Fast Detection of Maximum Common Subgraph via Deep Q-Learning

Detecting the Maximum Common Subgraph (MCS) between two input graphs is fundamental for applications in biomedical analysis, malware detection, cloud computing, etc. This is especially important in the task of drug design, where the successful extraction of common substructures in compounds can reduce the number of experiments needed to be conducted by humans. However, MCS computation is NP-hard, and state-of-the-art exact MCS solvers do not have worst-case time complexity guarantee and cannot handle large graphs in practice. Designing learning based models to find the MCS between two graphs in an approximate yet accurate way while utilizing as few labeled MCS instances as possible remains to be a challenging task. Here we propose RLMCS, a Graph Neural Network based model for MCS detection through reinforcement learning. Our model uses an exploration tree to extract subgraphs in two graphs one node pair at a time, and is trained to optimize subgraph extraction rewards via Deep Q-Networks. A novel graph embedding method is proposed to generate state representations for nodes and extracted subgraphs jointly at each step. Experiments on real graph datasets demonstrate that our model performs favorably to exact MCS solvers and supervised neural graph matching network models in terms of accuracy and efficiency.