It seems intuitive to solve a 2D dot-to-dot travelling salesman problem by eye using a greedy strategy. However we can only solve the TSP by eye if the graph is topographically accurate e.g. if A to B is 10 and A to C is 10 then B to C can't be 1000.
Is the greedy strategy still sub-optimal when we obey 2D scaling, ie travelling by plane? Below I managed to create a topographically accurate example where the greedy strategy is indeed sub optimal:
Starting at S:
S B C A S=> 2.83 + 4 + 5 + 2.2 => 14.03
S A B C S=> 2.2 + 3 + 4 + 3.16 => 12.36
Is there something special about the example above that will be common to all suboptimal greedy routes? Can geometry be used to minimize error?