Ideal polytopes and face structures of some combinatorial optimization problems

Given a finite set X and a family of "feasible" subsets F of X, the 0-1 polytope P (F is defined as the convex hull of all the characteristic vectors of members of F We show that under a certain assumption a special type of face of P(F) is equivalent to the ideal polytope of some pseudo-ordered set. Examples of families satisfying the assumption are those related to the maximum stable set problem, set packing and set partitioning problems, and vertex coloring problem. Using this fact, we propose a new heuristic for such problems and give results of our preliminary computational experiments for the maximum stable set problem.