Improving the Communication Pattern in MatrixVector Operations for Large ScaleFree Graphs by Disaggregation
Matrixvector multiplication is the key operation in any Krylovsubspace iteration method. We are interested in Krylov methods applied to problems associated with the graph Laplacian arising from large scalefree graphs. Furthermore, computations with graphs of this type on parallel distributedmemory computers are challenging. This is due to the fact that scalefree 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 matrixvector product. Here, 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 matrixvector operations for the original graph are performed via a factored triple matrixvector product involving the embedding graph. And even though the latter graph is larger, we are able to decrease the communication requirements considerably and improve the performance of the matrixvector product.
 Authors:

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 Emory Univ., Atlanta, GA (United States)
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Publication Date:
 OSTI Identifier:
 1225691
 Report Number(s):
 LLNLJRNL564237
Journal ID: ISSN 10648275
 DOE Contract Number:
 AC5207NA27344
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: SIAM Journal on Scientific Computing; Journal Volume: 35; Journal Issue: 5
 Publisher:
 SIAM
 Research Org:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE scalefree graphs; parallel computation; Laplacian matrices; disaggreation
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