Paper by Erik D. Demaine

Reference:

Michael A. Bender, David P. Bunde, Erik D. Demaine, Sándor P. Fekete, Vitus J. Leung, Henk Meijer, and Cynthia A. Phillips, “Communication-Aware Processor Allocation for Supercomputers”, Algorithmica, volume 50, number 2, February 2008, pages 279–298. Special issue of selected papers from the 9th Workshop on Algorithms and Data Structures, 2005.

Abstract:

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 L₁ distance. We present a natural approximation algorithm and show that it is a 7/4-approximation for two-dimensional 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 we report on experimental results.

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