大规模多重图与高基数稀疏矩阵的高效分布式转置
Efficient Distributed Transposition Of Large-Scale Multigraphs And High-Cardinality Sparse Matrices
摘要：
基于图形的表示是广泛的科学问题的基础。图形连接通常表示为压缩稀疏行格式的稀疏矩阵。大规模图依赖于分布式存储，将不同的行子集分配给计算节点。高效的矩阵转置是一个非常重要的操作，它提供了反向图路径和列有序矩阵视图。对于简单的图模型，这种操作已经得到了很好的研究。然而，它的解决方案的多重图和更高的基数连接矩阵是不存在的。我们先进的最先进的分布式换位方法，提供了一个理论模型，算法的细节，基于MPI的实现和证明这样复杂的模型的数学合理性。基准测试结果分别证明了完美平衡和异质平衡数据集的理想和几乎理想的缩放特性
英文摘要：
Graph-based representations underlie a wide range of scientific problems. Graph connectivity is typically represented as a sparse matrix in the Compressed Sparse Row format. Large-scale graphs rely on distributed storage, allocating distinct subsets of rows to compute nodes. Efficient matrix transpose is an operation of high importance, providing the reverse graph pathways and a column-ordered matrix view. This operation is well studied for simple graph models. Nevertheless, its resolution for multigraphs and higher-cardinality connectivity matrices is unexistent. We advance state-of-the-art distributed transposition methods by providing a theoretical model, algorithmic details, MPI-based implementation and proof of mathematical soundness for such complex models. Benchmark results demonstrate ideal and almost ideal scaling properties for perfectly- and heterogeneously-balanced datasets, respectively
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