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

Grey Ballard; James Demmel; Olga Holtz; Oded Schwartz

doi:10.1145/1989493.1989495

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

Grey Ballard^*, James Demmel, Olga Holtz, Oded Schwartz

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

22 Scopus citations

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.

Original language	English
Title of host publication	SPAA'11 - Proceedings of the 23rd Annual Symposium on Parallelism in Algorithms and Architectures
Pages	1-11
Number of pages	11
DOIs	https://doi.org/10.1145/1989493.1989495
State	Published - 2011
Externally published	Yes
Event	23rd ACM Symposium on Parallelism in Algorithms and Architectures, SPAA'11 - San Jose, CA, United States Duration: 4 Jun 2011 → 6 Jun 2011

Publication series

Name	Annual ACM Symposium on Parallelism in Algorithms and Architectures

Conference

Conference	23rd ACM Symposium on Parallelism in Algorithms and Architectures, SPAA'11
Country/Territory	United States
City	San Jose, CA
Period	4/06/11 → 6/06/11

Keywords

communication avoiding algorithms
fast matrix multiplication
i/o-complexity

Access to Document

10.1145/1989493.1989495

Cite this

Ballard, G., Demmel, J., Holtz, O., & Schwartz, O. (2011). Graph expansion and communication costs of fast matrix multiplication: Regular submission. In SPAA'11 - Proceedings of the 23rd Annual Symposium on Parallelism in Algorithms and Architectures (pp. 1-11). (Annual ACM Symposium on Parallelism in Algorithms and Architectures). https://doi.org/10.1145/1989493.1989495

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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.",

keywords = "communication avoiding algorithms, fast matrix multiplication, i/o-complexity",

author = "Grey Ballard and James Demmel and Olga Holtz and Oded Schwartz",

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doi = "10.1145/1989493.1989495",

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pages = "1--11",

booktitle = "SPAA'11 - Proceedings of the 23rd Annual Symposium on Parallelism in Algorithms and Architectures",

note = "23rd ACM Symposium on Parallelism in Algorithms and Architectures, SPAA'11 ; Conference date: 04-06-2011 Through 06-06-2011",

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Ballard, G, Demmel, J, Holtz, O & Schwartz, O 2011, Graph expansion and communication costs of fast matrix multiplication: Regular submission. in SPAA'11 - Proceedings of the 23rd Annual Symposium on Parallelism in Algorithms and Architectures. Annual ACM Symposium on Parallelism in Algorithms and Architectures, pp. 1-11, 23rd ACM Symposium on Parallelism in Algorithms and Architectures, SPAA'11, San Jose, CA, United States, 4/06/11. https://doi.org/10.1145/1989493.1989495

Graph expansion and communication costs of fast matrix multiplication: Regular submission. / Ballard, Grey; Demmel, James; Holtz, Olga et al.
SPAA'11 - Proceedings of the 23rd Annual Symposium on Parallelism in Algorithms and Architectures. 2011. p. 1-11 (Annual ACM Symposium on Parallelism in Algorithms and Architectures).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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

Abstract

Publication series

Conference

Keywords

Access to Document

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