Graph expansion and communication costs of fast matrix multiplication: regular submission

Authors:
Grey Ballard;James Demmel;Olga Holtz;Oded Schwartz
Affiliations:
University of California, Berkeley, Berkeley, CA, USA;University of California, Berkeley, Berkeley, CA, USA;University of California, Berkeley and TU-Berlin., Berkeley, CA, USA;University of California, Berkeley, University of California, Berk, CA, USA
Venue:
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
Year:
2011

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Abstract

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. For sequential algorithms these bounds are attainable and so optimal.