Isn't that set a circle?
Re:Bellman's lost in a forest problem
by HelloNurse on Monday September 17, 2018 @10:14AM
(#18006090)
Yes, and the solution for a circle of radius r is easy(going straight, you don't need to walk more than 2r; if you turn anywhere, you risk walking more than that).
Bellman put exact knowledge of the shape of the forest in the problem statement to make it nontrivial and therefore more difficult.
If you accidentally start in the middle, there will always be a worst case scenario route determined for any arbitrary curve and no way to pick between curves to find the best one.