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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| Published in: | SIAM journal on scientific computing Vol. 36; no. 5; pp. C568 - C590 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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01.01.2014
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| ISSN: | 1064-8275, 1095-7197 |
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| Abstract | 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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| AbstractList | 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. |
| Author | Akbudak, Kadir Aykanat, Cevdet |
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| Cites_doi | 10.1063/1.1372182 10.1007/BF02024486 10.1137/080737770 10.1021/ct200897x 10.1145/1089014.1089021 10.1137/110848244 10.1063/1.477969 10.1109/71.780863 10.1145/355791.355796 10.1016/j.jpdc.2007.11.002 10.1103/PhysRevB.47.10891 10.1063/1.473579 10.1016/0010-4655(95)00031-A 10.1109/5992.988653 10.1016/S0010-4655(00)00074-6 10.1063/1.474404 10.1002/(SICI)1096-9128(199704)9:4<255::AID-CPE250>3.0.CO;2-2 10.1177/1094342011403516 |
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| SubjectTerms | Algorithms Computation Libraries Mathematical models Multiplication Partitioning Replication Two dimensional |
| Title | Simultaneous Input and Output Matrix Partitioning for Outer-Product--Parallel Sparse Matrix-Matrix Multiplication |
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