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Given a graph, finding the distance-2 maximal independent set (MIS-2) of thevertices is a problem that is useful in several contexts such as algebraicmultigrid coarsening or multilevel graph partitioning. Such multilevel methodsrely on finding the independent vertices so they can be used as seeds foraggregation in a multilevel scheme. We present a parallel MIS-2 algorithm toimprove performance on modern accelerator hardware. This algorithm isimplemented using the Kokkos programming model to enable performanceportability. We demonstrate the portability of the algorithm and theperformance on a variety of architectures (x86/ARM CPUs and NVIDIA/AMD GPUs).The resulting algorithm is also deterministic, producing an identical resultfor a given input across all of these platforms. The new MIS-2 implementationoutperforms implementations in state of the art libraries like CUSP andViennaCL by 3-8x while producing similar quality results. We furtherdemonstrate the benefits of this approach by developing parallel graphcoarsening scheme for two different use cases. First, we develop an algebraicmultigrid (AMG) aggregation scheme using parallel MIS-2 and demonstrate thebenefits as opposed to previous approaches used in the MueLu multigrid packagein Trilinos. We also describe an approach for implementing a parallelmulticolor "cluster" Gauss-Seidel preconditioner using this MIS-2 coarsening,and demonstrate better performance with an efficient, parallel, multicolorGauss-Seidel algorithm.

Parallel, Portable Algorithms for Distance-2 Maximal Independent Set and Graph Coarsening