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

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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.

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Authors and Affiliations

  1. Department of Computer Science, Stony Brook University, Stony Brook, NY, 11794-4400, USA

    Michael A. Bender

  2. Department of Computer Science, Knox College, Galesburg, IL, 61401, USA

    David P. Bunde

  3. MIT Computer Science and Artificial Intelligence Laboratory, Cambridge, MA, 02139, USA

    Erik D. Demaine

  4. Dept. of Computer Science, Braunschweig University of Technology, 38106, Braunschweig, Germany

    Sándor P. Fekete

  5. Discrete Algorithms & Math. Department, Sandia National Laboratories, Albuquerque, NM, 87185-1318, USA

    Vitus J. Leung & Cynthia A. Phillips

  6. Department of Science, Roosevelt Academy, Middelburg (ZL), The Netherlands

    Henk Meijer

Authors
  1. Michael A. Bender
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  2. David P. Bunde
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  3. Erik D. Demaine
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  4. Sándor P. Fekete
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  5. Vitus J. Leung
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  6. Henk Meijer
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  7. Cynthia A. Phillips
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Correspondence to Sándor P. Fekete.

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Bender, M.A., Bunde, D.P., Demaine, E.D. et al. Communication-Aware Processor Allocation for Supercomputers: Finding Point Sets of Small Average Distance. Algorithmica 50, 279–298 (2008). https://doi.org/10.1007/s00453-007-9037-2

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