Provably Fast and Space-Efficient Parallel Biconnectivity (Abstract).

We propose the first parallel biconnectivity algorithm (FAST-BCC) that has optimal work, polylogarithmic span, and is space-efficient. Our algorithm creates a skeleton graph based on any spanning tree of the input graph. Then we use the connectivity information of the skeleton to compute the biconnectivity of the original input. We carefully analyze the correctness of our algorithm. We implemented FAST-BCC and compared it with existing implementations, including GBBS, Slota and Madduri's algorithm, and the sequential Hopcroft-Tarjan algorithm. We tested them on a 96-core machine on 27 graphs with varying edge distributions. FAST-BCC is faster than all existing baselines on each graph.