## Graph partitioning models for parallel computing (2000)

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Citations: | 73 - 3 self |

### BibTeX

@MISC{Hendrickson00graphpartitioning,

author = {Bruce Hendrickson and Tamara G. Kolda},

title = {Graph partitioning models for parallel computing},

year = {2000}

}

### Years of Citing Articles

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### Citations

1043 |
An efficient heuristic procedure for partitioning graphs
- Kernighan, Lin
- 1970
(Show Context)
Citation Context ...scheme. Any existing algorithm which handles weights on edges and vertices can be used to partition the smallest graph. The refinement often involves a greedy algorithm in the spirit of Kernighan-Lin =-=[22]-=-. Following the multilevel paradigm, efficient and effective partitioners have been developed for partitioning graphs to minimize edge cuts [2,14], minimize vertex cuts [16], and perform multi-constra... |

794 | A fast and high quality multilevel scheme for partitioning irregular graphs
- Karypis, Kumar
- 1998
(Show Context)
Citation Context ...partition the vertices of the graph into equally weighted sets in such a way that the weight of the edges crossing between sets is minimized. Well-known software packages such as Chaco [13] and METIS =-=[19]-=- can be used for this purpose. Note that the graph partitioning problem is NP-hard [9], so these tools merely apply heuristics to generate approximate solutions. Unfortunately, the standard graph part... |

443 |
A multilevel algorithm for partitioning graphs
- Hendrickson, Leland
- 1995
(Show Context)
Citation Context ...tition them. Fortunately, the multilevel paradigm for partitioning has proven to be quite robust and general. The multilevel approach was devised independently by several researchers in the early 90s =-=[2,6,14]-=- and popularized by the the Chaco [13] and METIS [19] partitioning tools. The basic idea is quite simple. A large graph is approximated by a sequence of smaller and smaller graphs. The smallest graph ... |

374 |
Some simplified NP-complete graph problems
- Garey, Johnson, et al.
- 1976
(Show Context)
Citation Context ...eight of the edges crossing between sets is minimized. Well-known software packages such as Chaco [13] and METIS [19] can be used for this purpose. Note that the graph partitioning problem is NP-hard =-=[9]-=-, so these tools merely apply heuristics to generate approximate solutions. Unfortunately, the standard graph partitioning approach has several significant shortcomings which are discussed in detail i... |

189 |
The Chaco user’s guide: Version 2.0
- Hendrickson, Leland
- 1995
(Show Context)
Citation Context ...ibed above and partition the vertices of the graph into equally weighted sets in such a way that the weight of the edges crossing between sets is minimized. Well-known software packages such as Chaco =-=[13]-=- and METIS [19] can be used for this purpose. Note that the graph partitioning problem is NP-hard [9], so these tools merely apply heuristics to generate approximate solutions. Unfortunately, the stan... |

149 | Multilevel algorithms for multi-constraint graph partitioning
- Karypis, Kumar
- 1998
(Show Context)
Citation Context ...raint Partitioning The bipartite model from x3.1 is able to describe some types of multi-phase calculations. An alternative approach is the multi-constraint partitioning model 10 of Karypis and Kumar =-=[21]-=-. Strictly speaking, the multi-constraint approach is not an alternative to other models but rather an augmentation. In the multiconstraint model, each vertex is assigned a vector of k weights which r... |

146 | A parallel hashed oct-tree n-body algorithm - Warren, Salmon - 1993 |

97 |
A Procedure for Placement of Standardçell VLSI Circuits
- Dunlop, Kernighan
- 1985
(Show Context)
Citation Context ...e off between partition quality and message locality. This same idea was developed independently in the circuit placement community to place circuit elements on a chip with short overall wire lengths =-=[7]-=-. Several algorithms for this problem have been devised including multilevel and spectral approaches [15]. 4 Partitioning Algorithms The different graph partitioning models reviewed in x3 are only via... |

