## Graph Partitioning and Parallel Solvers: Has the Emperor No Clothes? (Extended Abstract) (1998)

Venue: | In Proc. Irregular’98 |

Citations: | 44 - 2 self |

### BibTeX

@INPROCEEDINGS{Hendrickson98graphpartitioning,

author = {Bruce Hendrickson},

title = {Graph Partitioning and Parallel Solvers: Has the Emperor No Clothes? (Extended Abstract)},

booktitle = {In Proc. Irregular’98},

year = {1998},

pages = {218--225},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

Sparse matrix-vector multiplication is the kernel for many scientific computations. Parallelizing this operation requires the matrix to be divided among processors. This division is commonly phrased in terms of graph partitioning. Although this abstraction has proved to be very useful, it has significant flaws and limitations. The cost model implicit in this abstraction is only a weak approximation to the true cost of the parallel matrix-vector multiplication. And the graph model is unnecessarily restrictive. This paper will detail the shortcomings of the current paradigm and suggest directions for improvement and further research.

### Citations

864 | A fast and high quality multilevel scheme for partitioning irregular graphs
- Karypis, Kumar
- 1998
(Show Context)
Citation Context ...s is largely the result of two happy occurrences. First is the availability of good algorithms and software for partitioning graphs, motivated by parallel computing applications (eg. Chaco [2], METIS =-=[5]-=-, JOSTLE [11], PARTY [10] and SCOTCH [9]). Second is the excellent parallel efficiencies which can be obtained when solving differential equations. Clearly, the latter is a consequence of the former, ... |

202 |
The Chaco User’s Guide: Version 2.0
- Hendrickson, Leland
- 1994
(Show Context)
Citation Context ...is consensus is largely the result of two happy occurrences. First is the availability of good algorithms and software for partitioning graphs, motivated by parallel computing applications (eg. Chaco =-=[2]-=-, METIS [5], JOSTLE [11], PARTY [10] and SCOTCH [9]). Second is the excellent parallel efficiencies which can be obtained when solving differential equations. Clearly, the latter is a consequence of t... |

20 |
Mesh partitioning and load-balancing for distributed memory parallel systems
- Walshaw, Cross, et al.
- 1997
(Show Context)
Citation Context ... the result of two happy occurrences. First is the availability of good algorithms and software for partitioning graphs, motivated by parallel computing applications (eg. Chaco [2], METIS [5], JOSTLE =-=[11]-=-, PARTY [10] and SCOTCH [9]). Second is the excellent parallel efficiencies which can be obtained when solving differential equations. Clearly, the latter is a consequence of the former, right? Yes, a... |

12 | Partitioning sparse rectangular matrices for parallel processing
- Kolda
(Show Context)
Citation Context ... has no capacity to consider the larger problem. 5 A Better Combinatorial Model Some of the limitations discussed in x4.2 can be addressed by a more expressive model proposed by Kolda and Hendrickson =-=[3, 4, 8]-=-. The model uses a bipartite graph to represent the matrix. In this graph, there is a vertex for each row and another vertex for each column. An edge connects row vertex i to column vertex j if there ... |

10 |
Mesh partitioning for implicit computations via domain decomposition: impact and optimization of the subdomain aspect ratio
- Farhat, Maman, et al.
(Show Context)
Citation Context ... entirely clear, and they depend upon the details of the solution technique. But they are almost certainly not identical to the criteria for matrix-vector multiplication. For instance, Farhat, et al. =-=[1]-=- argue that the domains must have good aspect ratios (eg. not be long and skinny). It can also be important that subdomains are connected, even though the best partitions for matrix-vector multiplicat... |

1 |
Parallel algorithms for nonsymmetric iterative solvers
- Hendrickson, Kolda
(Show Context)
Citation Context ...tly compute z = A T w. This is useful for nonsymmetric matrices since many iterative methods for such matrices require both matrix-vector and matrix-transpose-vector products. Details can be found in =-=[3]-=-. 4 Problems with Graph Partitioning The standard graph partitioning problem addressed by codes like Chaco [2] and METIS [5] is the following. Divide the vertices of the graph into equally sized sets ... |

1 |
SCOTCH 3.1 user's guide, Tech. Rep. 1137-96, Laboratoire Bordelais de Recherche en Informatique, Universite
- Pellegrini
- 1996
(Show Context)
Citation Context ...urrences. First is the availability of good algorithms and software for partitioning graphs, motivated by parallel computing applications (eg. Chaco [2], METIS [5], JOSTLE [11], PARTY [10] and SCOTCH =-=[9]-=-). Second is the excellent parallel efficiencies which can be obtained when solving differential equations. Clearly, the latter is a consequence of the former, right? Yes, and no. Although the Emperor... |