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In the big picture, I'd like to know: if I sample $n$ points uniformly at random in the unit square, what is the probability that the shortest path that visits each one of them is very small? More ...

Suppose I have $n$ points $x_1,\dots,x_n$ that are all independent uniform samples in the unit square, and I'd like to find a short path (in terms of Euclidean length) that touches all of them (a ...