Matrix multiplication I/O-complexity by path routing

Jacob Scott, Olga Holtz, Oded Schwartz

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

14 Scopus citations

Abstract

We apply a novel technique based on path routings to obtain optimal I/O-complexity lower bounds for all Strassenlike fast matrix multiplication algorithms computed in serial or in parallel, assuming no reuse of nontrivial intermediate linear combinations. Given fast memory of size M, we prove an I/O-complexity lower bound of Ω ((n/√)ω0. M) for any Strassen-like matrix multiplication algorithm applied to n × n matrices of arithmetic complexity Ω(nω0) with ω0 < 3 under this assumption. This generalizes an approach by Ballard, Demmel, Holtz, and Schwartz that provides a tight lower bound for Strassen's matrix multiplication algorithm but which does not apply to algorithms with disconnected encoding or decoding components of the underlying computation graph or algorithms with multiply copied values. We overcome these challenges via a new graphtheoretical approach for proving I/O-complexity lower bounds without the use of edge expansions.

Original languageAmerican English
Title of host publicationSPAA 2015 - Proceedings of the 27th ACM Symposium on Parallelism in Algorithms and Architectures
PublisherAssociation for Computing Machinery
Pages35-45
Number of pages11
ISBN (Electronic)9781450335881
DOIs
StatePublished - 13 Jun 2015
Event27th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2015 - Portland, United States
Duration: 13 Jun 201515 Jun 2015

Publication series

NameAnnual ACM Symposium on Parallelism in Algorithms and Architectures
Volume2015-June

Conference

Conference27th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2015
Country/TerritoryUnited States
CityPortland
Period13/06/1515/06/15

Bibliographical note

Publisher Copyright:
Copyright © 2015 ACM.

Keywords

  • Communication-avoiding algorithms
  • Fast matrix multiplication
  • I/O-complexity

Fingerprint

Dive into the research topics of 'Matrix multiplication I/O-complexity by path routing'. Together they form a unique fingerprint.

Cite this