Hierarchical Parallel Matrix Multiplication on Large-Scale Distributed Memory Platforms

Jean-Noel Quintin, Khalid Hasanov, Alexey Lastovetsky

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations

Abstract

Matrix multiplication is a very important computation kernel both in its own right as a building block of many scientific applications and as a popular representative for other scientific applications. Cannon's algorithm which dates back to 1969 was the first efficient algorithm for parallel matrix multiplication providing theoretically optimal communication cost. However this algorithm requires a square number of processors. In the mid-1990s, the SUMMA algorithm was introduced. SUMMA overcomes the shortcomings of Cannon's algorithm as it can be used on a nonsquare number of processors as well. Since then the number of processors in HPC platforms has increased by two orders of magnitude making the contribution of communication in the overall execution time more significant. Therefore, the state of the art parallel matrix multiplication algorithms should be revisited to reduce the communication cost further. This paper introduces a new parallel matrix multiplication algorithm, Hierarchical SUMMA (HSUMMA), which is a redesign of SUMMA. Our algorithm reduces the communication cost of SUMMA by introducing a two-level virtual hierarchy into the two-dimensional arrangement of processors. Experiments on an IBM BlueGene/P demonstrate the reduction of communication cost up to 2.08 times on 2048 cores and up to 5.89 times on 16384 cores. © 2013 IEEE.
Original languageEnglish (US)
Title of host publication2013 42nd International Conference on Parallel Processing
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Pages754-762
Number of pages9
ISBN (Print)9780769551173
DOIs
StatePublished - Oct 2013
Externally publishedYes

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