Parallel Strong Connectivity Based on Faster Reachability

Computing strongly connected components (SCC) is among the most fundamental problems in graph processing. As today's realworld graphs are getting larger and larger, parallel SCC is increasingly important. SCC is challenging in the parallel setting and is particularly hard on large-diameter graphs. Many existing parallel SCC implementations can be even slower than Tarjan's sequential algorithm on large-diameter graphs.

To tackle this challenge, we propose an efficient parallel SCC implementation using a new parallel reachability algorithm. Our solution is based on a novel idea referred to as vertical granularity control (VGC). It breaks the synchronization barriers to increase parallelism and hide scheduling overhead. To use VGC in our SCC algorithm, we also design an efficient data structure called the parallel hash bag. It uses parallel dynamic resizing to avoid redundant work in maintaining frontiers (vertices processed in a round).

We implement the parallel SCC algorithm by Blelloch et al. (J. ACM, 2020) using our new parallel reachability algorithm. We compare our implementation to the state-of-the-art systems, including GBBS, iSpan, Multi-step, and our highly optimized Tarjan's (sequential) algorithm, on 18 graphs, including social, web, 𝑘-NN, and lattice graphs. On a machine with 96 cores, our implementation is the fastest on 16 out of 18 graphs. On average (geometric means) over all graphs, our SCC is 6.0× faster than the best previous parallel code (GBBS), 12.8× faster than Tarjan's sequential algorithms, and 2.7× faster than the best existing implementation on each graph.

We believe that our techniques are of independent interest. We also apply our parallel hash bag and VGC scheme to other graph problems, including connectivity and least-element lists (LE-lists). Our implementations improve the performance of the state-of-theart parallel implementations for these two problems.

• Theory of computation → Shared memory algorithms; Graph algorithms analysis.