I enjoy finding retrospectively obvious details from essays like this: an optimal solution won't have any crossing paths, and simply swapping cities is a handy

I enjoy finding retrospectively obvious details from essays like this: an optimal solution won't have any crossing paths, and simply swapping cities is a handy way to try detangling the path! The animated graphs make this plain, but is it required? Having never thought about the TSP much (and not really having the mathematical chops to prove it myself) I looked it up, and sure enough SO user lhf [0,1] had a link to a grindingly in-depth article about the problem [2]. [0] http://stackoverflow.com/questions/2444125/crossing-edges-in-the-travelling-salesman-problem http://stackoverflow.com/questions/2444125/crossing-edges-in... [1] http://stackoverflow.com/a/2444288 http://stackoverflow.com/a/2444288 [2] http://www.ams.org/samplings/feature-column/fcarc-tsp http://www.ams.org/samplings/feature-column/fcarc-tsp