4 ms·

If any path segments/lines intersect/cross on any plane, then the path is not a solution.

• bmm6o 10y ago
  I think the point is that random lines in space (dimension > 2) intersect with probability 0, and so that shortcut almost never applies.
  • jsprogrammer 10y ago
    You should be able to "wrap a hull" around all the points. If there is no hull that can be wrapped without intersecting a path segment, the path is not a solution. Basically you are checking for line-plane intersections. A solution should outline a "non-self-intersecting volume".
    • yongjik 10y ago
      Defining a convex hull in a 100-dimensional space requires 101 points. You can easily have a scenario where the only available "convex hull" is the one that contains the entire graph. In fact, I'm sure that a "randomly chosen" metric graph will be of this variety.
      • jsprogrammer 10y ago
        Sounds like something that would be easy to simulate and measure. Also, the hull needn't be convex.