On the performance of randomized embedding of reproduction trees in static networks

  • Authors:

  • Keqin Li

  • Affiliations:

  • Department of Computer Science, State University of New York, New Paltz, New York

  • Venue:
  • International Journal of Parallel Programming
  • Year:
  • 2003

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Abstract

High performance computing requires high quality load distribution of processes of a parallel application over processors in a parallel computer at runtime such that both the maximum load and dilation are minimized. The performance of a simple randomized tree embedding algorithm that dynamically supports tree-structured parallel computations on arbitrary static networks is analyzed in this paper. The algorithm spreads newly created tree nodes to neighboring processors, which actually provides randomized dilation-1 tree embedding in static networks. We develop a linear system of equations that characterizes expected loads on all processors under the reproduction tree model, which can generate trees of arbitrary size and shape. It is shown that as the tree size becomes large, the asymptotic performance ratio of the randomized tree embedding algorithm is the ratio of the maximum processor degree to the average processor degree. This implies that the simple randomized tree embedding algorithm is able to generate high quality load distributions on virtually all static networks commonly employed in parallel and distributed computing.