Quote:
Originally Posted by ilya239
So once the set of N points is fixed, and we pick different subsets of the N points and try to cover them with "donuts"  all donuts must be centered at the same point? We can't use a donut centered at p1 to cover {x1,x2} but a donut centered at a different point p2 to cover {x3,x4}? In other words, after picking N points, we pick ONE origin, and _then_ can pick donuts centered at that origin only?

Correct. You can choose any
points you want to work with (with a view to maximizing the number of dichotomies), so the origin is effectively arbitrary, but fixed, for a given set of points.