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.

最大独立集 (MIS) 寻求找到具有最大大小的顶点子集，使得其任何顶点都不相邻。本文开发了一种递归固定程序，该程序概括了现有的多时间算法，以解决允许单纯排序的弦图上的最大独立集问题。我们证明了广义固定程序是安全的；即，它不会从解空间中删除 MIS 问题的所有最优解。我们的计算结果表明，所提出的递归固定算法以及 MIS 的基本混合整数规划 (MIP) 优于问题的纯 MIP 表述。我们的代码、数据和结果可在 GitHub 上获取。