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arXiv 1504.04714cs.DCcs.MS
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基于树型异步通信的并行选择反演算法的scalability和负载均衡增强

Enhancing the scalability and load balancing of the parallel selected inversion algorithm via tree-based asynchronous communication

Mathias Jacquelin, Lin Lin, Nathan Wichmann, Chao Yang

摘要:

我们开发了一种方法,用于在大规模并行分布式存储器机器上提高最近开发的并行选择反演算法[Jacquelin,Lin和Yang 2014](名为PSelInv)的并行可扩展性。在PSelInv方法中,我们计算稀疏矩阵A的逆的选定元素,该稀疏矩阵A可以分解为A = LU,其中L是下三角形,U是上三角形。更新A-1的这些所选元素需要在由L和U的块循环分布创建的每个列或行通信组内的处理器子集之间进行受限的集体通信。我们描述了这种类型的限制集体通信可以通过使用异步点对点MPI通信功能结合基于二叉树的数据传播方案来实现。由于并行选择反演算法中可能同时发生多个受限的集体通信,因此需要使用启发式算法来防止参与多个集体通信的处理器接收到过多的消息。这种启发式算法使我们能够减少通信负载不平衡,提高所选反演算法的整体可扩展性。例如,当使用6,400个处理器时,我们观察到测试矩阵的加速超过5倍。它还减轻了由非均匀网络拓扑引入的性能变化。

英文摘要:

We develop a method for improving the parallel scalability of the recently developed parallel selected inversion algorithm [Jacquelin, Lin and Yang 2014], named PSelInv, on massively parallel distributed memory machines. In the PSelInv method, we compute selected elements of the inverse of a sparse matrix A that can be decomposed as A = LU, where L is lower triangular and U is upper triangular. Updating these selected elements of A-1 requires restricted collective communications among a subset of processors within each column or row communication group created by a block cyclic distribution of L and U. We describe how this type of restricted collective communication can be implemented by using asynchronous point-to-point MPI communication functions combined with a binary tree based data propagation scheme. Because multiple restricted collective communications may take place at the same time in the parallel selected inversion algorithm, we need to use a heuristic to prevent processors participating in multiple collective communications from receiving too many messages. This heuristic allows us to reduce communication load imbalance and improve the overall scalability of the selected inversion algorithm. For instance, when 6,400 processors are used, we observe over 5x speedup for test matrices. It also mitigates the performance variability introduced by an inhomogeneous network topology.

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