Simultaneous Input and Output Matrix Partitioning for Outer-Product--Parallel Sparse Matrix-Matrix Multiplication

For outer-product--parallel sparse matrix-matrix multiplication (SpGEMM) of the form $C\!=\!A\!\times\!B$, we propose three hypergraph models that achieve simultaneous partitioning of input and output matrices without any replication of input data. All three hypergraph models perform conformable one...

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Vydáno v:SIAM journal on scientific computing Ročník 36; číslo 5; s. C568 - C590
Hlavní autoři: Akbudak, Kadir, Aykanat, Cevdet
Médium: Journal Article
Jazyk:angličtina
Vydáno: 01.01.2014
Témata:
Algorithms
Computation
Libraries
Mathematical models
Multiplication
Partitioning
Replication
Two dimensional
ISSN:1064-8275, 1095-7197
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Shrnutí:For outer-product--parallel sparse matrix-matrix multiplication (SpGEMM) of the form $C\!=\!A\!\times\!B$, we propose three hypergraph models that achieve simultaneous partitioning of input and output matrices without any replication of input data. All three hypergraph models perform conformable one-dimensional (1D) columnwise and 1D rowwise partitioning of the input matrices $A$ and $B$, respectively. The first hypergraph model performs two-dimensional (2D) nonzero-based partitioning of the output matrix, whereas the second and third models perform 1D rowwise and 1D columnwise partitioning of the output matrix, respectively. This partitioning scheme induces a two-phase parallel SpGEMM algorithm, where communication-free local SpGEMM computations constitute the first phase and the multiple single-node-accumulation operations on the local SpGEMM results constitute the second phase. In these models, the two partitioning constraints defined on weights of vertices encode balancing computational loads of processors during the two separate phases of the parallel SpGEMM algorithm. The partitioning objective of minimizing the cutsize defined over the cut nets encodes minimizing the total volume of communication that will occur during the second phase of the parallel SpGEMM algorithm. An MPI-based parallel SpGEMM library is developed to verify the validity of our models in practice. Parallel runs of the library for a wide range of realistic SpGEMM instances on two large-scale parallel systems JUQUEEN (an IBM BlueGene/Q system) and SuperMUC (an Intel-based cluster) show that the proposed hypergraph models attain high speedup values.
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ISSN:1064-8275
1095-7197
DOI:10.1137/13092589X