基于稀疏矩阵核的最小生成森林并行计算
Parallel Minimum Spanning Forest Computation using Sparse Matrix Kernels
摘要：
使用稀疏线性代数的图形算法的公式已经产生了高度可扩展的分布式算法的问题，如连接和最短路径计算。我们开发的第一个配方的Awerbuch-Shiloach并行最小生成森林（MSF）算法使用线性代数原语。我们引入了一个多线性核，它对一个邻接矩阵和两个向量进行操作。该内核通过同时使用来自相邻边和顶点的信息来更新图顶点。此外，我们探索优化，以加快Awerbuch-Shiloach算法中的捷径步骤。我们实现这个MSF算法与Cyclops，一个分布式存储库的广义稀疏张量代数。我们分析了我们的实现在Stampede 2超级计算机上的并行可扩展性。
英文摘要：
Formulations of graph algorithms using sparse linear algebra have yielded highly scalable distributed algorithms for problems such as connectivity and shortest path computation. We develop the first formulation of the Awerbuch-Shiloach parallel minimum spanning forest (MSF) algorithm using linear algebra primitives. We introduce a multilinear kernel that operates on an adjacency matrix and two vectors. This kernel updates graph vertices by simultaneously using information from both adjacent edges and vertices. In addition, we explore optimizations to accelerate the shortcutting step in the Awerbuch-Shiloach algorithm. We implement this MSF algorithm with Cyclops, a distributed-memory library for generalized sparse tensor algebra. We analyze the parallel scalability of our implementation on the Stampede2 supercomputer.
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