## Decomposing irregularly sparse matrices for parallel matrix-vector multiplications (1996)

Venue: | LECTURE NOTES IN COMPUTER SCIENCE |

Citations: | 28 - 14 self |

### BibTeX

@INPROCEEDINGS{Catalyürek96decomposingirregularly,

author = {Ümit V. Catalyürek and Cevdet Aykanat},

title = {Decomposing irregularly sparse matrices for parallel matrix-vector multiplications},

booktitle = {LECTURE NOTES IN COMPUTER SCIENCE},

year = {1996},

publisher = {}

}

### Years of Citing Articles

### OpenURL

### Abstract

In this work, we show the de ciencies of the graph model for decomposing sparse matrices for parallel matrix-vector multiplication. Then, we propose two hypergraph models which avoid all de ciencies 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, con rm both the validity of our proposed hypergraph models and appropriateness of the multilevel approach to hypergraph partitioning.

### Citations

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(Show Context)
Citation Context ..., k represents the number of processors on the target multicomputer. Recently, multilevel graph partitioning heuristics are proposed leading to successful graph partitioning tools Chaco [8] and Metis =-=[10]-=-. We have also exploited the multilevel partitioning methods for the experimental veri cation of our proposed hypergraph models in two approaches. In the rst approach, Metis graph partitioning tool is... |

444 |
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Citation Context ...h models. Here, k represents the number of processors on the target multicomputer. Recently, multilevel graph partitioning heuristics are proposed leading to successful graph partitioning tools Chaco =-=[8]-=- and Metis [10]. We have also exploited the multilevel partitioning methods for the experimental veri cation of our proposed hypergraph models in two approaches. In the rst approach, Metis graph parti... |

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(Show Context)
Citation Context ...cally minimum partition. Each pass consists of a sequence of vertex swaps. The same swap strategy was applied to hypergraph partitioning problem by Schweikert-Kernighan [14]. Fiduccia-Mattheyses (FM) =-=[6]-=- introduced a faster implementation of KL algorithm for hypergraph partitioning. They proposed vertex move concept instead of vertex swap. This modi cation as well as proper data structures, e.g., buc... |

281 |
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Citation Context ...ad balance condition, and " represents the predetermined maximum load imbalance ratio allowed. We have used "=0:04 in all heuristics. Symmetric sparse matrices selected from Harwell-Boeing collection =-=[4]-=- and linear programming problems in NETLIB suite [7] are used for experimentation. Note that test matrices are restricted to symmetric matrices since graphs cannot be used to model unsymmetric square ... |

197 | Recent directions in netlist partitioning: A survey
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(Show Context)
Citation Context ...els. The performance of FM deteriorates for large and/or too sparse and/or dense graphs/hypergraphs. Many clustering algorithms have been proposed especially for hypergraphs to alleviate this problem =-=[2]-=-. Clustering corresponds to coalescing highly interacting vertices to supernodes as a preprocessing to FM. Recently, multilevel graph partitioning methods have been proposed leading to successful grap... |

125 |
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(Show Context)
Citation Context ...ined maximum load imbalance ratio allowed. We have used "=0:04 in all heuristics. Symmetric sparse matrices selected from Harwell-Boeing collection [4] and linear programming problems in NETLIB suite =-=[7]-=- are used for experimentation. Note that test matrices are restricted to symmetric matrices since graphs cannot be used to model unsymmetric square and rectangular matrices. Table 1 displays the chara... |

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53 |
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Citation Context ...ber of passes until it nds a locally minimum partition. Each pass consists of a sequence of vertex swaps. The same swap strategy was applied to hypergraph partitioning problem by Schweikert-Kernighan =-=[14]-=-. Fiduccia-Mattheyses (FM) [6] introduced a faster implementation of KL algorithm for hypergraph partitioning. They proposed vertex move concept instead of vertex swap. This modi cation as well as pro... |

44 | A hybrid multilevel/genetic approach for circuit partitioning
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(Show Context)
Citation Context ...for each selected pair of pins (vertices). Note that this scheme is an experimental e ort to alleviate the above mentioned problem. We use T =50 and F =5 in accordance to the recommendations given in =-=[1]-=-. 4.2 A Multilevel Hypergraph Partitioning Heuristic In this work, we exploit the successful multilevel methodology proposed and implemented for graph partitioning (Metis [10]) to develop a new multil... |

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Citation Context ...balance reduces to the domain decomposition problem, where the sparse matrix A constitutes the domain of problem. Almost all domain decomposition methods proposed in the literature employ graph model =-=[9, 13]-=-.Inthiswork, we show the de ciencies of the graph model for decomposing sparse matrices for parallel matrix vector multiplication. The rst de ciency is that it can only be used for symmetric square ma... |

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(Show Context)
Citation Context ...balance reduces to the domain decomposition problem, where the sparse matrix A constitutes the domain of problem. Almost all domain decomposition methods proposed in the literature employ graph model =-=[9, 13]-=-.Inthiswork, we show the de ciencies of the graph model for decomposing sparse matrices for parallel matrix vector multiplication. The rst de ciency is that it can only be used for symmetric square ma... |

25 | Iterative algorithms for solution of large sparse systems of linear equations
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(Show Context)
Citation Context ...ors, inner product(s) of dense vectors, and sparse-matrix vector product of the form y = Ax, wherey and x are dense vectors, and A is a matrix with the same sparsity structure as the coe cient matrix =-=[5, 12]-=-. All of these basic operations can be performed concurrently by distributing either the rows or the columns of the matrix A and the components of the dense vectors in the same way. These two decompos... |

2 | Ahypergraph model for mapping repeated sparse matrix-vector product computations onto multicomputers - Catalyurek, Aykanat - 1995 |

2 |
A set of new mapping and colloring heuristics for distributed-memory parallel processors
- Pommerell, Annaratone, et al.
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Citation Context ...ors, inner product(s) of dense vectors, and sparse-matrix vector product of the form y = Ax, wherey and x are dense vectors, and A is a matrix with the same sparsity structure as the coe cient matrix =-=[5, 12]-=-. All of these basic operations can be performed concurrently by distributing either the rows or the columns of the matrix A and the components of the dense vectors in the same way. These two decompos... |

2 |
Iterative algorithms for solution of large sparse systems of linear equations on hypercubes
- Ercal, Aykanat, et al.
- 1988
(Show Context)
Citation Context ...ors, inner product(s) of dense vectors, and sparse-matrix vector product of the form y = Ax, wherey and x are dense vectors, and A is a matrix with the same sparsity structure as the coe cient matrix =-=[5, 12]-=-. All of these basic operations can be performed concurrently by distributing either the rows or the columns of the matrix A and the components of the dense vectors in the same way. These two decompos... |