基于通信感知的超级计算机处理器分配
Communication-Aware Processor Allocation for Supercomputers
摘要：
本文给出了处理器分配算法，最大限度地减少分配的处理器之间的平均通信跳数的网格架构，在占用细胞的存在。在自由网格上分配处理器的简单问题已经由Karp，McKellar和Wong研究过，他们证明了解决方案具有非平凡结构;他们留下了问题的复杂性。相关的聚类问题如下：给定Re^d中的n个点，找到k个使它们的平均成对L1距离最小的点。我们提出了一个自然的近似算法，并表明它是一个7/4近似的二维网格。对于d维空间，近似保证是2-（1/2d），这是紧的。我们还给出了一个多项式时间近似计划（PTAS）的常数维d，并报告实验结果。
英文摘要：
This paper gives processor-allocation algorithms for minimizing the average number of communication hops between the assigned processors for grid architectures, in the presence of occupied cells. The simpler problem of assigning processors on a free grid has been studied by Karp, McKellar, and Wong who show that the solutions have nontrivial structure; they left open the complexity of the problem. The associated clustering problem is as follows: Given n points in Re^d, find k points that minimize their average pairwise L1 distance. We present a natural approximation algorithm and show that it is a 7/4-approximation for 2D grids. For d-dimensional space, the approximation guarantee is 2-(1/2d), which is tight. We also give a polynomial-time approximation scheme (PTAS) for constant dimension d, and report on experimental results.
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