We study the traveling salesman problem in the hyperbolic plane of Gaussian
curvature −1. Let α denote the minimum distance between any two input
points. Using a new separator theorem and a new rerouting argument, we give an
nO(log2n)max(1,1/α) algorithm for Hyperbolic TSP. This is
quasi-polynomial time if α is at least some absolute constant, and it
grows to nO(n) as α decreases to log2n/n. (For
even smaller values of α, we can use a planarity-based algorithm of
Hwang et al. (1993), which gives a running time of nO(n).)Comment: SoCG 202