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Algorithmica

, Volume 50, Issue 2, pp 279–298 | Cite as

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

  • Michael A. Bender
  • David P. Bunde
  • Erik D. Demaine
  • Sándor P. FeketeEmail author
  • Vitus J. Leung
  • Henk Meijer
  • Cynthia A. Phillips
Article

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 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.

Keywords

Processor allocation Supercomputers Communication cost Manhattan distance Clustering Approximation Polynomial-time approximation scheme (PTAS) 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Michael A. Bender
    • 1
  • David P. Bunde
    • 2
  • Erik D. Demaine
    • 3
  • Sándor P. Fekete
    • 4
    Email author
  • Vitus J. Leung
    • 5
  • Henk Meijer
    • 6
  • Cynthia A. Phillips
    • 5
  1. 1.Department of Computer ScienceStony Brook UniversityStony BrookUSA
  2. 2.Department of Computer ScienceKnox CollegeGalesburgUSA
  3. 3.MIT Computer Science and Artificial Intelligence LaboratoryCambridgeUSA
  4. 4.Dept. of Computer ScienceBraunschweig University of TechnologyBraunschweigGermany
  5. 5.Discrete Algorithms & Math. DepartmentSandia National LaboratoriesAlbuquerqueUSA
  6. 6.Department of ScienceRoosevelt AcademyMiddelburg (ZL)The Netherlands

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