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A New Parallel Matrix Multiplication Algorithm for Wormhole-Routed All-Port 2D/3D Torus Networks

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Mathematical Methods in Engineering

Abstract

A new matrix multiplication algorithm is proposed for massively parallel supercomputers with 2D/3D, all-port torus interconnection networks. The proposed algorithm is based on the traditional row-by-column multiplication matrix product model and employs a special routing pattern for better scalability. It compares favorably to the variants of Cannon’s and DNS algorithms since it allows matrices of the same size to be multiplied on a higher number of processors due to lower data communications overhead.

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Notes

  1. 1.

    A review of these methods can be found in Chap. 47, Handbook of Linear Algebra [1].

  2. 2.

    Throughout the paper, we assume that the matrix multiplication operation is to be performed such that this initial mapping is preserved at the end of the operation.

  3. 3.

    For a good intro to routing in general and wormhole routing in particular, see [5].

References

  1. Bini DA (2007) Fast matrix multiplication. In: Hogben L (ed) Handbook of linear algebra. Chapman & Hall/CRC press, Boca Raton (Chap. 47)

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  2. Cannon LE (1969) A cellular computer to implement the kalman filter algorithm. Ph. D. Thesis, Montana State University

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  3. Grama A, Gupta A, Karypis G, Kumar V (2003) Introduction to parallel computing, 2nd edn. Addison Wesle, Eugene

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  4. Imre KM, Baransel C, Artuner H (2010) Efficient and scalable routing algorithms for collective communication operations on 2D All-Port Torus networks. Int J Parallel Progr 39(6):746–782

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  5. Ni LM, McKinley PK (1993, February) A survey of wormhole routing techniques in direct networks. Computer 26(2):62–76

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  6. Strassen V (1969) Gaussian elimination is not optimal. Numer Math 13:354–356

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  7. Winograd S (1971) On multiplication of 2 × 2 matrices. Linear Algebra Appl 4:381–388

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Author information

Authors and Affiliations

  1. Saltus Yazılım Ltd., Hacettepe University Technopolis, Ankara, Turkey

    Cesur Baransel

  2. Dept. of Computer Engineering, Hacettepe University, Ankara, Turkey

    Kayhan Imre & Harun Artuner

Authors
  1. Cesur Baransel
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  2. Kayhan Imre
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  3. Harun Artuner
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Corresponding author

Correspondence to Cesur Baransel .

Editor information

Editors and Affiliations

  1. Coimbra Institute of Engineering, Coimbra, Portugal

    Nuno Miguel Fonseca Ferreira

  2. Dept of Electrical Engineering, Institute of Engineering of Porto, Porto, Portugal

    José António Tenreiro Machado

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© 2014 Springer Science+Business Media Dordrecht

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Baransel, C., Imre, K., Artuner, H. (2014). A New Parallel Matrix Multiplication Algorithm for Wormhole-Routed All-Port 2D/3D Torus Networks. In: Fonseca Ferreira, N., Tenreiro Machado, J. (eds) Mathematical Methods in Engineering. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7183-3_2

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  • DOI: https://doi.org/10.1007/978-94-007-7183-3_2

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-7182-6

  • Online ISBN: 978-94-007-7183-3

  • eBook Packages: EngineeringEngineering (R0)

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