Communication-aware processor allocation for supercomputers

We give processor- allocation algorithms for grid architectures, where the objective is to select processors from a set of available processors to minimize the average number of communication hops. The associated clustering problem is as follows: Given n points in R-d, find a size-k subset with minimum average pairwise L, distance. We present a natural approximation algorithm and show. that it is a 7/4- approximation for 2D grids. In d dimensions, 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.