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# Graph Expansion and Communication Costs of Fast Matrix Multiplication

@article{Ballard2012GraphEA, title={Graph Expansion and Communication Costs of Fast Matrix Multiplication}, author={Grey Ballard and James Demmel and Olga Holtz and Oded Schwartz}, journal={J. ACM}, year={2012}, volume={59}, pages={32:1-32:23} }

- Published 2012 in J. ACM
DOI:10.1145/2395116.2395121

The communication cost of algorithms (also known as I/O-complexity) is shown to be closely related to the expansion properties of the corresponding computation graphs. We demonstrate this on Strassen's and other fast matrix multiplication algorithms, and obtain the first lower bounds on their communication costs.
In the sequential case, where the processor has a fast memory of size <i>M</i>, too small to store three <i>n</i>-by-<i>n</i> matrices, the lower bound on the number of words moved… CONTINUE READING

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