T. Merge trees of periodic filtrations. arXiv. doi:10.48550/arXiv.2408.16575
Edelsbrunner, H., & Heiss, T. (n.d.). Merge trees of periodic filtrations. arXiv. https://doi.org/10.48550/arXiv.2408.16575
Edelsbrunner, Herbert, and Teresa Heiss. “Merge Trees of Periodic Filtrations.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2408.16575.
H. Edelsbrunner and T. Heiss, “Merge trees of periodic filtrations,” arXiv. .
Edelsbrunner H, Heiss T. Merge trees of periodic filtrations. arXiv, 10.48550/arXiv.2408.16575.
Edelsbrunner, Herbert, and Teresa Heiss. “Merge Trees of Periodic Filtrations.” ArXiv, doi:10.48550/arXiv.2408.16575.
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