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Communication Dans Un Congrès Année : 2020

Lexicographic optimal homologous chains and applications to point cloud triangulations

Résumé

This paper considers a particular case of the Optimal Homologous Chain Problem (OHCP), where optimality is meant as a minimal lexicographic order on chains induced by a total order on simplices. The matrix reduction algorithm used for persistent homology is used to derive polynomial algorithms solving this problem instance, whereas OHCP is NP-hard in the general case. The complexity is further improved to a quasilinear algorithm by leveraging a dual graph minimum cut formulation when the simplicial complex is a strongly connected pseudomanifold. We then show how this particular instance of the problem is relevant, by providing an application in the context of point cloud triangulation.
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Dates et versions

hal-02391240 , version 1 (03-12-2019)

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  • HAL Id : hal-02391240 , version 1

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David Cohen-Steiner, André Lieutier, Julien Vuillamy. Lexicographic optimal homologous chains and applications to point cloud triangulations. SoCG 2020 - 36th International Symposium on Computational Geometry, Jun 2020, Zurich, Switzerland. ⟨hal-02391240⟩
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