On the co-NP-Completeness of the Zonotope Containment Problem

We introduce a new type of norm for non-degenerate zonotopes to solve the point containment problem, i.e., whether a point lies in a zonotope. With this norm we prove the co-NP-completeness of the zonotope containment problem, i.e., whether a zonotope is contained within another one. We propose novel algorithms to solve the zonotope containment problem exactly in polynomial time when fixing the dimension or the number of generators of either of the two zonotopes. In addition, we propose an optimisation-based algorithm, that is particularly suitable for disproving containment for zonotopes.     «

We introduce a new type of norm for non-degenerate zonotopes to solve the point containment problem, i.e., whether a point lies in a zonotope. With this norm we prove the co-NP-completeness of the zonotope containment problem, i.e., whether a zonotope is contained within another one. We propose novel algorithms to solve the zonotope containment problem exactly in polynomial time when fixing the dimension or the number of generators of either of the two zonotopes. In addition, we propose an optim...     »