Communication-aware processor allocation for supercomputers

  • Authors:

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

  • Affiliations:

  • Department of Computer Science, SUNY Stony Brook, Stony Brook, NY;Department of Computer Science, University of Illinois, Urbana, IL;MIT Computer Science and Artificial Intelligence Laboratory, Cambridge, MA;Dept. of Mathematical Optimization, Braunschweig University of Technology, Braunschweig, Germany;Discrete Algorithms & Math Department, Sandia National Laboratories, Albuquerque, NM;Dept. of Computing and Information Science, Queen's University, Kingston, Ontario, Canada;Discrete Algorithms & Math Department, Sandia National Laboratories, Albuquerque, NM

  • Venue:
  • WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
  • Year:
  • 2005

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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 $\mathcal{R}^d$, find a size-k subset with minimum average pairwise L1 distance. We present a natural approximation algorithm and show that it is a $\frac{7}{4}$-approximation for 2D 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 report on experimental results.