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.
Persistent homology and Euler integral transforms.Journal of Applied and Computational Topology, 2(1):55–60, Oct 2018
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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.