Neural Maximum Common Subgraph Detection with Guided Subgraph Extraction

Maximum Common Subgraph (MCS) is defined as the largest subgraph that is commonly present in both graphs of a graph pair. Exact MCS detection is NP-hard, and its state-of-the-art exact solver based on heuristic search is slow in practice without any time complexity guarantee. Given the huge importance of this task yet the lack of fast solver, we propose an efficient MCS detection algorithm, NeuralMCS, consisting of a novel neural network model that learns the node-node correspondence from the ground-truth MCS result, and a subgraph extraction procedure that uses the neural network output as guidance for final MCS prediction. The whole model guarantees polynomial time complexity with respect to the number of the nodes of the larger of the two input graphs. Experiments on four real graph datasets show that the proposed model is 48.1 x faster than the exact solver and more accurate than all the existing competitive approximate approaches to MCS detection.