Determine whether the two classes are linearly separable (algorithmically in 2D)

Question

There are two classes, let\'s call them X and O. A number of elements belonging to these classes are spread out in the xy-plane. Here is an example where the two classes are

Answer 1

You can probably apply linear programming to this problem. I'm not sure of its computational complexity in formal terms, but the technique is successfully applied to very large problems covering a wide range of domains.