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European Conference on Parallel Processing

Euro-Par 2011: Euro-Par 2011: Parallel Processing Workshops pp 450–459Cite as

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Column-Based Matrix Partitioning for Parallel Matrix Multiplication on Heterogeneous Processors Based on Functional Performance Models

Column-Based Matrix Partitioning for Parallel Matrix Multiplication on Heterogeneous Processors Based on Functional Performance Models

  • David Clarke30,
  • Alexey Lastovetsky30 &
  • Vladimir Rychkov30 
  • Conference paper
  • 1399 Accesses

  • 22 Citations

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7155)

Abstract

In this paper we present a new data partitioning algorithm to improve the performance of parallel matrix multiplication of dense square matrices on heterogeneous clusters. Existing algorithms either use single speed performance models which are too simplistic or they do not attempt to minimise the total volume of communication. The functional performance model (FPM) is more realistic then single speed models because it integrates many important features of heterogeneous processors such as the processor heterogeneity, the heterogeneity of memory structure, and the effects of paging. To load balance the computations the new algorithm uses FPMs to compute the area of the rectangle that is assigned to each processor. The total volume of communication is then minimised by choosing a shape and ordering so that the sum of the half-perimeters is minimised. Experimental results demonstrate that this new algorithm can reduce the total execution time of parallel matrix multiplication in comparison to existing algorithms.

Keywords

  • Parallel matrix multiplication
  • functional performance models
  • heterogeneous platforms
  • load balance
  • data partitioning

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References

  1. Beaumont, O., Boudet, V., Rastello, F., Robert, Y.: Matrix Multiplication on Heterogeneous Platforms. IEEE Trans. Parallel Distrib. Syst. 12(10), 1033–1051 (2001)

    CrossRef  MathSciNet  Google Scholar 

  2. Blackford, L., Choi, J., Cleary, A., et al.: ScaLAPACK: A Portable Linear Algebra Library for Distributed Memory Computers - Design Issues and Performance. In: Supercomputing, p. 5. IEEE (1996)

    Google Scholar 

  3. Clarke, D., Lastovetsky, A., Rychkov, V.: Dynamic Load Balancing of Parallel Computational Iterative Routines on Highly Heterogeneous HPC Platforms. Parallel Process. Lett. 21(2), 195–217 (2011)

    CrossRef  MathSciNet  Google Scholar 

  4. Dongarra, J., Pineau, J.F., Robert, Y., Vivien, F.: Matrix Product on Heterogeneous Master-Worker Platforms. In: PPoPP 2008, pp. 53–62. ACM (2008)

    Google Scholar 

  5. Goto, K., van de Geijn, R.A.: Anatomy of high-performance matrix multiplication. ACM Trans. Math. Softw. 34(3), 1–12 (2008)

    CrossRef  Google Scholar 

  6. Kalinov, A., Klimov, S.: Optimal Mapping of a Parallel Application Processes onto Heterogeneous Platform. In: Proceedings of 19th IEEE International Parallel and Distributed Processing Symposium, p. 123. IEEE (2005)

    Google Scholar 

  7. Kalinov, A., Lastovetsky, A.: Heterogeneous Distribution of Computations While Solving Linear Algebra Problems on Networks of Heterogeneous Computers. In: Sloot, P.M.A., Hoekstra, A.G., Bubak, M., Hertzberger, B. (eds.) HPCN-Europe 1999. LNCS, vol. 1593, pp. 191–200. Springer, Heidelberg (1999)

    Google Scholar 

  8. Lastovetsky, A., Reddy, R.: Data Partitioning with a Functional Performance Model of Heterogeneous Processors. Int. J. High Perform. Comput. Appl. 21(1), 76–90 (2007)

    CrossRef  Google Scholar 

  9. Lastovetsky, A., Reddy, R., Rychkov, V., Clarke, D.: Design and Implementation of Self-Adaptable Parallel Algorithms for Scientific Computing on Highly Heterogeneous HPC Platforms. [cs.DC] (2011), arXiv:1109.3074v1

