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Communication-Aware Processor Allocation for Supercomputers

Michael A. Bender·David P. Bunde·Erik D. Demaine·Sandor P. Fekete·Vitus J. Leung·Henk Meijer·Cynthia A. Phillips
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Abstract

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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Michael A. Bender, David P. Bunde, Erik D. Demaine, Sandor P. Fekete, Vitus J. Leung, Henk Meijer, Cynthia A. Phillips. 2005-12-06. Communication-Aware Processor Allocation for Supercomputers. https://arxiv.org/abs/cs/0407058

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