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Optimal circulant graphs as low-latency network topologies

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Abstract

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 strengths of the Cartesian products in exploiting global communication with data traffic patterns of specific applications or internal algorithms.

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Acknowledgements

The authors thank Stony Brook Research Computing and Cyberinfrastructure, and the Institute for Advanced Computational Science at Stony Brook University for access to the high-performance SeaWulf computing system, which was made possible by a $1.4M National Science Foundation grant (#1531492). The authors also thank Dr. A. Y. Romanov for beneficial suggestions on the manuscript via e-mails.

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  1. Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York, 11794, USA

    Xiaolong Huang & Yuefan Deng

  2. Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, Avenida Arlindo Béttio 1000, São Paulo, SP, CEP 03828-000, Brazil

    Alexandre F. Ramos

  3. Mathematics, Division of Science, New York University Abu Dhabi, Saadiyat Island, Abu Dhabi, United Arab Emirates

    Yuefan Deng

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Huang, X., F. Ramos, A. & Deng, Y. Optimal circulant graphs as low-latency network topologies. J Supercomput 78, 13491–13510 (2022). https://doi.org/10.1007/s11227-022-04396-5

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