91 | Analysis of multilevel graph partitioning
- Karypis, Kumar
- 1995
(Show Context)
Citation Context ...partitioner in advance. A better solution is to partition on the parallel machine when the job is initiated. A number of parallel partitioners have been implemented including Jostle [28] and ParMETIS =-=[20]-=-. This is an active area of research. (4) Partitioning for domain decomposition. Domain decomposition is a numerical technique in which a large grid is broken into smaller pieces. The solver works on ... |

70 |
A heuristic for reducing fill in sparse matrix factorization
- Bui, Jones
- 1993
(Show Context)
Citation Context ...tition them. Fortunately, the multilevel paradigm for partitioning has proven to be quite robust and general. The multilevel approach was devised independently by several researchers in the early 90s =-=[2,6,14]-=- and popularized by the the Chaco [13] and METIS [19] partitioning tools. The basic idea is quite simple. A large graph is approximated by a sequence of smaller and smaller graphs. The smallest graph ... |

61 | C.: Hypergraph-partitioning based decomposition for parallel sparse-matrix vector multiplication
- Catalyürek, Aykanat
- 1999
(Show Context)
Citation Context ...7]. Boundary cuts can also be employed in the bipartite graph model from x3.1. 8 A more elegant expression of this metric is in the hypergraph model proposed by C atalyurek, Aykanat, Pinar, and Pinar =-=[3,4,25]-=-. A hypergraph is a generalization of a graph in which edges can include more than two vertices. A hypergraph, G = (V; H), consists of a set of vertices, V , and a set of hyperedges,sH. Each hyperedge... |

60 | A parellel bottom-up clustering algorithm with applications to circuit partitioning in VLSI design
- Cong, Smith
- 1993
(Show Context)
Citation Context ...tition them. Fortunately, the multilevel paradigm for partitioning has proven to be quite robust and general. The multilevel approach was devised independently by several researchers in the early 90s =-=[2,6,14]-=- and popularized by the the Chaco [13] and METIS [19] partitioning tools. The basic idea is quite simple. A large graph is approximated by a sequence of smaller and smaller graphs. The smallest graph ... |

59 | An e cient heuristic procedure for partitioning graphs - Kernighan, Lin - 1970 |

48 | Improving the runtime and quality of nested dissection ordering
- Hendrickson, Rothberg
- 1998
(Show Context)
Citation Context ...he spirit of Kernighan-Lin [22]. Following the multilevel paradigm, efficient and effective partitioners have been developed for partitioning graphs to minimize edge cuts [2,14], minimize vertex cuts =-=[16]-=-, and perform multi-constraint partitioning [21]. The same approach has been successfully used to partition hypergraphs to minimize cut hyperedges [6,18,5] and to partition bipartite graphs [12]. The ... |

46 |
PaToH: A Multilevel Hypergraph Partitioning Tool, Version 3.0
- Çatalyürek, Aykanat
- 1999
(Show Context)
Citation Context ... minimize edge cuts [2,14], minimize vertex cuts [16], and perform multi-constraint partitioning [21]. The same approach has been successfully used to partition hypergraphs to minimize cut hyperedges =-=[6,18,5]-=- and to partition bipartite graphs [12]. The flexibility of the technique makes it well suited to address a range of different partitioning models and metrics. 5 Conclusions and Directions for Further... |

41 | Graph partitioning and parallel solvers: Has the emperor no clothes? In IRREGULAR’98: solving irregularly structured problems
- Hendrickson
- 1998
(Show Context)
Citation Context ...lso suffers from a lack of expressibility which limits the applications it can address. This paper is an extension of and an elaboration upon Hendrickson's critique of the standard partitioning model =-=[10]-=-. Whereas Hendrickson restricted his concerns to matrix-vector products, in the current paper we show that the same issues plague virtually all applications of graph partitioning to parallel computati... |

