Noah: Neural-optimized A* Search Algorithm for Graph Edit Distance Computation

Graph Edit Distance (GED) is a classical graph similarity metric that can be tailored to a wide range of applications. However, the exact GED computation is NP-complete, which means it is only feasible for small graphs only. And therefore, approximate GED computation methods are used in most realworld applications. However, traditional practices and end-to-end learning-based methods have their shortcomings when applied for approximate GED computation. The former relies on experience and usually performs not well. The latter is only capable of computing similarity scores between graphs without an actual edit path, which is crucial in specific problems (e.g., Graph Alignment, Semantic Role Labeling). Meanwhile, it assumes that one of the graphs is seen before, which is not in line with the GED computation problem. This paper proposes a novel approach Noah, which combines A* search algorithm and graph neural networks to compute approximate GED in a more effective and intelligent way. The combination is mainly reflected in two aspects. First, we learn the estimated cost function h(•) by Graph Path Networks. Pre-training GEDs and corresponding edit paths are also incorporated for training the model, therefore helping optimize the search direction of A* search algorithm. Second, we learn an elastic beam size that can help reduce search size and satisfy various user settings. Experimental results demonstrate the practical effectiveness of our approach on several tasks and suggest that our approach significantly outperforms the state-ofthe-art methods.