Algorithm to find two points furthest away from each other

Question

Im looking for an algorithm to be used in a racing game Im making. The map/level/track is randomly generated so I need to find two locations, start and goal, that makes use

Answer 1

It sounds like what you want is the end points separated by the graph diameter. A fairly good and easy to compute approximation is to pick a random point, find the farthest point from that, and then find the farthest point from there. These last two points should be close to maximally separated.

For a rectangular maze, this means that two flood fills should get you a pretty good pair of starting and ending points.