A New Approach To The Stable Set Problem Based On Ellipsoids

A new exact approach to the stable set problem is presented, which attempts to avoids the pitfalls of existing approaches based on linear and semidefinite programming. The method begins by constructing an ellipsoid that contains the stable set polytope and has the property that the upper bound obtained by optimising over it is equal to the Lovasz theta number. This ellipsoid is then used to derive cutting planes, which can be used within a linear programming-based branch-and-cut algorithm. Preliminary computational results indicate that the cutting planes are strong and easy to generate.