K-set (geometry) (original) (raw)

In discrete geometry, a -set of a finite point set in the Euclidean plane is a subset of elements of that can be strictly separated from the remaining points by a line. More generally, in Euclidean space of higher dimensions, a -set of a finite point set is a subset of elements that can be separated from the remaining points by a hyperplane. In particular, when (where is the size of ), the line or hyperplane that separates a -set from the rest of is a halving line or halving plane.