Decomposing linear programs for parallel solution

Pınar, Ali; Çatalyürek, Ümit V.; Aykanat, Cevdet; Pınar, Mustafa Ç.

doi:10.1007/3-540-60902-4_50

Cited by 12 publications

(14 citation statements)

References 9 publications

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“…A more elegant expression of this metric is in the hypergraph model proposed by Qatalyurek, Aykanat, Pinar, and Pinar [3,4,25]. A hypergraph is a generalization of a graph in which edges can include more than two vertices.…”

Section: A Hypergraph Modelmentioning

confidence: 99%

Graph partitioning models for parallel computing

2000

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Calculations can naturally be described as graphs in which vertices represent computation and edges reflect data dependencies. By partitioning the vertices of a graph, the calculation can be divided among processors of a parallel computer. However, the standard methodology for graph partitioning minimizes the wrong metric and lacks expressibility. We survey several recently proposed alternatives and discuss their relative merits.

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Section: A Hypergraph Modelmentioning

confidence: 99%

Graph partitioning models for parallel computing

2000

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“…We will first briefly discuss the row-net and column-net models we proposed for representing rectangular as well as symmetric and nonsymmetric square matrices in our earlier work [7,8,38,37]. These two models are duals: the row-net representation of a matrix is equal to the column-net representation of its transpose.…”

Section: Matrix Theoretical View Of the Relationship Between Hp And Gmentioning

confidence: 99%

Partitioning Hypergraphs in Scientific Computing Applications through Vertex Separators on Graphs

Kayaaslan¹,

Pınar²,

Çatalyürek³

et al. 2012

SIAM J. Sci. Comput.

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Abstract. The modeling flexibility provided by hypergraphs has drawn a lot of interest from the combinatorial scientific community, leading to novel models and algorithms, their applications, and development of associated tools. Hypergraphs are now a standard tool in combinatorial scientific computing. The modeling flexibility of hypergraphs, however, comes at a cost: algorithms on hypergraphs are inherently more complicated than those on graphs, which sometimes translates to nontrivial increases in processing times. Neither the modeling flexibility of hypergraphs nor the runtime efficiency of graph algorithms can be overlooked. Therefore, the new research thrust should be how to cleverly trade off between the two. This work addresses one method for this trade-off by solving the hypergraph partitioning problem by finding vertex separators on graphs. Specifically, we investigate how to solve the hypergraph partitioning problem by seeking a vertex separator on its net intersection graph (NIG), where each net of the hypergraph is represented by a vertex, and two vertices share an edge if their nets have a common vertex. We propose a vertex-weighting scheme to attain good node-balanced hypergraphs, since the NIG model cannot preserve node-balancing information. Vertex-removal and vertex-splitting techniques are described to optimize cut-net and connectivity metrics, respectively, under the recursive bipartitioning paradigm. We also developed implementations of our proposed hypergraph partitioning formulations by adopting and modifying a state-of-the-art graph partitioning by vertex separator tool onmetis. Experiments conducted on a large collection of sparse matrices demonstrate the effectiveness of our proposed techniques.

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“…Introduction. Hypergraph-partitioning-based models for parallel sparse matrix-vector multiply operations [3,4,9] have gained widespread acceptance. These models can address partitionings of rectangular, unsymmetric square, and symmetric square matrices.…”

mentioning

confidence: 99%

“…There may be three main reasons for this. First, the works [3,9] had limited distribution, and therefore the models were more widely introduced in [4]. Second, rectangular matrices were not discussed explicitly in [4].…”

mentioning

confidence: 99%

Revisiting Hypergraph Models for Sparse Matrix Partitioning

Uçar¹,

Aykanat²

2007

SIAM Rev.

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Abstract.We provide an exposition of hypergraph models for parallelizing sparse matrix-vector multiplies. Our aim is to emphasize the expressive power of hypergraph models. First, we set forth an elementary hypergraph model for the parallel matrix-vector multiply based on one-dimensional (1D) matrix partitioning. In the elementary model, the vertices represent the data of a matrix-vector multiply, and the nets encode dependencies among the data. We then apply a recently proposed hypergraph transformation operation to devise models for 1D sparse matrix partitioning. The resulting 1D partitioning models are equivalent to the previously proposed computational hypergraph models and are not meant to be replacements for them. Nevertheless, the new models give us insights into the previous ones and help us explain a subtle requirement, known as the consistency condition, of hypergraph partitioning models. Later, we demonstrate the flexibility of the elementary model on a few 1D partitioning problems that are hard to solve using the previously proposed models. We also discuss extensions of the proposed elementary model to two-dimensional matrix partitioning.

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Decomposing linear programs for parallel solution

Cited by 12 publications

References 9 publications

Graph partitioning models for parallel computing

Graph partitioning models for parallel computing

Partitioning Hypergraphs in Scientific Computing Applications through Vertex Separators on Graphs

Revisiting Hypergraph Models for Sparse Matrix Partitioning

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