An Augmentation Algorithm for the Maximum Weighted Stable Set Problem

Edge projection is a specialization of Lovász and Plummer's clique reduction when restricted to edges. A concept of augmenting sequences of edge-projections is defined w.r.t. a stable set S. It is then proved the equivalence between the optimality of S and the existence of an augmenting sequence w.r.t. S. This result is then exploited to develop a new tabu-search heuristic for the Maximum Stable Set Problem (weighted and unweighted). The resulting code proved to be competitive with the best codes presented in the literature.