Improving the Communication Pattern in Matrix-Vector Operations for Large Scale-Free Graphs by Disaggregation
- Emory Univ., Atlanta, GA (United States)
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
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. Furthermore, 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. 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 matrix-vector operations for the original graph are performed via a factored triple matrix-vector 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 matrix-vector product.
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC52-07NA27344
- OSTI ID:
- 1225691
- Report Number(s):
- LLNL-JRNL-564237
- Journal Information:
- SIAM Journal on Scientific Computing, Vol. 35, Issue 5; ISSN 1064-8275
- Publisher:
- SIAM
- Country of Publication:
- United States
- Language:
- English
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