Cycle-free cuts of mutual rank probability relations

Cycle-free cuts of mutual rank probability relations

It is well known that the linear extension majority (LEM) relation of a poset of size n ≥ 9 can contain cycles. In this paper we are interested in obtaining minimum cutting levels αm such that the crisp relation obtained from the mutual rank probability relation by setting to 0 its elements smaller than or equal to αm, and to 1 its other elements, is free from cycles of length m. In a first par...

Chvatal Rank 1 Cuts and Combinatorial Bender ’ s Cuts

On the Rank of Disjunctive Cuts

Let L be a family of lattice-free polyhedra in R containing the splits. Given a polyhedron P in R, we characterize when a valid inequality for P ∩(Z×R) can be obtained with a finite number of disjunctive cuts corresponding to the polyhedra in L. We also characterize the lattice-free polyhedra M such that all the disjunctive cuts corresponding to M can be obtained with a finite number of disjunc...

Inferring High-Dimensional Causal Relations using Free Probability Theory

Intersection Cuts with Infinite Split Rank

We consider mixed integer linear programs where free integer variables are expressed in terms of nonnegative continuous variables. When this model only has two integer variables, Dey and Louveaux characterized the intersection cuts that have infinite split rank. We show that, for any number of integer variables, the split rank of an intersection cut generated from a rational lattice-free polyto...