Parallel sparse matrix-vector and matrix-transpose-vector multiplication using compressed sparse blocks

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Parallel sparse matrix-vector and matrix-transpose-vector multiplication using compressed sparse blocks (2009)

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by Aydın Buluç , Jeremy T. Fineman , Matteo Frigo , John R. Gilbert , Charles E. Leiserson

Venue:	IN SPAA
Citations:	26 - 1 self

BibTeX

@INPROCEEDINGS{Buluç09parallelsparse,
    author = {Aydın Buluç and Jeremy T. Fineman and Matteo Frigo and John R. Gilbert and Charles E. Leiserson},
    title = {Parallel sparse matrix-vector and matrix-transpose-vector multiplication using compressed sparse blocks},
    booktitle = {IN SPAA},
    year = {2009},
    pages = {233--244},
    publisher = {}
}

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Abstract

This paper introduces a storage format for sparse matrices, called compressed sparse blocks (CSB), which allows both Ax and A T x to be computed efficiently in parallel, where A is an n × n sparse matrix with nnz ≥ n nonzeros and x is a dense n-vector. Our algorithms use Θ(nnz) work (serial running time) and Θ ( √ nlgn) span (critical-path length), yielding a parallelism of Θ(nnz / √ nlgn), which is amply high for virtually any large matrix. The storage requirement for CSB is esssentially the same as that for the morestandard compressed-sparse-rows (CSR) format, for which computing Ax in parallel is easy but A T x is difficult. Benchmark results indicate that on one processor, the CSB algorithms for Ax and A T x run just as fast as the CSR algorithm for Ax, but the CSB algorithms also scale up linearly with processors until limited by offchip memory bandwidth.

Keyphrases

compressed sparse block parallel sparse matrix-vector matrix-transpose-vector multiplication sparse matrix csb algorithm large matrix offchip memory bandwidth benchmark result algorithm use morestandard compressed-sparse-rows storage format nnz nonzeros dense n-vector nnz nlgn storage requirement serial running time csr algorithm critical-path length

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