Scalable Parallel Algorithms for Unstructured Problems

Kumar, Vipin; Grama, Ananth; Gupta, Anshul; Karypis, George

doi:10.1007/978-1-4757-6130-6_5

Cited by 25 publications

(34 citation statements)

References 23 publications

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“…This procedure, known as Floyd's algorithm, requires O(N 3 ) operations. More efficient algorithms exploiting the sparse structure of the neighborhood graph can be found in (38). 17.…”

mentioning

confidence: 99%

Nonlinear Dimensionality Reduction

Lee¹,

Verleysen²

2007

Information Science and Statistics

838

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23; right 36, 13, and 27); superior frontal gyrus (left Ϫ9, 31, and 45; right 17, 35, and 37). 17. Although the improvement in WM performance with cholinergic enhancement was a nonsignificant trend in the current study (P ϭ 0.07), in a previous study (9) with a larger sample (n ϭ 13) the effect was highly significant (P Ͻ 0.001). In the current study, we analyzed RT data for six of our seven subjects because the behavioral data for one subject were unavailable due to a computer failure. The difference in the significance of the two findings is simply a result of the difference in sample sizes. A power analysis shows that the size of the RT difference and variability in the current sample would yield a significant result (P ϭ 0.01) with a sample size of 13. During the memory trials, mean RT was 1180 ms during placebo and 1119 ms during physostigmine. During the control trials, mean RT was 735 ms during placebo and 709 ms during physostigmine, a difference that did not approach significance (P ϭ 0.24), suggesting that the effect of cholinergic enhancement on WM performance is not due to a nonspecific increase in arousal.18. Matched-pair t tests (two-tailed) were used to test the significance of drug-related changes in the volume of regions of interest that showed significant response contrasts.

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“…This procedure, known as Floyd's algorithm, requires O(N 3 ) operations. More efficient algorithms exploiting the sparse structure of the neighborhood graph can be found in (38). 17.…”

mentioning

confidence: 99%

Nonlinear Dimensionality Reduction

Lee¹,

Verleysen²

2007

Information Science and Statistics

838

View full text Add to dashboard Cite

show abstract

“…Message sizes are represented by len P . Processors allocated to a job communicate with each other using the all-to-all communication pattern [8,15,17]. In all-to-all communication, each processor allocated to a job sends a packet to all other processors allocated to the same job.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…Advances in switching techniques such as wormhole switching [15], have made communication latency less sensitive to the distance between communicating nodes [4]. This has made allocating a job to non-contiguous processors plausible in long- …”

Section: Non-contiguous Allocation Strategiesmentioning

confidence: 99%

“…Although non-contiguous allocation increases message contention in the network, lifting the contiguity condition is expected to reduce processor fragmentation and increase processor utilization [4,12,17]. It is the introduction of wormhole switching [1,15] that has lead researchers to consider non-contiguous allocation on multicomputer networks with a long communication distances, such as the 2D mesh [1,4,12,17]. This is due to the fact that one of main advantages of wormhole switching over earlier switching techniques, e.g.…”

Section: Introductionmentioning

confidence: 99%

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The effect of real workloads and stochastic workloads on the performance of allocation and scheduling algorithms in 2D mesh multicomputers

Bani-Mohammad

Ould‐Khaoua

Mackenzie

et al. 2008

2008 IEEE International Symposium on Parallel and Distributed Processing

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“…Each iteration of CG involves, in order of computational dependency, one SpMxV, two inner-products, and three DAXPY computations. DAXPY computations do not involve communication, whereas inner-product computations necessitate a post global reduction operation [19] on results of the two local inner-products. In rowwise striping, pre-communication operations needed for SpMxV and the global reduction operation constitute pre-and post-synchronization points, respectively, for the aggregate of one local SpMxV and two local innerproduct computations.…”

Section: A Better Load Balancing Model For Iterative Solversmentioning

confidence: 99%

Fast optimal load balancing algorithms for 1D partitioning

Pınar

Aykanat

2004

Journal of Parallel and Distributed Computing

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The one-dimensional decomposition of nonuniform workload arrays with optimal load balancing is investigated. The problem has been studied in the literature as the ''chains-on-chains partitioning'' problem. Despite the rich literature on exact algorithms, heuristics are still used in parallel computing community with the ''hope'' of good decompositions and the ''myth'' of exact algorithms being hard to implement and not runtime efficient. We show that exact algorithms yield significant improvements in load balance over heuristics with negligible overhead. Detailed pseudocodes of the proposed algorithms are provided for reproducibility. We start with a literature review and propose improvements and efficient implementation tips for these algorithms. We also introduce novel algorithms that are asymptotically and runtime efficient. Our experiments on sparse matrix and direct volume rendering datasets verify that balance can be significantly improved by using exact algorithms. The proposed exact algorithms are 100 times faster than a single sparse-matrix vector multiplication for 64-way decompositions on the average. We conclude that exact algorithms with proposed efficient implementations can effectively replace heuristics. r 2004 Elsevier Inc. All rights reserved.

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Scalable Parallel Algorithms for Unstructured Problems

Cited by 25 publications

References 23 publications

Nonlinear Dimensionality Reduction

Nonlinear Dimensionality Reduction

The effect of real workloads and stochastic workloads on the performance of allocation and scheduling algorithms in 2D mesh multicomputers

Fast optimal load balancing algorithms for 1D partitioning

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