Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

Communication-Optimal Parallel Recursive Rectangular Matrix Multiplication

James Demmel, David Eliahu, Armando Fox, Shoaib Ashraf Kamil, Benjamin Lipshitz, Oded Schwartz and Omer Spillinger

EECS Department
University of California, Berkeley
Technical Report No. UCB/EECS-2012-205
October 24, 2012

http://www.eecs.berkeley.edu/Pubs/TechRpts/2012/EECS-2012-205.pdf

Communication-optimal algorithms are known for square matrix multiplication. Here, we obtain the first communication-optimal algorithm for all dimensions of rectan- gular matrices. Combining the dimension-splitting technique of Frigo, Leiserson, Prokop and Ramachandran (1999) with the recursive BFS/DFS approach of Ballard, Demmel, Holtz, Lipshitz and Schwartz (2012) allows for a communication-optimal as well as cache- and network-oblivious algorithm. Moreover, the implementation is simple: approximately 50 lines of code for the shared-memory version. Since the new algorithm minimizes communication across the network, between NUMA domains, and between levels of cache, it performs well in practice on both shared- and distributed-memory machines. We show significant speedups over existing parallel linear algebra libraries both on a 32-core shared-memory machine and on a distributed-memory supercomputer.


BibTeX citation:

@techreport{Demmel:EECS-2012-205,
    Author = {Demmel, James and Eliahu, David and Fox, Armando and Kamil, Shoaib Ashraf and Lipshitz, Benjamin and Schwartz, Oded and Spillinger, Omer},
    Title = {Communication-Optimal Parallel Recursive Rectangular Matrix Multiplication},
    Institution = {EECS Department, University of California, Berkeley},
    Year = {2012},
    Month = {Oct},
    URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2012/EECS-2012-205.html},
    Number = {UCB/EECS-2012-205},
    Abstract = {Communication-optimal algorithms are known for square matrix multiplication. Here, we obtain the first communication-optimal algorithm for all dimensions of rectan- gular matrices. Combining the dimension-splitting technique of Frigo, Leiserson, Prokop and Ramachandran (1999) with the recursive BFS/DFS approach of Ballard, Demmel, Holtz, Lipshitz and Schwartz (2012) allows for a communication-optimal as well as cache- and network-oblivious algorithm. Moreover, the implementation is simple: approximately 50 lines of code for the shared-memory version. Since the new algorithm minimizes communication across the network, between NUMA domains, and between levels of cache, it performs well in practice on both shared- and distributed-memory machines. We show significant speedups over existing parallel linear algebra libraries both on a 32-core shared-memory machine and on a distributed-memory supercomputer.}
}

EndNote citation:

%0 Report
%A Demmel, James
%A Eliahu, David
%A Fox, Armando
%A Kamil, Shoaib Ashraf
%A Lipshitz, Benjamin
%A Schwartz, Oded
%A Spillinger, Omer
%T Communication-Optimal Parallel Recursive Rectangular Matrix Multiplication
%I EECS Department, University of California, Berkeley
%D 2012
%8 October 24
%@ UCB/EECS-2012-205
%U http://www.eecs.berkeley.edu/Pubs/TechRpts/2012/EECS-2012-205.html
%F Demmel:EECS-2012-205