    Google Scholar 

  10. Lastovetsky, A., Reddy, R.: Distributed Data Partitioning for Heterogeneous Processors Based on Partial Estimation of Their Functional Performance Models. In: Lin, H.-X., Alexander, M., Forsell, M., Knüpfer, A., Prodan, R., Sousa, L., Streit, A. (eds.) Euro-Par 2009. LNCS, vol. 6043, pp. 91–101. Springer, Heidelberg (2010)

    CrossRef  Google Scholar 

  11. Lastovetsky, A., Reddy, R.: Two-Dimensional Matrix Partitioning for Parallel Computing on Heterogeneous Processors Based on Their Functional Performance Models. In: Lin, H.-X., Alexander, M., Forsell, M., Knüpfer, A., Prodan, R., Sousa, L., Streit, A. (eds.) Euro-Par 2009. LNCS, vol. 6043, pp. 112–121. Springer, Heidelberg (2010)

    CrossRef  Google Scholar 

  12. Zhuo, L., Prasanna, V.K.: Optimizing Matrix Multiplication on Heterogeneous Reconfigurable Systems. In: PARCO 2007, pp. 561–568 (2007)

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Computer Science and Informatics, University College Dublin, Belfield, Dublin, 4, Ireland

    David Clarke, Alexey Lastovetsky & Vladimir Rychkov

Authors
  1. David Clarke
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  2. Alexey Lastovetsky
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  3. Vladimir Rychkov
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Editor information

Editors and Affiliations

  1. Scilytics, Koellnerhofgasse 3/15A, 1010, Vienna, Austria

    Michael Alexander

  2. ICAR-CNR, Via P. Castellino, 111, 80131, Napoli, Italy

    Pasqua D’Ambra

  3. University of Amsterdam, 1090, Amsterdam, Netherlands

    Adam Belloum

  4. Innovative Computing Laboratory, The University of Tennessee, USA

    George Bosilca

  5. Department of Experimental Medicine and Clinic, University Magna Græcia, 88100, Catanzaro, Italy

    Mario Cannataro

  6. Computer Science Department, University of Pisa, Italy

    Marco Danelutto

  7. Second University of Naples, Italy

    Beniamino Di Martino

  8. TU München, Boltzmannstr. 3, 85748, Garching, Germany

    Michael Gerndt

  9. Equipe Runtime, INRIA Bordeaux Sud-Ouest, 33405, Talence Cedex, France

    Emmanuel Jeannot & Raymond Namyst & 

  10. Equipe HIEPACS, INRIA Bordeaux Sud-Ouest, 33405, Talence Cedex, France

    Jean Roman

  11. Oak Ridge National Laboratory, Computer Science and Mathematics Division, 37831-6164, Oak Ridge, TN, USA

    Stephen L. Scott

  12. Department of Scientific Computing, University of Vienna, Nordbergstr. 15/3C, 1090, Vienna, Austrial

    Jesper Larsson Traff

  13. Computer Science and Mathematics Division, Oak Ridge National Laboratory, 37831, Oak Ridge, TN, USA

    Geoffroy Vallée

  14. Technische Universität München, Germany

    Josef Weidendorfer

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© 2012 Springer-Verlag Berlin Heidelberg

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Cite this paper

Clarke, D., Lastovetsky, A., Rychkov, V. (2012). Column-Based Matrix Partitioning for Parallel Matrix Multiplication on Heterogeneous Processors Based on Functional Performance Models. In: Alexander, M., et al. Euro-Par 2011: Parallel Processing Workshops. Euro-Par 2011. Lecture Notes in Computer Science, vol 7155. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29737-3_50

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  • DOI: https://doi.org/10.1007/978-3-642-29737-3_50

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  • Print ISBN: 978-3-642-29736-6

  • Online ISBN: 978-3-642-29737-3

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