Abstract
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 withk lines. For every fixedk in any fixed dimension, it takes polynomial time to recognize whether two sets of points can be separated withk hyperplanes.
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Megiddo, N. On the complexity of polyhedral separability. Discrete Comput Geom 3, 325–337 (1988). https://doi.org/10.1007/BF02187916
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DOI: https://doi.org/10.1007/BF02187916