Building and using polyhedral hierarchies

In this paper, we study some relationships between polyhedral convex sets and generalized polyhedral convex sets. In particular, we clarify by a counterexample that the necessary and sufficient conditions for the separation of a convex set and a ...

Let B^n be a hyperball in R^n, n>=2, and denote B"Z^n=B^n@?Z^n. Define polyhedral facet complexity of B"Z^n as FC(B"Z^n)=min"P{f"n"-"1(P)} where P is an enclosing polyhedron for B"Z^n (i.e., P"Z=P@?Z^n=B"Z^n) and f"n"-"1(P) is the number of the (n-1)-...

The $$W_v$$Wv-path conjecture due to Klee and Wolfe states that any two vertices of a simple polytope can be joined by a path that does not revisit any facet. This is equivalent to the well-known Hirsch conjecture. Klee proved that the $$W_v$$Wv-path ...