Single-Source Regular Path Querying in Terms of Linear Algebra

Two-way regular path queries (2-RPQs) allow one to use regular languages over edges and inverted edges in edge-labelled graph to constrain paths of interest. 2-RPQs are (partially) adopted in different real-world graph analysis systems and have become a part of the GQL ISO standard. However the performance of 2-RPQs on real-world graphs remains a bottleneck for wider adoption. Utilisation of high-performance sparse linear algebra libraries for the algorithm implementation allows one to achieve significant speedup over competitors on real-world data and queries. We propose a new breadth-first-search-based algorithm that leverages linear algebra for evaluating single-source regular path queries. We integrate it into the LAGraph graph processing algorithm infrastructure and provide in-depth performance comparison on the large real-world knowledge bases. Additionally, we present extensive analysis of its performance across different query types using synthetic data, comparing it with various databases and other linear algebra-based approaches.