TY - GEN

T1 - Communication optimal parallel multiplication of sparse random matrices

AU - Ballard, Grey

AU - Buluç, Aydin

AU - Demmel, James

AU - Grigori, Laura

AU - Lipshitz, Benjamin

AU - Schwartz, Oded

AU - Toledo, Sivan

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Communication-avoiding algorithms

KW - Communication-cost lower bounds

KW - Random graphs

KW - Sparse matrix multiplication

UR - http://www.scopus.com/inward/record.url?scp=84883515454&partnerID=8YFLogxK

U2 - 10.1145/2486159.2486196

DO - 10.1145/2486159.2486196

M3 - Conference contribution

AN - SCOPUS:84883515454

SN - 9781450315722

T3 - Annual ACM Symposium on Parallelism in Algorithms and Architectures

SP - 222

EP - 231

BT - SPAA 2013 - Proceedings of the 25th ACM Symposium on Parallelism in Algorithms and Architectures

PB - Association for Computing Machinery

T2 - 25th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2013

Y2 - 23 July 2013 through 25 July 2013

ER -