I have a (unit) hypercube containing several points. I want to partition it, and take "slices" (also hypercubes) off it until all these previously contained points are outside the resulting final hypercube. I want to end up with the hypercube that retains the greatest volume compared to the original hypercube.
I'm looking for an algorithm that will achieve this... and finding nothing. I wonder if I were to take each point in turn, consider the hyperplane partitions I could make through that point, select the one which "shaves" the least amount of volume from the hypercube, and repeat for all points... would that be guaranteed to yield the result I seek?