Distributed Algorithms for the Graph Biconnectivity and Least Common Ancestor Problems

Graph connectivity analysis is one of the primary ways to analyze the topological structure of social networks. Graph biconnectivity decompositions are of particular interest due to how they identify cut vertices and cut edges in a network. We present the first, to our knowledge, implementation of a distributed-memory parallel biconnectivity algorithm. As part of our algorithm, we also require the computation of least common ancestors (LCAs) of non-tree edge endpoints in a BFS tree. As such, we also propose a novel distributed algorithm for the LCA problem. Using our implementations, we observe up to a 14.8× speedup from 1 to 128 MPI ranks for computing a biconnectivity decomposition.