We consider three well-studied polyhedral relaxations for the maximum cut problem: the metric polytope of the complete graph, the metric polytope of a general graph, and the relaxation of the bipartite subgraph polytope. The metric polytope of the complete graph can be described with a polynomial

We present a general framework for designing semidefinite relaxations for constrained 0-1 quadratic programming and show how valid inequalities of the cut--polytope can be used to strengthen these relaxations. As examples we improve the #--function and give a semidefinite relaxation

optimal” solution of the basic semidefinite Max-Cut relaxation, strengthened by triangle inequalities. The expensive part of our bounding procedure is solving the basic semidefinite relaxation of the Max-Cut problem, which has to be done several times during the bound-ing process. We review other solution

of gradually tighter polyhedral relaxations of MAP-MRF is obtained by adding zero interactions. We propose a cutting plane algorithm, where cuts correspond to adding zero interactions and the separation problem to finding an unsatisfiable constraint satisfaction subproblem. Next, we show that certain high

In this paper we present a method for finding exact solutions of the Max-Cut problem max x T Lx such that x ∈ {±1} n. We use a semidefinite relaxation combined with triangle inequalities, which we solve with the bundle method. This approach is due to Fischer, Gruber, Rendl, and Sotirov [12

We study polyhedral relaxations for the linear ordering problem.

, this paper introduces a method by which reaction-diffusion textures are created to match the geometry of an arbitrary polyhedral surface. This is accomplished by creating a mesh over a given surface and then simulating the reactiondiffusion process directly on this mesh. This avoids the often difficult task

We provide a review and synthesis of polyhedral approaches to machine scheduling problems. The choice of decision variables is the prime determinant of various formulations for such problems. Constraints, such as facet inducing inequalities for corresponding polyhedra, are often needed, in addition

Hyperbolic polynomials elegantly encode a rich class of convex cones that includes polyhedral and spectrahedral cones. Hyperbolic polynomials are closed under taking polars and the corresponding cones – the derivative cones – yield relaxations for the associated optimization problem and exhibit

the linear programming relaxation always yields integral solutions. We prove this conjecture showing that the constraint matrices of these problems are unimodular. This establishes the integrality of the relaxation polyhedra since the linear programs are in standard form. However, the matrices are not