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PARALLEL SPARSE MATRIX-MATRIX MULTIPLICATION AND INDEXING: IMPLEMENTATION AND EXPERIMENTS
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DOI：10.1137/110848244.png)
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Abstract
En 中文
Generalized sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many high performance graph algorithms as well as for some linear solvers, such as algebraic multigrid. Here we show that SpGEMM also yields efficient algorithms for general sparse-matrix indexing in distributed memory, provided that the underlying SpGEMM implementation is sufficiently flexible and scalable. We demonstrate that our parallel SpGEMM methods, which use two-dimensional block data distributions with serial hypersparse kernels, are indeed highly flexible, scalable, and memory-efficient in the general case. This algorithm is the first to yield increasing speedup on an unbounded number of processors; our experiments show scaling up to thousands of processors in a variety of test scenarios.
Keywords:
parallel computing
numerical linear algebra
sparse matrix-matrix multiplication
SpGEMM
sparse matrix indexing
sparse matrix assignment
two-dimensional data decomposition
hypersparsity
graph algorithms
sparse SUMMA
subgraph extraction
graph contraction
graph batch update
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