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Journal Articles Discrete and Computational Geometry Year : 2022

Lexicographic Optimal Homologous Chains and Applications to Point Cloud Triangulations

Abstract

This paper considers a particular case of the Optimal Homologous Chain Problem (OHCP) for integer modulo 2 coefficients, 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 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 and versions

hal-03870128 , version 1 (24-11-2022)

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David Cohen-Steiner, André Lieutier, Julien Vuillamy. Lexicographic Optimal Homologous Chains and Applications to Point Cloud Triangulations. Discrete and Computational Geometry, 2022, 68, ⟨10.1007/s00454-022-00432-6⟩. ⟨hal-03870128⟩
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