OrbitSI: An Orbit-based Algorithm for the Subgraph Isomorphism Search Problem

The Subgraph Isomorphism (SI) search problem searches for embeddings of a pattern graph within a data graph. Efficient heuristic algorithms for the SI search problem are often structured around a Depth-First Search (DFS) tree-based search to find matching subgraphs. These algorithms comprise three segments: filtering, ordering and enumeration. Filtering and ordering are critical in reducing the runtime of the enumeration segment. As such, various properties of vertices are used to filter out impossible matches and determine the most efficient enumeration order. In this paper, we propose using the graphs’ local topological information to strengthen the filtering and ordering segments of a heuristic algorithm, going beyond the properties of vertices and their immediate neighbours, which make up the state-of-the-art strategies. We use orbit counts of 4-vertex graphlets to characterise the local topology near a vertex, which provides valuable structural information while keeping the computational effort for analysing the topology affordable. Our new algorithm, OrbitSI, improves the overall runtime across eight datasets, each containing one data graph and 1800 pattern graphs, by factors of 2.69 to 11.49 compared to four state-of-the-art algorithms.