Faster algorithms compute the integral bottleneck distance between PHTs in Õ(n^5) time and the max version in Õ(n^3) time for R^2 and Õ(n^5) for R^3.
Asymptotic improvements on the ex- act matching distance for 2-parameter persistence.Journal of Computational Geometry, 14(1):309–342, Dec
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Computing the Bottleneck Distance between Persistent Homology Transforms
Faster algorithms compute the integral bottleneck distance between PHTs in Õ(n^5) time and the max version in Õ(n^3) time for R^2 and Õ(n^5) for R^3.