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The Kronecker product-based algorithm for context-free path querying (CFPQ)was proposed by Orachev et al. (2020). We reduce this algorithm to operationsover Boolean matrices and extend it with the mechanism to extract all paths ofinterest. We also prove $O(n^3/\log{n})$ time complexity of the proposedalgorithm, where n is a number of vertices of the input graph. Thus, we providethe alternative way to construct a slightly subcubic algorithm for CFPQ whichis based on linear algebra and incremental transitive closure (a classicgraph-theoretic problem), as opposed to the algorithm with the same complexityproposed by Chaudhuri (2008). Our evaluation shows that our algorithm is a goodcandidate to be the universal algorithm for both regular and context-free pathquerying.

One Algorithm to Evaluate Them All: Unified Linear Algebra Based Approach to Evaluate Both Regular and Context-Free Path Queries