Graph Expansion Analysis for Communication Costs of Fast Rectangular Matrix Multiplication

Grey Ballard; James Demmel; Olga Holtz; Benjamin Lipshitz; Oded Schwartz

doi:10.1007/978-3-642-34862-4_2

Graph Expansion Analysis for Communication Costs of Fast Rectangular Matrix Multiplication

Grey Ballard, James Demmel, Olga Holtz, Benjamin Lipshitz, Oded Schwartz

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

11 Scopus citations

Abstract

Graph expansion analysis of computational DAGs is useful for obtaining communication cost lower bounds where previous methods, such as geometric embedding, are not applicable. This has recently been demonstrated for Strassen’s and Strassen-like fast square matrix multiplication algorithms. Here we extend the expansion analysis approach to fast algorithms for rectangular matrix multiplication, obtaining a new class of communication cost lower bounds. These apply, for example to the algorithms of Bini et al. (1979) and the algorithms of Hopcroft and Kerr (1971). Some of our bounds are proved to be optimal.

Original language	English
Title of host publication	Design and Analysis of Algorithms - 1st Mediterranean Conference on Algorithms, MedAlg 2012, Proceedings
Editors	Guy Even, Dror Rawitz
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	13-36
Number of pages	24
ISBN (Print)	9783642348617
DOIs	https://doi.org/10.1007/978-3-642-34862-4_2
State	Published - 2012
Externally published	Yes
Event	1st Mediterranean Conference on Algorithms, MedAlg 2012 - Kibbutz Ein Gedi, Israel Duration: 3 Dec 2012 → 5 Dec 2012

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	7659 LNNS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	1st Mediterranean Conference on Algorithms, MedAlg 2012
Country/Territory	Israel
City	Kibbutz Ein Gedi
Period	3/12/12 → 5/12/12

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2012.

Access to Document

10.1007/978-3-642-34862-4_2

Cite this

Ballard, G., Demmel, J., Holtz, O., Lipshitz, B., & Schwartz, O. (2012). Graph Expansion Analysis for Communication Costs of Fast Rectangular Matrix Multiplication. In G. Even, & D. Rawitz (Eds.), Design and Analysis of Algorithms - 1st Mediterranean Conference on Algorithms, MedAlg 2012, Proceedings (pp. 13-36). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7659 LNNS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-642-34862-4_2

Ballard, Grey ; Demmel, James ; Holtz, Olga et al. / Graph Expansion Analysis for Communication Costs of Fast Rectangular Matrix Multiplication. Design and Analysis of Algorithms - 1st Mediterranean Conference on Algorithms, MedAlg 2012, Proceedings. editor / Guy Even ; Dror Rawitz. Springer Science and Business Media Deutschland GmbH, 2012. pp. 13-36 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "Graph expansion analysis of computational DAGs is useful for obtaining communication cost lower bounds where previous methods, such as geometric embedding, are not applicable. This has recently been demonstrated for Strassen{\textquoteright}s and Strassen-like fast square matrix multiplication algorithms. Here we extend the expansion analysis approach to fast algorithms for rectangular matrix multiplication, obtaining a new class of communication cost lower bounds. These apply, for example to the algorithms of Bini et al. (1979) and the algorithms of Hopcroft and Kerr (1971). Some of our bounds are proved to be optimal.",

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

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doi = "10.1007/978-3-642-34862-4_2",

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Ballard, G, Demmel, J, Holtz, O, Lipshitz, B & Schwartz, O 2012, Graph Expansion Analysis for Communication Costs of Fast Rectangular Matrix Multiplication. in G Even & D Rawitz (eds), Design and Analysis of Algorithms - 1st Mediterranean Conference on Algorithms, MedAlg 2012, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7659 LNNS, Springer Science and Business Media Deutschland GmbH, pp. 13-36, 1st Mediterranean Conference on Algorithms, MedAlg 2012, Kibbutz Ein Gedi, Israel, 3/12/12. https://doi.org/10.1007/978-3-642-34862-4_2

Graph Expansion Analysis for Communication Costs of Fast Rectangular Matrix Multiplication. / Ballard, Grey; Demmel, James; Holtz, Olga et al.
Design and Analysis of Algorithms - 1st Mediterranean Conference on Algorithms, MedAlg 2012, Proceedings. ed. / Guy Even; Dror Rawitz. Springer Science and Business Media Deutschland GmbH, 2012. p. 13-36 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7659 LNNS).

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

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Ballard G, Demmel J, Holtz O, Lipshitz B, Schwartz O. Graph Expansion Analysis for Communication Costs of Fast Rectangular Matrix Multiplication. In Even G, Rawitz D, editors, Design and Analysis of Algorithms - 1st Mediterranean Conference on Algorithms, MedAlg 2012, Proceedings. Springer Science and Business Media Deutschland GmbH. 2012. p. 13-36. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-34862-4_2

Graph Expansion Analysis for Communication Costs of Fast Rectangular Matrix Multiplication

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