Optimizing Parallel Graph Connectivity Computation via Subgraph Sampling

Connected component identification is a fundamental problem in graph analytics, serving as a basis for subsequent computations in a wide range of applications. To determine connectivity, several parallel algorithms, whose complexity is proportional to the number of edges or graph diameter, have been proposed. However, an optimal algorithm may extract graph components by working proportionally to the number of vertices, which can be orders of magnitude lower than the number of edges. We propose Afforest: an extension of the Shiloach-Vishkin connected components algorithm that approaches optimal work efficiency by processing subgraphs in each iteration. We prove the convergence of the algorithm, analyze its work efficiency characteristics, and provide further techniques to speed up processing graphs containing a huge component. Designed with modern parallel architectures in mind, we show that the algorithm exhibits higher memory locality than existing methods. Using both synthetic and real-world graphs, we demonstrate that Afforest achieves speedups of up to 67x over the state-of-the-art on multi-core CPUs (Broadwell, POWER8) and up to 23x on GPUs (Pascal).