Parallelization of Reordering Algorithms for Bandwidth and Wavefront Reduction

Karantasis, Konstantinos I.; Lenharth, Andrew; Nguyen, Donald; Garzarán, María Jesús; Pingali, Keshav

doi:10.1109/sc.2014.80

Cited by 29 publications

(23 citation statements)

References 32 publications

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“…The Unordered Parallel RCM proposed by [7] is based on the construction of a level structure, and an RCM-valid permutation is built after a complete level structure is computed. The four major algorithms steps are presented and detailed in the next sections.…”

Section: Unordered Parallel Rcm Algorithmmentioning

confidence: 99%

“…Computing the number of nodes per level of a graph in a parallel way can be separated in three stages as described by the Algorithm 3 originally presented by [7]. In the initial stage, all nodes of the graph are divided among the set of threads.…”

Section: B Counting Nodes By Level (Step 2)mentioning

confidence: 99%

“…Nevertheless, the advances toward the massive use of multi-core processors on scientific computation has leveraged significant performance improvements related to the solution of sparse matrices problems. In this context, in 2014 [7] described the first parallelization of the RCM algorithm, which was based on the speculative parallel model. In this parallelism model, a runtime system detects dependence violations between concurrent computations and rolls back conflicting computations as needed [8].…”

Section: Introductionmentioning

confidence: 99%

“…Algorithms of this type exhibit a complex pattern of parallelism which must be found and exploited at runtime [10]. To explore this kind of parallelism and to reduce the programming burden, [7] use the Galois system [11] which gives support to the speculative parallelism.…”

Section: Introductionmentioning

confidence: 99%

“…Making use of another parallel model, this paper proposes a non-speculative OpenMP-based implementation of the Unordered Parallel RCM algorithm presented by Karantasis et al [7]. This implementation strategy was considered once the non-speculative parallel model is the traditional manner to speedup every type of algorithm, and the OpenMP [12] framework for parallelism is widely used in industry as well as in academia.…”

Section: Introductionmentioning

confidence: 99%

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A Non-Speculative Parallelization of Reverse Cuthill-McKee Algorithm for Sparse Matrices Reordering

Rodrigues

Bóeres

Catabriga

2017

Proceedings of the 2017 Federated Conference on Computer Science and Information Systems

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Abstract-This work presents a new parallel non-speculative implementation of the Unordered Reverse Cuthill-McKee algorithm. Reordering quality (bandwidth reduction) and reordering performance (CPU time) are evaluated in comparison with a serial implementation of the algorithm made available by the state-of-the-art mathematical software library HSL. The bandwidth reductions reached by our parallel RCM were more than 90% for several large matrices out of the ones tested, and the time reordering improvement was up to 57.82%. Speedups higher than 3.0X were achieved with the parallel RCM. The underlying parallelism was supported by the OpenMP framework and three strategies for reducing idle threads were incorporated into the algorithm.

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Section: Unordered Parallel Rcm Algorithmmentioning

confidence: 99%

Section: B Counting Nodes By Level (Step 2)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Non-Speculative Parallelization of Reverse Cuthill-McKee Algorithm for Sparse Matrices Reordering

Rodrigues

Bóeres

Catabriga

2017

Proceedings of the 2017 Federated Conference on Computer Science and Information Systems

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Bandwidth and Wavefront Reduction for Static Variable Ordering in Symbolic Reachability Analysis

Meijer

Pol

2016

Lecture Notes in Computer Science

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We demonstrate the applicability of bandwidth and wavefront reduction algorithms to static variable ordering. In symbolic model checking event locality plays a major role in time and memory usage. For example, in Petri nets event locality can be captured by dependency matrices, where nonzero entries indicate whether a transition modifies a place. The quality of event locality has been expressed as a metric called (weighted) event span. The bandwidth of a matrix is a metric indicating the distance of nonzero elements to the diagonal. Wavefront is a metric indicating the degree of nonzeros on one end of the diagonal of the matrix. Bandwidth and wavefront are well studied metrics used in sparse matrix solvers. In this work we prove that span is limited by twice the bandwidth of a matrix. This observation makes bandwidth reduction algorithms useful for obtaining good variable orders. One major issue we address is that the reduction algorithms can only be applied on symmetric matrices, while the dependency matrices are asymmetric. We show that the Sloan algorithm executed on the total graph of the adjacency graph gives the best variable orders. Practically, we demonstrate that our work allows to call standard sparse matrix operations in Boost and ViennaCL, computing very good static variable orders in milliseconds. Future work is promising, because a whole new spectrum of more off-the-shelf algorithms, including metaheuristic ones, become available for variable ordering.

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An efficient memory data organization strategy for application-characteristic graph processing

Peng

Wang

Shi

et al. 2021

Front. Comput. Sci.

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Graph processing has received significant attention for its ability to cope with large-scale and complex unstructured data in the real-world. However, most of the graph processing applications exhibit an irregular memory access pattern which leads to a poor locality in the memory access stream [1], and [2] reveals that the sub-optimal use of the cache hierarchy can result in the CPU only works in the range of 10% to 45% of the overall graph processing time. Furthermore, the operating characteristics are discrepant in various graph applications [3], which cause the efficiency of existing graph processing frameworks is bogged down by a single memory organization. Consequently, how to design an efficient memory data organization strategy is key to accelerating graph processing.In the current literature, existing optimized memory data organization strategies could improve locality during graph processing to some extent, but there are still some deficiencies: (1) inability to combine the memory access pattern with the structural information of a graph well; (2) limited efficiency and a lot of preprocessing overhead on the large-scale graphs; (3) only a single memory data organization to deal with all graph applications or design for some specific graph processing tasks.To address the above challenges, we propose GMDO, an efficient memory data organization strategy based on the application operating characteristics. Specifically, GMDO consists of GMDO-VR and GMDO-VI for traversal and iterative applications, respectively, the former adopts the relevance degree to organize data more granular to ensure the locality during traversal, while the latter accelerates vertex convergence based on the vertex influence to deal with the long-tailed distribution in the iteration.In a nutshell, our contributions are summarized as follows:• We explore the dynamic running characteristics for traversal and iterative applications, and demonstrate that no single solution is adapted for both graph domains.

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Parallelization of Reordering Algorithms for Bandwidth and Wavefront Reduction

Cited by 29 publications

References 32 publications

A Non-Speculative Parallelization of Reverse Cuthill-McKee Algorithm for Sparse Matrices Reordering

A Non-Speculative Parallelization of Reverse Cuthill-McKee Algorithm for Sparse Matrices Reordering

Bandwidth and Wavefront Reduction for Static Variable Ordering in Symbolic Reachability Analysis

An efficient memory data organization strategy for application-characteristic graph processing

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