Revisiting the I/O-complexity of fast matrix multiplication with recomputations

Roy Nissim, Oded Schwartz

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

5 Scopus citations

Abstract

Communication costs, between processors and across the memory hierarchy, often dominate the runtime of algorithms. Can we trade these costs for recomputations? Most algorithms do not utilize recomputation for this end, and most communication cost lower bounds assume no recomputation, hence do not address this fundamental question. Recently, Bilardi and De Stefani (2017), and Bilardi, Scquizzato, and Silvestri (2018) showed that recomputations cannot reduce communication costs in Strassen's fast matrix multiplication and in fast Fourier transform. We extend the former bound and show that recomputations cannot reduce communication costs for a few other fast matrix multiplication algorithms.

Original languageAmerican English
Title of host publicationProceedings - 2019 IEEE 33rd International Parallel and Distributed Processing Symposium, IPDPS 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages482-490
Number of pages9
ISBN (Electronic)9781728112466
DOIs
StatePublished - May 2019
Event33rd IEEE International Parallel and Distributed Processing Symposium, IPDPS 2019 - Rio de Janeiro, Brazil
Duration: 20 May 201924 May 2019

Publication series

NameProceedings - 2019 IEEE 33rd International Parallel and Distributed Processing Symposium, IPDPS 2019

Conference

Conference33rd IEEE International Parallel and Distributed Processing Symposium, IPDPS 2019
Country/TerritoryBrazil
CityRio de Janeiro
Period20/05/1924/05/19

Bibliographical note

Publisher Copyright:
© 2019 IEEE

Keywords

  • Fast Matrix Multiplication
  • I/O-complexity
  • Memory Hierarchy
  • Parallel Computation
  • Recomputation

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