Introducing VF3: A new algorithm for subgraph isomorphism

Several graph-based applications require to detect and locate occurrences of a pattern graph within a larger target graph. Subgraph isomorphism is a widely adopted formalization of this problem. While subgraph isomorphism is NP-Complete in the general case, there are algorithms that can solve it in a reasonable time on the average graphs that are encountered in specific real-world applications. In 2015 we introduced one such algorithm, VF2Plus, that was specifically designed for the large graphs encountered in bioinformatics applications. VF2Plus was an evolution of VF2, which had been considered for many years one of the fastest available algorithms. In turn, VF2Plus proved to be significantly faster than its predecessor, and among the fastest algorithms on bioinformatics graphs. In this paper we propose a further evolution, named VF3, that adds new improvements specifically targeted at enhancing the performance on graphs that are at the same time large and dense, that are currently the most problematic case for the state-of-the-art algorithms. The effectiveness of VF3 has been experimentally validated using several publicly available datasets, showing a significant speedup with respect to its predecessor and to the other most advanced state-of-the-art algorithms.