33 |
Separators: A Unified Geometric Approach to Graph Partitioning
- Points
- 1991
(Show Context)
Citation Context ...is is not true of more general problems with more complex data dependencies. Second, computational grids generally exhibit a high degree of geometric locality which ensures that good partitions exist =-=[26]-=-. If the grid size, n, is increased while the number of processors is held fixed, the ratio of 4 communication volume to computational work grows as n \Gamma1=3 in three dimensions and n \Gamma1=2 in ... |

32 | A new algorithm for multi-objective graph partitioning - Schloegel, Karypis, et al. - 1999 |

30 | Computational results for parallel unstructured mesh computations - Jones, Plassman - 1994 |

27 | Some simpli�ed NP-complete graph problems. Theoretical computer science - Garey, Johnson |

19 |
Mesh partitioning and load-balancing for distributed memory parallel systems
- Walshaw, Cross, et al.
(Show Context)
Citation Context ... information to a partitioner in advance. A better solution is to partition on the parallel machine when the job is initiated. A number of parallel partitioners have been implemented including Jostle =-=[28]-=- and ParMETIS [20]. This is an active area of research. (4) Partitioning for domain decomposition. Domain decomposition is a numerical technique in which a large grid is broken into smaller pieces. Th... |

16 |
Static mapping by dual recursive bipartitioning of process and architecture graphs
- Pellegrini
- 1994
(Show Context)
Citation Context ...e applied, they may be easier to work with. 3.4 Skewed partitioning Yet another alternative to the standard partitioning model is the skewed partitioning partitioning approach developed by Pellegrini =-=[24]-=- and Hendrickson, Leland and Van Driessche [15]. As with the multi-constraint model, skewed partitioning is really an augmentation of any of the other graph partitioning models rather than a true alte... |

15 | Driessche. Skewed graph partitioning
- Hendrickson, Leland, et al.
- 1997
(Show Context)
Citation Context ... Skewed partitioning Yet another alternative to the standard partitioning model is the skewed partitioning partitioning approach developed by Pellegrini [24] and Hendrickson, Leland and Van Driessche =-=[15]-=-. As with the multi-constraint model, skewed partitioning is really an augmentation of any of the other graph partitioning models rather than a true alternative. In the skewed model, each vertex is al... |

11 | Partitioning sparse rectangular matrices for parallel processing
- Kolda
- 1457
(Show Context)
Citation Context ...roblematic for iterative solvers on unsymmetric or non-square matrices. When using preconditioners, the inability of the standard model to capture multiple phase calculations are also problematic. In =-=[11,12,23]-=- Kolda and Hendrickson propose a bipartite graph model for describing matrixvector multiplication which addresses some of these shortcomings. The bipartite model can also be applied to other applicati... |

9 | Decomposing linear programs for parallel solution
- Pınar, Çatalyürek, et al.
- 1996
(Show Context)
Citation Context ...7]. Boundary cuts can also be employed in the bipartite graph model from x3.1. 8 A more elegant expression of this metric is in the hypergraph model proposed by C atalyurek, Aykanat, Pinar, and Pinar =-=[3,4,25]-=-. A hypergraph is a generalization of a graph in which edges can include more than two vertices. A hypergraph, G = (V; H), consists of a set of vertices, V , and a set of hyperedges,sH. Each hyperedge... |

9 |
Mesh Partitioning for Implicit Computations via Domain Decomposition
- Farhat, Maman, et al.
- 1995
(Show Context)
Citation Context ...ly clear, and they depend upon the details of the solution technique. But they are almost certainly not identical to the criteria used to minimize parallel communication. For instance, Farhat, et al. =-=[8]-=- argue that the domains must have good aspect ratios (e.g., not be long and skinny). It can also be important that subdomains are connected, even though the best partitions for parallel communication ... |

