Communication optimal parallel multiplication of sparse random matrices

Grey Ballard, Aydin Buluç, James Demmel, Laura Grigori, Benjamin Lipshitz, Oded Schwartz, Sivan Toledo

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

Abstract

Parallel algorithms for sparse matrix-matrix multiplication typically spend most of their time on inter-processor communication rather than on computation, and hardware trends predict the relative cost of communication will only increase. Thus, sparse matrix multiplication algorithms must minimize communication costs in order to scale to large processor counts. In this paper, we consider multiplying sparse matrices corresponding to Erdo″s- Rényi random graphs on distributedmemory parallel machines. We prove a new lower bound on the expected communication cost for a wide class of algorithms. Our analysis of existing algorithms shows that, while some are optimal for a limited range of matrix density and number of processors, none is optimal in general. We obtain two new parallel algorithms and prove that they match the expected communication cost lower bound, and hence they are optimal.

Original languageEnglish
Title of host publicationSPAA 2013 - Proceedings of the 25th ACM Symposium on Parallelism in Algorithms and Architectures
PublisherAssociation for Computing Machinery
Pages222-231
Number of pages10
ISBN (Print)9781450315722
DOIs
StatePublished - 2013
Event25th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2013 - Montreal, QC, Canada
Duration: 23 Jul 201325 Jul 2013

Publication series

NameAnnual ACM Symposium on Parallelism in Algorithms and Architectures

Conference

Conference25th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2013
Country/TerritoryCanada
CityMontreal, QC
Period23/07/1325/07/13

Keywords

  • Communication-avoiding algorithms
  • Communication-cost lower bounds
  • Random graphs
  • Sparse matrix multiplication

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