Parallel Graph Coloring For Manycore Architectures

Graph algorithms are challenging to parallelize on manycore architectures due to complex data dependencies and irregular memory access. We consider the well studied problem of coloring the vertices of a graph. In many applications it is important to compute a coloring with few colors in near-linear time. In parallel, the optimistic (speculative) coloring method by Gebremedhin and Manne [1] is the preferred approach but it needs to be modified for manycore architectures. We discuss a range of implementation issues for this vertex-based optimistic approach. We also propose a novel edge-based optimistic approach that has more parallelism and is better suited to GPUs. We study the performance empirically on two architectures (Xeon Phi and GPU) and across many data sets (from finite element problems to social networks). Our implementation uses the Kokkos library, so it is portable across platforms. We show that on GPUs, we significantly reduce the number of colors (geometric mean 4X, but up to 48X) as compared to the widely used cuSPARSE library. In addition, our edge-based algorithm is 1.5 times faster on average than cuSPARSE, where it has speedups up to 139X on a circuit problem. We also show the effect of the coloring on a conjugate gradient solver using multi-colored Symmetric Gauss-Seidel method as preconditioner; the higher coloring quality found by the proposed methods reduces the overall solve time up to 33% compared to cuSPARSE.