The 0-1 inverse maximum stable set problem

In this paper we study the 0-1 inverse maximum stable set problem, denoted by IS{0,1}. Given a graph and a stable set (not necessarily maximum), it is to delete a minimum number of vertices to make the given stable set maximum in the new graph. We also consider IS{0,1} against a specific algorithm such as Greedy and 2opt, which is denoted by IS{0,1},greedy and IS{0,1},2opt, respectively. We prove the NP-hardness of these problems and an approximation ratio of 2 − Θ( 1 √ log∆ ) for IS{0,1},2opt. In addition, we restrict IS{0,1} to some classes of perfect graphs such as comparability and chordal graphs, and we study its tractability. Finally, we compare the hardness of IS{0,1} and IS{0,1},2opt for some other classes of graphs.