Combinatorial types of bicyclic polytopes

Combinatorial Aspects of Convex Polytopes

Some Examples for Combinatorial Faces of Combinatorial Polytopes

DIRK OLIVER THEIS ABSTRACT. Let P be a d-dimensional polyhedron in Rd and S a non-empty proper face. The trivial fact that every linear inequality which is valid for P is also valid for P is can be understood as a projective mapping π : P → S from the polar of P to the polar of S. This mapping defines a subdivision of S by taking all intersections of images of faces of P. In this paper we inves...

On the Extension Complexity of Combinatorial Polytopes

In this paper we extend recent results of Fiorini et al. on the extension complexity of the cut polytope and related polyhedra. We first describe a lifting argument to show exponential extension complexity for a number of NP-complete problems including subset-sum and three dimensional matching. We then obtain a relationship between the extension complexity of the cut polytope of a graph and tha...

The combinatorial stages of chromatic scheduling polytopes

Chromatic scheduling polytopes arise as solution sets of the bandwidth allocation problem in certain radio access networks. This problem is NP-hard, and admits no polynomial time algorithms with a fixed approximation ratio. As algorithms based on cutting planes have shown to be successful for many other combinatorial optimization problems, the goal is to apply such methods to the bandwidth allo...

Combinatorial equivalence of Chromatic Scheduling Polytopes

Point-to-Multipoint systems are one kind of radio systems supplying wireless access to voice/data communication networks. Capacity constraints typically force the reuse of frequencies but, on the other hand, no interference must be caused thereby. This leads to the bandwidth allocation problem, a special case of so-called chromatic scheduling problems. Both problems are NP-Hard, and there exist...