A Polytime Preprocess Algorithm for the Maximum Independent Set Problem

The maximum independent set (MIS) seeks to find a subset of vertices with the maximum size such that no pair of its vertices are adjacent. This paper develops a recursive fixing procedure that generalizes the existing polytime algorithm to solve the maximum independent set problem on chordal graphs, which admit simplicial orderings. We prove that the generalized fixing procedure is safe; i.e., it does not remove all optimal solutions of the MIS problem from the solution space. Our computational results show that the proposed recursive fixing algorithm, along with the basic mixed integer programming (MIP) of the MIS, outperforms the pure MIP formulation of the problem. Our codes, data, and results are available on GitHub.