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Title: 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. 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.
 [1] ;  [2]
  1. Emory Univ., Atlanta, GA (United States)
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 1064-8275
DOE Contract Number:
Resource Type:
Journal Article
Resource Relation:
Journal Name: SIAM Journal on Scientific Computing; Journal Volume: 35; Journal Issue: 5
Research Org:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org:
Country of Publication:
United States
97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE scale-free graphs; parallel computation; Laplacian matrices; disaggreation