A quasi-polynomial algorithm for well-spaced hyperbolic TSP: https://arxiv.org/abs/2002.05414
This new preprint by Sándor Kisfaludi-Bak (accepted to SoCG) just came out and caught my attention. TSP is NP-hard for Euclidean points or close-together hyperbolic points. This paper shows that it's much easier when the points are widely spaced in the hyperbolic plane. The idea is to separate the input by a short line segment that the solution crosses few times and apply dynamic programming.
Thanks, @11011110, that wasn't it, so there should be yet another one :) I'll make sure to tag you when I my collection grows.
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