Communication optimal parallel multiplication of sparse random matrices

  • Authors:

  • Grey Ballard;Aydin Buluc;James Demmel;Laura Grigori;Benjamin Lipshitz;Oded Schwartz;Sivan Toledo

  • Affiliations:

  • University of California Berkeley, Berkeley, CA, USA;Lawrence Berkeley National Laboratory, Ber, CA, USA;University of California Berkeley, Berkeley, CA, USA;INRIA Paris - Rocquencourt, Paris, France;University of California Berkeley, Berkeley, CA, USA;University of California Berkeley, Berkeley, CA, USA;Tel-Aviv University, Tel-Aviv, Israel

  • Venue:
  • Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
  • Year:
  • 2013

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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 Erdős-Rényi random graphs on distributed-memory 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.