Improving the Communication Pattern in Matrix-Vector Operations for Large Scale-Free Graphs by Disaggregation

Matrix-vector multiplication is the key operation in any Krylov-subspace iteration method. We are interested in Krylov methods applied to problems associated with the graph Laplacian arising from large scale-free graphs. Computations with graphs of this type on parallel distributed-memory computers...

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Veröffentlicht in:SIAM journal on scientific computing 2013-01, Vol.35 (5), p.S465-S486
Hauptverfasser: Kuhlemann, Verena, Vassilevski, Panayot S
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Sprache:eng
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Zusammenfassung:Matrix-vector multiplication is the key operation in any Krylov-subspace iteration method. We are interested in Krylov methods applied to problems associated with the graph Laplacian arising from large scale-free graphs. Computations with graphs of this type on parallel distributed-memory computers are challenging. This is due to the fact that scale-free graphs have a degree distribution that follows a power law, and currently available graph partitioners are not efficient for such an irregular degree distribution. The lack of a good partitioning leads to excessive interprocessor communication requirements during every matrix-vector product. We present an approach to alleviate this problem based on embedding the original irregular graph into a more regular one by disaggregating (splitting up) vertices in the original graph. The matrix-vector operations for the original graph are performed via a factored triple matrix-vector product involving the embedding graph. Even though the latter graph is larger, we are able to decrease the communication requirements considerably and improve the performance of the matrix-vector product. [PUBLICATION ABSTRACT]
ISSN:1064-8275
1095-7197
DOI:10.1137/12088313X