Minimizing Communication Cost in Fine-Grain Partitioning of Sparse Matrices

Uçar, Bora; Aykanat, Cevdet

doi:10.1007/978-3-540-39737-3_115

Cited by 9 publications

(14 citation statements)

References 14 publications

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“…Some works on 2D models do not take the communication volume into account, however they provide an upper bound on the number of messages communicated [40][41][42][43][44] . On the other hand, there are 2D models that aim at reducing volume, with or without providing a bound on the maximum number of messages [33,[45][46][47][48][49][50] . 2D partitioning models in the literature can further be categorized into three classes: checkerboard partitioning [47,49,50] (also known as coarse-grain partitioning), jagged partitioning [45,49] and fine-grain partitioning [46,4 8,4 9] .…”

Section: Related Workmentioning

confidence: 99%

“…These models aim at reducing latency costs usually at the expense of increasing bandwidth costs. Similar models have been investigated [48,53] , but they are based on 1D and 2D fine-grain models. (ii) All proposed and investigated partitioning models are realized on two iterative methods CGNE and CGNR implemented with the widely adopted PETSc toolkit [59] .…”

Section: Motivation and Contributionsmentioning

confidence: 99%

“…We also briefly review the 2D fine-grain model and compare it to checkerboard and jagged models as we evaluate it in our experiments. Note that a model to reduce latency overhead of fine-grain partitioning has already been investigated [48] . All proposed models are discussed on parallel w = Ap.…”

Section: Reducing Latency Cost In 2d Partitioning Modelsmentioning

confidence: 99%

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Reducing latency cost in 2D sparse matrix partitioning models

Selvitopi

Aykanat

2016

Parallel Computing

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a b s t r a c tSparse matrix partitioning is a common technique used for improving performance of parallel linear iterative solvers. Compared to solvers used for symmetric linear systems, solvers for nonsymmetric systems offer more potential for addressing different multiple communication metrics due to the flexibility of adopting different partitions on the input and output vectors of sparse matrix-vector multiplication operations. In this regard, there exist works based on one-dimensional (1D) and two-dimensional (2D) fine-grain partitioning models that effectively address both bandwidth and latency costs in nonsymmetric solvers. In this work, we propose two new models based on 2D checkerboard and jagged partitioning. These models aim at minimizing total message count while maintaining a balance on communication volume loads of processors; hence, they address both bandwidth and latency costs. We evaluate all partitioning models on two nonsymmetric system solvers implemented using the widely adopted PETSc toolkit and conduct extensive experiments using these solvers on a modern system (a BlueGene/Q machine) successfully scaling them up to 8K processors. Along with the proposed models, we put practical aspects of eight evaluated models (two 1D-and six 2D-based) under thorough analysis. To the best of our knowledge, this is the first work that analyzes practical performance of 2D models on this scale. Among evaluated models, the models that rely on 2D jagged partitioning obtain the most promising results by striking a balance between minimizing bandwidth and latency costs.

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Section: Related Workmentioning

confidence: 99%

Section: Motivation and Contributionsmentioning

confidence: 99%

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Reducing latency cost in 2D sparse matrix partitioning models

Selvitopi

Aykanat

2016

Parallel Computing

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“…Finding a partition on the vectors x and y is referred to as the vector partitioning operation, and it can be performed in three different ways: by decoding the partition given on A [2]; in a post-processing step using the partition on the matrix [7,8,13]; or explicitly partitioning the vectors during partitioning the matrix [9]. In any of these cases, the vector partitioning for matrix-vector operations is called symmetric if x and y have the same partition, and non-symmetric otherwise.…”

Section: Parallel Matrix-vector Multiply Algorithmsmentioning

confidence: 99%

“…During the last decade, several successful hypergraph-based models and methods were proposed for sparse matrix partitioning [1][2][3][4][5][6][7][8][9][10]. These models and methods have gained wide acceptance in the literature for efficient parallelization of sparse matrix-vector multiply operations.…”

Section: Introductionmentioning

confidence: 99%

A Matrix Partitioning Interface to PaToH in MATLAB

2010

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We present the PaToH MATLAB Matrix Partitioning Interface. The interface provides support for hypergraph-based sparse matrix partitioning methods which are used for efficient parallelization of sparse matrix-vector multiplication operations. The interface also offers tools for visualizing and measuring the quality of a given matrix partition. We propose a novel, multilevel, 2D coarsening-based 2D matrix partitioning method and implement it using the interface. We have performed extensive comparison of the proposed method against our implementation of orthogonal recursive bisection and fine-grain methods on a large set of publicly available test matrices. The conclusion of the experiments is that the new method can compete with the fine-grain method while also suggesting new research directions.

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