This work presents a graph neural network (GNN) framework for solving the maximum independent set (MIS) problem, inspired by dynamic programming (DP). Specifically, given a graph, we propose a DP-like recursive algorithm based on GNNs that firstly constructs two smaller sub-graphs, predicts the one with the larger MIS, and then uses it in the next recursive call. To train our algorithm, we require annotated comparisons of different graphs concerning their MIS size. Annotating the comparisons with the output of our algorithm leads to a self-training process that results in more accurate self-annotation of the comparisons and vice versa. We provide numerical evidence showing the superiority of our method vs prior methods in multiple synthetic and real-world datasets.

翻译：本文提出了一种受动态规划启发的图神经网络框架，用于解决最大独立集问题。具体而言，给定一个图，我们基于图神经网络设计了一种类动态规划的递归算法：首先构造两个更小的子图，预测其中具有更大最大独立集的那个子图，并将其用于下一轮递归调用。为训练我们的算法，需要标注不同图在最大独立集规模上的比较结果。用算法自身的输出标注这些比较结果，会形成一个自训练过程，使得比较结果的自标注更准确，反之亦然。我们提供了数值证据，表明在多个合成数据集和真实数据集上，本方法优于先前方法。