A Lagrangian Relaxation for the Maximum Stable Set Problem

We propose a new integer programming formulation for the problem of finding a maximum stable set of a graph based on representatives of stable sets. In addition, we investigate exact solutions provided by a Lagrangian decomposition of this formulation in which only one constraint is relaxed. Some computational experiments were carried out with an effective multi-threaded implementation of our algorithm in a multi-core system, and their results are presented.