Given $n$ nodes uniformly distributed in $[0,1]^2$, consider the nearest neighbor algorithm to solve traveling salesman problem, i.e., each time I select the nearest neighbor not visited so far as the next node to visit, my question is: what is the expected length of such TSP tour?

This is inspired by a recent question. Given a positive integer $n\in\mathbb{N}$, is there a setting of finitely many points and a designated "starting point" $s$ in $\mathbb{R}^2$ such that the nearest-neighbor algorithm (described below) gives a tour that is $n$ times longer than the optimal s...