Graph neural networks have been successful for machine learning, 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 graph sparsifiers 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 sparsifier. The proposed method consistently outperforms several standard approximation algorithms on different types of graphs and often finds the optimal solution.

翻译：图神经网络在机器学习以及诸如子图同构问题和旅行商问题等组合优化与图问题中已取得显著成功。本文提出一种融合图神经网络与蒙特卡洛树搜索的图稀疏化计算方法。首先训练一个以部分解为输入、输出待添加新节点的图神经网络，随后将该神经网络应用于蒙特卡洛搜索以计算稀疏化解。该方法在多种类型图结构上持续优于多个标准近似算法，且通常能获得最优解。