Algorithms for finding connected separators between antipodal points

A set (or a collection of sets) contained in the Euclidean space R m is symmetric if it is invariant under the antipodal map. Given a symmetric unicoherent polyhedron X (like an n-dimensional cube or a sphere) and an odd real function f defined on vertices of a certain symmetric triangulation of X, we algorithmically construct a connected symmetric separator of X by choosing a subcollection of the triangulation. Each element of the subcollection contains the vertices v and u such that f ( v ) f ( u ) ⩽ 0 .