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 proceedingConference contributionpeer-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 languageAmerican English
Title of host publicationDesign and Analysis of Algorithms - 1st Mediterranean Conference on Algorithms, MedAlg 2012, Proceedings
EditorsGuy Even, Dror Rawitz
PublisherSpringer Science and Business Media Deutschland GmbH
Pages13-36
Number of pages24
ISBN (Print)9783642348617
DOIs
StatePublished - 2012
Externally publishedYes
Event1st Mediterranean Conference on Algorithms, MedAlg 2012 - Kibbutz Ein Gedi, Israel
Duration: 3 Dec 20125 Dec 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7659 LNNS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference1st Mediterranean Conference on Algorithms, MedAlg 2012
Country/TerritoryIsrael
CityKibbutz Ein Gedi
Period3/12/125/12/12

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2012.

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