The minimum dominating set of graph has been widely used in many fields, but its solution is NP-hard. The complexity and approximation accuracy of existing algorithms need to be improved. In this paper, we introduce rough set theory to solve the dominating set of undirected graph. First, the adjacency matrix of undirected graph is used to establish an induced decision table, and the minimum dominating set of undirected graph is equivalent to the minimum attribute reduction of its induced decision table. Second, based on rough set theory, the significance of attributes (i.e., vertices) based on the approximate quality is defined in induced decision table, and a heuristic approximation algorithm of minimum dominating set is designed by using the significance of attributes (i.e., vertices) as heuristic information. This algorithm uses forward and backward search mechanism, which not only ensures to find a minimal dominating set, but also improves the approximation accuracy of minimum dominating set. In addition, a cumulative strategy is used to calculate the positive region of induced decision table, which effectively reduces the computational complexity. Finally, the experimental results on public datasets show that our algorithm has obvious advantages in running time and approximation accuracy of the minimum dominating set.

图的最小支配集已被广泛应用于许多领域，但其解决方案是 NP-hard。现有算法的复杂度和逼近精度有待提高。在本文中，我们引入粗糙集理论来解决无向图的支配集。首先，利用无向图的邻接矩阵建立诱导决策表，无向图的最小支配集相当于其诱导决策表的最小属性约简。其次，基于粗糙集理论，在归纳决策表中定义了基于近似质量的属性（即顶点）的显着性，并利用属性（即顶点）的显着性设计了最小支配集的启发式逼近算法。 ) 作为启发式信息。该算法采用前向和后向搜索机制，既保证了找到最小支配集，又提高了最小支配集的逼近精度。此外，采用累积策略计算诱导决策表的正区域，有效降低了计算复杂度。最后，在公共数据集上的实验结果表明，我们的算法在运行时间和最小支配集的逼近精度上具有明显的优势。