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Accession Number ADA580140
Title Communication Optimal Parallel Multiplication of Sparse Random Matrices.
Publication Date Feb 2013
Media Count 19p
Personal Author A. Buluc B. Lipshitz G. Ballard J. Demmel L. Grigori
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 Erdos-Renyi 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.
Keywords Algorithms
Multiplication
Sparse matrix


 
Source Agency Non Paid ADAS
NTIS Subject Category 72B - Algebra, Analysis, Geometry, & Mathematical Logic
Corporate Author California Univ., Berkeley. Dept. of Electrical Engineering and Computer Science.
Document Type Technical report
Title Note Technical rept.
NTIS Issue Number 1325
Contract Number HR0011-12-2-0016

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