论文标题
距离-2最大独立集和图形粗化的平行，便携式算法
Parallel, Portable Algorithms for Distance-2 Maximal Independent Set and Graph Coarsening
论文作者
论文摘要
鉴于图，找到顶点的距离-2最大独立集（MIS-2）是一个问题，在多种情况下，例如代数多族块或多级图形分区。这种多级方法依赖于找到独立的顶点，因此可以将它们用作多级方案中的种子。我们提出了一种平行的MIS-2算法，以提高现代加速器硬件的性能。该算法是使用Kokkos编程模型实现的，以启用性能可移植性。我们演示了算法的可移植性以及各种体系结构（X86/ARM CPU和NVIDIA/AMD GPU）的性能。所得算法也是确定性的，在所有这些平台上给定输入产生了相同的结果。新的MIS-2实施优于尖峰和VIENNACL等最先进的图书馆的实现，同时产生相似的质量结果。我们通过开发两个不同用例的平行图修整方案来进一步证明这种方法的好处。首先，我们使用平行MIS-2开发了代数多机（AMG）聚合方案，并证明了与Trilinos中Muelu Multigrid包装中使用的先前方法相反。我们还描述了一种使用此MIS-2粗化实现并行多色“群集”高斯预处理器的方法，并通过有效，并行，多色高斯 - seidel算法来表现更好的性能。
Given a graph, finding the distance-2 maximal independent set (MIS-2) of the vertices is a problem that is useful in several contexts such as algebraic multigrid coarsening or multilevel graph partitioning. Such multilevel methods rely on finding the independent vertices so they can be used as seeds for aggregation in a multilevel scheme. We present a parallel MIS-2 algorithm to improve performance on modern accelerator hardware. This algorithm is implemented using the Kokkos programming model to enable performance portability. We demonstrate the portability of the algorithm and the performance on a variety of architectures (x86/ARM CPUs and NVIDIA/AMD GPUs). The resulting algorithm is also deterministic, producing an identical result for a given input across all of these platforms. The new MIS-2 implementation outperforms implementations in state of the art libraries like CUSP and ViennaCL by 3-8x while producing similar quality results. We further demonstrate the benefits of this approach by developing parallel graph coarsening scheme for two different use cases. First, we develop an algebraic multigrid (AMG) aggregation scheme using parallel MIS-2 and demonstrate the benefits as opposed to previous approaches used in the MueLu multigrid package in Trilinos. We also describe an approach for implementing a parallel multicolor "cluster" Gauss-Seidel preconditioner using this MIS-2 coarsening, and demonstrate better performance with an efficient, parallel, multicolor Gauss-Seidel algorithm.
