Persistent homology inmetric

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Gabriele Beltramo, Primoz Skraba

Published: 2022, Last Modified: 05 Nov 2025Comput. Geom. 2022EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: Highlights•A counterexample to Alpha and Čech filtrations equivalence in Chebyshev distance.•Definition of Alpha flag and Minibox complexes.•Algorithms to find Minibox edges in two, three, and higher dimensions.•Alpha flag, Minibox, and Čech complexes have same 0 and 1-persistence diagrams.•Minibox filtrations speed up persistence computations.