LACC: A Linear-Algebraic Algorithm for Finding Connected Components in Distributed Memory

Finding connected components is one of the most widely used operations on a graph. Optimal serial algorithms for the problem have been known for half a century, and many competing parallel algorithms have been proposed over the last several decades under various different models of parallel computation. This paper presents a parallel connected-components algorithm that can run on distributed-memory computers. Our algorithm uses linear algebraic primitives and is based on a PRAM algorithm by Awerbuch and Shiloach. We show that the resulting algorithm, named LACC for Linear Algebraic Connected Components, outperforms competitors by a factor of up to 12x for small to medium scale graphs. For large graphs with more than 50B edges, LACC scales to 4K nodes (262K cores) of a Cray XC40 supercomputer and outperforms previous algorithms by a significant margin. This remarkable performance is accomplished by (1) exploiting sparsity that was not present in the original PRAM algorithm formulation, (2) using high-performance primitives of Combinatorial BLAS, and (3) identifying hot spots and optimizing them away by exploiting algorithmic insights.