Graph neural networks are useful for learning problems, as well as for combinatorial and graph problems such as the Subgraph Isomorphism Problem and the Traveling Salesman Problem. We describe an approach for computing Steiner Trees by combining a graph neural network and Monte Carlo Tree Search. We first train a graph neural network that takes as input a partial solution and proposes a new node to be added as output. This neural network is then used in a Monte Carlo search to compute a Steiner tree. The proposed method consistently outperforms the standard 2-approximation algorithm on many different types of graphs and often finds the optimal solution.

翻译：图神经网络对于学习问题，以及诸如子图同构问题和旅行商问题等组合与图问题非常有用。我们描述了一种通过结合图神经网络与蒙特卡洛树搜索来计算Steiner树的方法。首先训练一个以部分解为输入、输出建议添加新节点的图神经网络，随后将该神经网络用于蒙特卡洛搜索以计算Steiner树。所提出的方法在多种不同类型的图上持续优于标准的2-近似算法，并常能求得最优解。