Universality of the Local Marginal Polytope

We show that solving the LP relaxation of the MAP inference problem in graphical models (also known as the min-sum problem, energy minimization, or weighted constraint satisfaction) is not easier than solving any LP. More precisely, any polytope is linear-time represent able by a local marginal polytope and any LP can be reduced in linear time to a linear optimization (allowing infinite weights) over a local marginal polytope.