Single-Purpose Algorithms vs. a Generic Graph Summarizer for Computing $k$-Bisimulations on Large Graphs

We investigate whether a generic graph summarization approach BRS can outperform an existing single-purpose parallel algorithm for bisimulation. Furthermore, we investigate whether an existing sequential bisimulation algorithm can effectively be computed by the parallel BRS algorithm and how such generic implementations compete against a parallel variant. To give a fair comparison, we have reimplemented the original algorithms in the same framework as was used for the generic BRS algorithm. We evaluate the performance of the two native implementations against the implementations in the BRS algorithm for $k$-bisimulation with $k=1, \dots, 10$, using five real-world and synthetic graph datasets containing between $100$ million and two billion edges. Our results show that our generic BRS algorithm outperforms the respective native bisimulation algorithms for any value of~$k$. The generic algorithm has no disadvantage over the native parallel algorithm. Furthermore, the execution times of the generic BRS algorithm for the native parallel and native sequential bisimulation variants are very similar. This shows that the bisimulation variant computed by the native sequential algorithm can be effectively computed in parallel by our BRS algorithm. These insights open a new path for efficiently computing bisimulations on large graphs.