Block-diagonal semidenfinite programming hierarchies for 0/1 programming

Lovász and Schrijver, and later Lasserre, proposed hierachies of semidefinite programming relaxation for general 0/1 linear programming problems. In this paper these two constructions are revisited and two new, block-diagonal hierarchies are proposed. They have the advantage of being computationally less costly while being at least as strong as the Lovász-Schrijver hierarchy. Our construction is applied to the stable set problem and experimental results of Paley graphs are reported.