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

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

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.

[1] Shmuel Winograd,et al. On multiplication of 2 × 2 matrices , 1971 .

[2] D. Bini. Fast Matrix Multiplication in Handbook of Linear Algebra , 2007 .

[3] Lynn Elliot Cannon,et al. A cellular computer to implement the kalman filter algorithm , 1969 .

[4] Dario Bini. Fast Matrix Multiplication , 2006 .

[5] George Karypis,et al. Introduction to Parallel Computing Solution Manual , 2003 .

[6] L. Hogben. Handbook of Linear Algebra , 2006 .

[7] Fast Matrix Multiplication via Group Actions , 2009 .

[8] Lionel M. Ni,et al. A survey of wormhole routing techniques in direct networks , 1993, Computer.

[9] V. Strassen. Gaussian elimination is not optimal , 1969 .

[10] David Notkin,et al. Computer science in Japanese universities , 1993, Computer.

[11] Harun Artuner,et al. Efficient and Scalable Routing Algorithms for Collective Communication Operations on 2D All-Port Torus Networks , 2011, International Journal of Parallel Programming.