... Boundary nodes are connected to at least one FE node which is mapped to another processor. Fo... more ... Boundary nodes are connected to at least one FE node which is mapped to another processor. For example, in Fig. ... [8] CL Seitz, The cosmic cube, Commun. ... [19] NK Madsen, GH Rodrigue and JI Karush, Matrix multiplication by diagonals on a vector parallel proces sor, Inform. ...
In this work, we show the deficiencies of the graph model for decomposing sparse matrices for par... more In this work, we show the deficiencies of the graph model for decomposing sparse matrices for parallel matrix-vector multiplication. Then, we propose two hypergraph models which avoid all deficiencies of the graph model. The proposed models reduce the decomposition problem to the well-known hypergraph partitioning problem widely encountered in circuit partitioning in VLSI. We have implemented fast Kernighan-Lin based graph and hypergraph partitioning heuristics and used the successful multilevel graph partitioning tool (Metis) for the experimental evaluation of the validity of the proposed hypergraph models. We have also developed a multilevel hypergraph partitioning heuristic for experimenting the performance of the multilevel approach on hypergraph partitioning. Experimental results on sparse matrices, selected from Harwell-Boeing collection and NETLIB suite, confirm both the validity of our proposed hypergraph models and appropriateness of the multilevel approach to hypergraph partitioning.
IEEE Transactions on Parallel and Distributed Systems, 1999
AbstractÐIn this work, we show that the standard graph-partitioning-based decomposition of sparse... more AbstractÐIn this work, we show that the standard graph-partitioning-based decomposition of sparse matrices does not reflect the actual communication volume requirement for parallel matrix-vector multiplication. We propose two computational hypergraph models which ...
Coarse grain parallelism inherent in the solution of Linear Programming (LP) problems with block ... more Coarse grain parallelism inherent in the solution of Linear Programming (LP) problems with block angular constraint matrices has been exploited in recent research works. However, these approaches suffer from unscalability and load imbalance since they exploit only the existing block angular structure of the LP constraint matrix. In this paper, we consider decomposing LP constraint matrices to obtain block angular structures with specified number of blocks for scalable parallelization. We propose hypergraph models to represent LP constraint matrices for decomposition. In these models, the decomposition problem reduces to the well-known hypergraph partitioning problem. A Kernighan-Lin based multiway hypergraph partitioning heuristic is implemented for experimenting with the performance of the proposed hypergraph models on the decomposition of the LP problems selected from NETLIB suite. Initial results are promising and justify further research on other hypergraph partitioning heuristics for decomposing large LP problems.
... Boundary nodes are connected to at least one FE node which is mapped to another processor. Fo... more ... Boundary nodes are connected to at least one FE node which is mapped to another processor. For example, in Fig. ... [8] CL Seitz, The cosmic cube, Commun. ... [19] NK Madsen, GH Rodrigue and JI Karush, Matrix multiplication by diagonals on a vector parallel proces sor, Inform. ...
In this work, we show the deficiencies of the graph model for decomposing sparse matrices for par... more In this work, we show the deficiencies of the graph model for decomposing sparse matrices for parallel matrix-vector multiplication. Then, we propose two hypergraph models which avoid all deficiencies of the graph model. The proposed models reduce the decomposition problem to the well-known hypergraph partitioning problem widely encountered in circuit partitioning in VLSI. We have implemented fast Kernighan-Lin based graph and hypergraph partitioning heuristics and used the successful multilevel graph partitioning tool (Metis) for the experimental evaluation of the validity of the proposed hypergraph models. We have also developed a multilevel hypergraph partitioning heuristic for experimenting the performance of the multilevel approach on hypergraph partitioning. Experimental results on sparse matrices, selected from Harwell-Boeing collection and NETLIB suite, confirm both the validity of our proposed hypergraph models and appropriateness of the multilevel approach to hypergraph partitioning.
IEEE Transactions on Parallel and Distributed Systems, 1999
AbstractÐIn this work, we show that the standard graph-partitioning-based decomposition of sparse... more AbstractÐIn this work, we show that the standard graph-partitioning-based decomposition of sparse matrices does not reflect the actual communication volume requirement for parallel matrix-vector multiplication. We propose two computational hypergraph models which ...
Coarse grain parallelism inherent in the solution of Linear Programming (LP) problems with block ... more Coarse grain parallelism inherent in the solution of Linear Programming (LP) problems with block angular constraint matrices has been exploited in recent research works. However, these approaches suffer from unscalability and load imbalance since they exploit only the existing block angular structure of the LP constraint matrix. In this paper, we consider decomposing LP constraint matrices to obtain block angular structures with specified number of blocks for scalable parallelization. We propose hypergraph models to represent LP constraint matrices for decomposition. In these models, the decomposition problem reduces to the well-known hypergraph partitioning problem. A Kernighan-Lin based multiway hypergraph partitioning heuristic is implemented for experimenting with the performance of the proposed hypergraph models on the decomposition of the LP problems selected from NETLIB suite. Initial results are promising and justify further research on other hypergraph partitioning heuristics for decomposing large LP problems.
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