Communication-Aware Processor Allocation for Supercomputers

Details Communication-Aware Processor Allocation for Supercomputers Communication-Aware Processor Allocation for Supercomputers

2004-07-24

arxiv.org/abs/cs/0407058v2

Computer Science

Data Structures and Algorithms

19 pages, 7 figures, 1 table, Latex, submitted for journal publication. Previous version is extended abstract (14 pages), appe

Scientific paper

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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