Parallel Strong Connectivity Based on Faster Reachability

Computing biconnected components (BCC) of a graph is a fundamental graph problem. The canonical parallel BCC algorithm is the Tarjan-Vishkin algorithm, which has O(n + m) optimal work and polylogarithmic span on a graph with n vertices and m edges. ...

In this paper, we propose a parallel strongly connected components (SCC) implementation that is efficient on a wide range of graphs. Our speedup comes from two novel techniques: vertical granularity control (VGC) and parallel hash bag.

We present the first parallel fixed-parameter algorithm for subgraph isomorphism in planar graphs, bounded-genus graphs, and, more generally, all minor-closed graphs of locally bounded treewidth. Our randomized low depth algorithm has a near-linear work ...