Emulations between QSM, BSP and LogP: a framework for general-purpose parallel algorithm design

  • Authors:

  • Vijaya Ramachandran;Brian Grayson;Michael Dahlin

  • Affiliations:

  • Department of Computer Sciences, University of Texas, Austin, TX;Motorola Somerset Design Center, Austin, TX;Department of Computer Sciences, University of Texas, Austin, TX

  • Venue:
  • Journal of Parallel and Distributed Computing
  • Year:
  • 2003

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Abstract

We present work-preserving emulations with small slowdown between LogP and two other parallel models: BSP and QSM. In conjunction with earlier work-preserving emulations between QSM and BSP, these results establish a close correspondence between these three general-purpose parallel models. Our results also correct and improve on results reported earlier on emulations between BSP and LogP. In particular we shed new light on the relative power of stalling and non-stalling LogP models.The QSM is a shared-memory model with only two parameters--p, the number of processors, and g, a bandwidth parameter. The simplicity of the QSM parameters makes QSM a convenient model for parallel algorithm design, and simple work-preserving emulations of QSM on BSP and QSM on LogP show that algorithms designed for the QSM will also map quite well to these other models. The simplicity and generality of QSM present a strong case for the use of QSM as the model of choice for parallel algorithm design.We present QSM algorithms for three basic problems--prefix sums, sample sort and list ranking. We show that these algorithms are optimal in terms of both the total work performed and the number of 'phases' for input sizes of practical interest. For prefix sums, we present a matching lower bound that shows our algorithm to be optimal over the complete range of these parameters. We then examine the predicted and simulated performance of these algorithms. These results suggest that QSM analysis will predict algorithm performance quite accurately for problem sizes that arise in practice.