An efficient pruning method for subgraph matching in large-scale graphs

Subgraph matching, as a challenging problem in the graph area, has a wide range of applications from social networks to computational biology. It refers to finding the occurrences of a query graph in a given large graph. Subgraph matching is considered an NP-complete problem in the literature. In order to reduce the computational complexity of subgraph matching, pruning the search space with heuristics, e.g., topological features, have been studied broadly. In this paper, we propose a novel pruning strategy in subgraph matching to reduce the size of search space, named Eigen Decomposition Pruning. EDP uses local spectral features to prune the search space instead of directly using topological features. Firstly, it generates a Local Laplacian Matrix (LLM) for each candidate solution. Then, it prunes the false positive candidates from the search space using the spectral features of these LLMs. An LLM is defined to capture the features in the localities of a graph and imposes a low computation overhead. Additionally, EDP recognizes more false positive candidates than previous methods due to more informative spectral features of LLM, which results in a noticeable decrease in the overall time of subgraph matching. To assess the performance of our algorithm, it is applied to both real and synthetic datasets and is compared against four well-known methods in this field. The theoretical analysis and experimental results confirm the effectiveness of the proposed method.