A New Record of Graph Enumeration Enabled by Parallel Processing

Xu, Zhipeng; Huang, Xiaolong; Jiménez, Fabián; Deng, Yuefan

doi:10.3390/math7121214

Cited by 8 publications

(5 citation statements)

References 25 publications

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“…Feng et al further explored 6D mesh/iBT on custom routing algorithms [25] and performance evaluation by simulation [24]. Deng et al implemented parallel exhaustive search of regular graphs [47] and random search with rotational symmetry to obtain small and large (near) optimal topologies and evaluated the performance by benchmarking both on real clusters and simulation platform [22]. More small optimal topologies with symmetries and other special properties were produced and presented in a structured table [53].…”

Section: Related Workmentioning

confidence: 99%

Optimal circulant graphs as low-latency network topologies

Huang¹,

Ramos²,

Deng³

2022

Preprint

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Communication latency has become one of the determining factors for the performance of parallel clusters. To design low-latency network topologies for high-performance computing clusters, we optimize the diameters, mean path lengths, and bisection widths of circulant topologies. We obtain a series of optimal circulant topologies of size 2 5 through 2 10 and compare them with torus and hypercube of the same sizes and degrees. We further benchmark on a broad variety of applications including effective bandwidth, FFTE, Graph 500 and NAS parallel benchmarks to compare the optimal circulant topologies and Cartesian products of optimal circulant topologies and fully connected topologies with corresponding torus and hypercube. Simulation results demonstrate superior potentials of the optimal circulant topologies for communication-intensive applications. We also find the

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Section: Related Workmentioning

confidence: 99%

Optimal circulant graphs as low-latency network topologies

Huang¹,

Ramos²,

Deng³

2022

Preprint

Self Cite

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“…The proposed method may find its uses in testing symmetry [37], as a homogeneity test [38] and, of course, in the process of detecting outliers [39].…”

Section: The Patterns In the Order Statisticsmentioning

confidence: 99%

Detecting Extreme Values with Order Statistics in Samples from Continuous Distributions

Jäntschi

2020

Mathematics

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In the subject of statistics for engineering, physics, computer science, chemistry, and earth sciences, one of the sampling challenges is the accuracy, or, in other words, how representative the sample is of the population from which it was drawn. A series of statistics were developed to measure the departure between the population (theoretical) and the sample (observed) distributions. Another connected issue is the presence of extreme values-possible observations that may have been wrongly collected-which do not belong to the population selected for study. By subjecting those two issues to study, we hereby propose a new statistic for assessing the quality of sampling intended to be used for any continuous distribution. Depending on the sample size, the proposed statistic is operational for known distributions (with a known probability density function) and provides the risk of being in error while assuming that a certain sample has been drawn from a population. A strategy for sample analysis, by analyzing the information about quality of the sampling provided by the order statistics in use, is proposed. A case study was conducted assessing the quality of sampling for ten cases, the latter being used to provide a pattern analysis of the statistics.

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“…Hence, an optimal graph has the properties of minimal diameter, minimal MPL, high throughput and high symmetry. We searched for the optimal graphs by enumeration using the same method as in [13] on supercomputers, and adopted data partially from [13]. In particular, we exhaustively calculated the diameters and MPLs of ∼ 10 12 and 10 13 graphs for (21,4) and (32, 3) respectively while, for the special case of (32, 4), the number of non-isomorphic graphs is too massive to exhaustively search.…”

Section: Optimal Graphsmentioning

confidence: 99%

“…Xu et al [12] applied these graphs to creating larger networks by using the Cartesian product, resolving scale limitations. To fill the family of optimal graphs, we use the exhaustive search as mentioned in [13] to find the graphs with the minimal MPL and other properties aiming for optimizing interconnection networks. These graphs can be used in NoC directly or, combining with hierarchical method or Cartesian products, used as the interconnects for clusters.…”

Section: Introductionmentioning

confidence: 99%