Node Embedding and Cosine Similarity for Efficient Maximum Common Subgraph Discovery

Finding the maximum common induced subgraph is a fundamental problem in computer science. Proven to be NP-hard in the 1970s, it has, nowadays, countless applications that still motivate the search for efficient algorithms and practical heuristics. In this work, we extend a state-of-the-art branch-and-bound exact algorithm with new techniques developed in the deep-learning domain, namely graph neural networks and node embeddings, effectively transforming an efficient yet uninformed depth-first search into an effective best-first search. The change enables the algorithm to find suitable solutions within a limited budget, pushing forward the method’s time efficiency and applicability on larger graphs. We evaluate the usage of the L2 norm of the node embeddings and the Cumulative Cosine Similarity to classify the nodes of the graphs. Our experimental analysis on standard graphs compares our heuristic against the original algorithm and a recently tweaked version that exploits reinforcement learning. The results demonstrate the effectiveness and scalability of the proposed approach, compared with the state-of-the-art algorithms. In particular, this approach results in improved results on over 90% of the larger graphs; this would be more challenging in a constrained industrial scenario.