This is inspired by a [recent question][1].

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 solution starting at $s$?

>> Starting at $s$, pick the nearest neighbor not visited so far as the next node to visit.

**EDIT**: If the answer is no, what is the maximum value that the ratio $r$ of "nearest neighbor trip" vs "best trip" can take?

  [1]: https://mathoverflow.net/questions/210049/length-of-nearest-neighbor-path-in-travel-salesman-problem