Evaluation Criteria for Sparse Matrix Storage Formats

Langr, Daniel; Tvrdík, Pavel

doi:10.1109/tpds.2015.2401575

Cited by 109 publications

(69 citation statements)

References 52 publications

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“…• Authors rarely present algorithms for preprocessing of matrices, which are necessary for assessment of the suitability of their formats for a given application [6]. We have not found a case where format authors provided efficient parallel implementations of algorithms for the computation of the number of nonzero blocks in nonexperimental forms.…”

Section: G Overview Of State-of-the-artmentioning

confidence: 95%

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Efficient parallel evaluation of block properties of sparse matrices

Šimeček

Langr

2016

Annals of Computer Science and Information Systems

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Abstract-Many storage formats for sparse matrices have been developed. Majority of these formats can be parametrized, so the algorithm for finding optimal parameters is crucial. For overall efficiency, it is important to reduce the execution time of this preprocessing. In this paper, we propose a new algorithm for the determination of the number of nonzero blocks of the given size in a sparse matrix. The proposed algorithm requires relatively a small amount of auxiliary memory. Our approach is based on the Morton reordering and bitwise manipulations. We also present a parallel (multithreaded) version and evaluate its performance and space complexity.

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Section: G Overview Of State-of-the-artmentioning

confidence: 95%

“…In the further text, we will denote them as basic hierarchical format (BHF), for details see [6], [8], [9]. Coordinates of the upper left corners of these blocks are aligned to multiples of 2 c .…”

Section: E Hierarchical Formatsmentioning

confidence: 99%

Efficient parallel evaluation of block properties of sparse matrices

Šimeček

Langr

2016

Annals of Computer Science and Information Systems

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“…The first one did nothing useful at all, which allowed us to evaluate the algorithm itself without any application-dependent computations; we call this processor a do-nothing processor. 3 The second processor was designed for the problem of finding an optimal block size when storing A in the ABHSF; we call it the ABHSF-opt processor. This processor calculated and summed the contributions of blocks to the overall memory footprint of A.…”

Section: A Processorsmentioning

confidence: 99%

“…The optimization criterion of ABHSF is represented by the total memory footprint of A which is being minimized. This is a very common optimization criterion for storage formats in general (not only UB formats), since the performance of SpMV is limited by bandwidths of memory subsystems on modern HPC architectures [3].…”

Section: Introductionmentioning

confidence: 99%

Block Iterators for Sparse Matrices

Langr

Šimeček

Dytrych

2016

Annals of Computer Science and Information Systems

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Abstract-Finding an optimal block size for a given sparse matrix forms an important problem for storage formats that partition matrices into uniformly-sized blocks. Finding a solution to this problem can take a significant amount of time, which, effectively, may negate the benefits that such a format brings into sparse-matrix computations. A key for an efficient solution is the ability to quickly iterate, for a particular block size, over matrix nonzero blocks. This work proposes an efficient parallel algorithm for this task and evaluate it experimentally on modern multi-core and many-core high performance computing (HPC) architectures.

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“…Moreover, Kumbhar [9] pointed out that once an application (in particular a non-linear solver) needs repeated format conversion after a fixed small number of iterations, the new formats may degrade overall performance. Furthermore, Langr and Tvrdík [10] demonstrated that isolated SpMV performance is insufficient to evaluate a new format. Thus more evaluation criteria, such as format conversion cost and memory footprint, must be taken into consideration.…”

Section: Introductionmentioning

confidence: 99%

Speculative segmented sum for sparse matrix-vector multiplication on heterogeneous processors

Liu

Vinter

2015

Parallel Computing

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Sparse matrix-vector multiplication (SpMV) is a central building block for scientific software and graph applications. Recently, heterogeneous processors composed of different types of cores attracted much attention because of their flexible core configuration and high energy efficiency. In this paper, we propose a compressed sparse row (CSR) format based SpMV algorithm utilizing both types of cores in a CPU-GPU heterogeneous processor. We first speculatively execute segmented sum operations on the GPU part of a heterogeneous processor and generate a possibly incorrect results. Then the CPU part of the same chip is triggered to re-arrange the predicted partial sums for a correct resulting vector. On three heterogeneous processors from Intel, AMD and nVidia, using 20 sparse matrices as a benchmark suite, the experimental results show that our method obtains significant performance improvement over the best existing CSR-based SpMV algorithms.

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Evaluation Criteria for Sparse Matrix Storage Formats

Cited by 109 publications

References 52 publications

Efficient parallel evaluation of block properties of sparse matrices

Efficient parallel evaluation of block properties of sparse matrices

Block Iterators for Sparse Matrices

Speculative segmented sum for sparse matrix-vector multiplication on heterogeneous processors

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