On the complexity of polyhedral separability

It is NP-complete to recognize whether two sets of points in general space can be separated by two hyperplanes. It is NP-complete to recognize whether two sets of points in the plane can be separated with k lines. For every fixed k in any fixed dimension, it takes polynomial time to recognize whether two sets of points can be separated with k hyperplanes. © 1988 Springer-Verlag New York Inc.