8 |
Dynamic load balancing with a spectral bisection algorithm for the constrained graph partitioning problem
- Driessche, Roose
- 1995
(Show Context)
Citation Context ...on be similar to the existing one to limit the amount of data that needs to be moved. This can be encoded in the preference values by giving each datum a preference to remain in its current partition =-=[27]-=-. The magnitude of the preference values can be adjusted to trade off between partition quality and reduction in data movement. Another use for preference values is to encourage communicating objects ... |

8 | Decomposing irregularly sparse matrices for parallel matrix-vector multiplication - Catalyuerek, Aykanat - 1117 |

7 |
Hypergraph partitioning using multilevel approach: application in VLSI domain
- Karypis, Aggarwal, et al.
- 1997
(Show Context)
Citation Context ... minimize edge cuts [2,14], minimize vertex cuts [16], and perform multi-constraint partitioning [21]. The same approach has been successfully used to partition hypergraphs to minimize cut hyperedges =-=[6,18,5]-=- and to partition bipartite graphs [12]. The flexibility of the technique makes it well suited to address a range of different partitioning models and metrics. 5 Conclusions and Directions for Further... |

6 |
Private Communication
- Karypis
(Show Context)
Citation Context ...antity the boundary cut of a partition. The observation that boundary cuts are the more appropriate metric was made in [10] and motivated a modification in METIS to minimize this more accurate metric =-=[17]-=-. Boundary cuts can also be employed in the bipartite graph model from x3.1. 8 A more elegant expression of this metric is in the hypergraph model proposed by C atalyurek, Aykanat, Pinar, and Pinar [3... |

4 |
Partitioning nonsquare and nonsymmetric matrices for parallel processing
- Hendrickson, Kolda
(Show Context)
Citation Context ...on which first computes y = Ax and then z = A T y; this effectively maps from x-space to y-space and back to x-space. (The data layout and communication for application of A and A T is identical; see =-=[12]-=-). This brings us to the last two important issues. The third limitation of the standard model is that it assumes that the input and output of the calculation are the size. For example, when A is rect... |

4 | A heuristic for reducing ®ll in sparse matrix factorization - Bui, Jones - 1993 |

3 |
Hypergraph-partitioning based decomposition for parallel sparsematrix vector multiplication
- atalyurek, Aykanat
- 1999
(Show Context)
Citation Context ...7]. Boundary cuts can also be employed in the bipartite graph model from x3.1. A more elegant expression of this metric is in the hypergraph model proposed by C�� atalyurek, Aykanat, Pinar, and Pi=-=nar [3,4,25]-=-. A hypergraph is a generalization of a graph in which edges can include more than two vertices. A hypergraph, G = (V; H), consists of a set of vertices, V , and a set of hyperedges,sH. Each hyperedge... |

3 | Partitioning sparse rectangular matrices for parallel computations of Ax and A T v, in: Applied Parallel Computing
- Hendrickson, Kolda
- 1998
(Show Context)
Citation Context ...roblematic for iterative solvers on unsymmetric or non-square matrices. When using preconditioners, the inability of the standard model to capture multiple phase calculations are also problematic. In =-=[11,12,23]-=- Kolda and Hendrickson propose a bipartite graph model for describing matrixvector multiplication which addresses some of these shortcomings. The bipartite model can also be applied to other applicati... |

3 | Separators: a uni geometric approach to graph partitioning - Points - 1990 |

2 | A hierarchical partition model for adaptive ®nite element computation - Teresco, Beall, et al. |

1 |
Private Communication
- Aykanat
- 1998
(Show Context)
Citation Context ...ication by over 30% on average over the standard partitioning approach. However, for reasons discussed in x2.1, the gains were more modest for matrices from grid calculations, generally less than 10% =-=[1]-=-. In addition to resolving the principle problem of the edge cut metric, the hypergraph approach is more expressive than the standard model. It can encode problems in with unsymmetric dependencies and... |

1 | A new approach for parallel multigrid adaption - Stiller, Boryczko, et al. - 1999 |