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首页> 外文期刊>IEEE Transactions on Parallel and Distributed Systems >On supernode transformation with minimized total running time
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On supernode transformation with minimized total running time

机译：在超节点转换上，以最小的总运行时间

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摘要

With the objective of minimizing the total execution time of a parallel program on a distributed memory parallel computer, this paper discusses how to find an optimal supernode size and optimal supernode relative side lengths of a supernode transformation (also known as tiling). We identify three parameters of supernode transformation: supernode size, relative side lengths, and cutting hyperplane directions. For algorithms with perfectly nested loops and uniform dependencies, for sufficiently large supernodes and number of processors, and for the case where multiple supernodes are mapped to a single processor, we give an order n polynomial whose real positive roots include the optimal supernode size. For two special cases, 1) two-dimensional algorithm problems and 2) n-dimensional algorithm problems, where the communication cost is dominated by the startup penalty and, therefore, can be approximated by a constant, we give a closed form expression for the optimal supernode size, which is independent of the supernode relative side lengths and cutting hyperplanes. For the case where the algorithm iteration index space and the supernodes are hyperrectangular, we give closed form expressions for the optimal supernode relative side lengths. Our experiment shows a good match of the closed form expressions with experimental data.
机译：为了最大程度地减少分布式内存并行计算机上并行程序的总执行时间，本文讨论了如何找到最佳超级节点大小和超级节点转换（也称为平铺）的最佳超级节点相对边长。我们确定了超节点转换的三个参数：超节点大小，相对边长和切割超平面方向。对于具有完美嵌套循环和统一依存关系的算法，对于足够大的超节点和数量的处理器，以及将多个超节点映射到单个处理器的情况，我们给出n阶多项式，其实际正根包括最优超节点的大小。对于两个特殊情况，1）二维算法问题和2）n维算法问题，其中通信成本由启动惩罚决定，因此可以由一个常数近似，我们给出一个封闭形式的表达式最佳超节点大小，它与超节点相对边长和切割超平面无关。对于算法迭代索引空间和超节点为超矩形的情况，我们给出了最优超节点相对边长的闭合形式表达式。我们的实验显示了封闭形式表达式与实验数据的良好匹配。

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