Communication-Aware Processor Allocation for Supercomputers: Finding Point Sets of Small Average Distance

  • Authors:

  • Michael A. Bender;David P. Bunde;Erik D. Demaine;Sándor P. Fekete;Vitus J. Leung;Henk Meijer;Cynthia A. Phillips

  • Affiliations:

  • Stony Brook University, Department of Computer Science, 11794-4400, Stony Brook, NY, USA;Knox College, Department of Computer Science, 61401, Galesburg, IL, USA;MIT Computer Science and Artificial Intelligence Laboratory, 02139, Cambridge, MA, USA;Braunschweig University of Technology, Dept. of Computer Science, 38106, Braunschweig, MA, Germany;Sandia National Laboratories, Discrete Algorithms & Math. Department, 87185-1318, Albuquerque, NM, USA;Roosevelt Academy, Department of Science, 87185-1318, Middelburg (ZL), NM, The Netherlands;Sandia National Laboratories, Discrete Algorithms & Math. Department, 87185-1318, Albuquerque, NM, USA

  • Venue:
  • Algorithmica
  • Year:
  • 2008

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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 L 1 distance. We present a natural approximation algorithm and show that it is a $\frac{7}{4}$-approximation for two-dimensional grids; in d dimensions, the approximation guarantee is $2-\frac{1}{2d}$, which is tight. We also give a polynomial-time approximation scheme (PTAS) for constant dimension d, and we report on experimental results.