An effective model to decompose Linear Programs for parallel solution

Pınar, Ali; Aykanat, Cevdet

doi:10.1007/3-540-62095-8_64

Cited by 4 publications

(5 citation statements)

References 10 publications

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“…The hypergraph-based approach can also be applied to rectangular matrices, as shown by Pinar et al [40] for the partitioning of rectangular LP matrices. (Taking a different approach, Pinar and Aykanat [38] transform rectangular LP matrices to an undirected graph representing the interaction between the rows, thus enabling the use of graph partitioners. This minimizes an approximation to the communication volume.…”

Section: Introductionmentioning

confidence: 99%

A Two-Dimensional Data Distribution Method for Parallel Sparse Matrix-Vector Multiplication

Vastenhouw¹,

Bisseling²

2005

SIAM Rev.

191

196

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A new method is presented for distributing data in sparse matrix-vector multiplication. The method is two-dimensional, tries to minimize the true communication volume, and also tries to spread the computation and communication work evenly over the processors. The method starts with a recursive bipartitioning of the sparse matrix, each time splitting a rectangular matrix into two parts with a nearly equal number of nonzeros. The communication volume caused by the split is minimized. After the matrix partitioning, the input and output vectors are partitioned with the objective of minimizing the maximum communication volume per processor. Experimental results of our implementation, Mondriaan, for a set of sparse test matrices show a reduction in communication volume compared to one-dimensional methods, and in general a good balance in the communication work. Experimental timings of an actual parallel sparse matrix-vector multiplication on an SGI Origin 3800 computer show that a sufficiently large reduction in communication volume leads to savings in execution time.

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Section: Introductionmentioning

confidence: 99%

A Two-Dimensional Data Distribution Method for Parallel Sparse Matrix-Vector Multiplication

Vastenhouw¹,

Bisseling²

2005

SIAM Rev.

191

196

View full text Add to dashboard Cite

show abstract

“…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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“…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 [8,9,45,44]. 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 Relation Between Hp And Gpvsmentioning

confidence: 99%

“…What motivates us to investigate NIGs to solve HP problems arising in scientific computing applications is that in many applications, definition of balance cannot be very precise [3,44,45] or there are additional constraints that cannot be easily incorporated into partitioning algorithms and tools [47]; or partitioning is used as part of a divide-and-conquer algorithm [46]. For instance, hypergraph models can be used to permute a linear program (LP) constraint matrix to a block angular form for parallel solution with decomposition methods.…”

Section: Introductionmentioning

confidence: 99%

Hypergraph Partitioning through Vertex Separators on Graphs

Kayaaslan,

Pinar,

Catalyurek

et al. 2011

Preprint

Self Cite

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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 translate 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 NIG model cannot preserve node balancing information. Vertex-removal and vertex-splitting techniques are described to optimize cutnet and connectivity metrics, respectively, under the recursive bipartitioning paradigm. We also developed an implementation for our GPVS-based HP formulations by adopting and modifying a state-of-the-art GPVS tool onmetis. Experiments conducted on a large collection of sparse matrices confirmed the validity of our proposed techniques.

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An effective model to decompose Linear Programs for parallel solution

Cited by 4 publications

References 10 publications

A Two-Dimensional Data Distribution Method for Parallel Sparse Matrix-Vector Multiplication

A Two-Dimensional Data Distribution Method for Parallel Sparse Matrix-Vector Multiplication

Partitioning Hypergraphs in Scientific Computing Applications through Vertex Separators on Graphs

Hypergraph Partitioning through Vertex Separators on Graphs

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