Symmetry-guided design of topologies for supercomputer networks

Alan U. Sabino, Miguel F. S. Vasconcelos, Yuefan Deng and Alexandre F. Ramos
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Alan U. Sabino: Escola de Artes, Ciências e Humanidades, Universidade de São Paulo. Av. Arlindo Béttio, 1000. São Paulo, SP, 03.828-000, Brazil†Núcleo de Estudos Interdisciplinares em Sistemas Complexos, Universidade de São Paulo. Av. Arlindo Béttio, 1000. São Paulo, SP, 03.828-000, Brazil‡Dept. de Radiologia e Oncologia – Fac. de Medicina, Universidade de São Paulo, Travessa da Rua Dr. Ovídio, Pires de Campos, 75. São Paulo, 05403-010, Brazil§Centro do Pesquisa Translacional em Oncologia, Instituto do Câncer do Estado de São Paulo, Av. Dr. Arnaldo, 251, São Paulo, SP, 01246-000, Brazil
Miguel F. S. Vasconcelos: Escola de Artes, Ciências e Humanidades, Universidade de São Paulo. Av. Arlindo Béttio, 1000. São Paulo, SP, 03.828-000, Brazil†Núcleo de Estudos Interdisciplinares em Sistemas Complexos, Universidade de São Paulo. Av. Arlindo Béttio, 1000. São Paulo, SP, 03.828-000, Brazil‡Dept. de Radiologia e Oncologia – Fac. de Medicina, Universidade de São Paulo, Travessa da Rua Dr. Ovídio, Pires de Campos, 75. São Paulo, 05403-010, Brazil§Centro do Pesquisa Translacional em Oncologia, Instituto do Câncer do Estado de São Paulo, Av. Dr. Arnaldo, 251, São Paulo, SP, 01246-000, Brazil
Yuefan Deng: #xB6;Shandong Computer Science Center (National Supercomputer Centre in Jinan), Jinan, Shandong 250101, P. R. China∥Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794, USA**Department of Data and Computer Science, Sun Yat-Sen University, Guangdong 510006, P. R. China
Alexandre F. Ramos: Escola de Artes, Ciências e Humanidades, Universidade de São Paulo. Av. Arlindo Béttio, 1000. São Paulo, SP, 03.828-000, Brazil†Núcleo de Estudos Interdisciplinares em Sistemas Complexos, Universidade de São Paulo. Av. Arlindo Béttio, 1000. São Paulo, SP, 03.828-000, Brazil‡Dept. de Radiologia e Oncologia – Fac. de Medicina, Universidade de São Paulo, Travessa da Rua Dr. Ovídio, Pires de Campos, 75. São Paulo, 05403-010, Brazil§Centro do Pesquisa Translacional em Oncologia, Instituto do Câncer do Estado de São Paulo, Av. Dr. Arnaldo, 251, São Paulo, SP, 01246-000, Brazil¶Shandong Computer Science Center (National Supercomputer Centre in Jinan), Jinan, Shandong 250101, P. R. China

International Journal of Modern Physics C (IJMPC), 2018, vol. 29, issue 07, 1-17

Abstract: A family of graphs optimized as the topologies for interconnection networks is proposed. The needs of such topologies with minimal diameters and minimal mean path lengths are met by special constructions of the weight vectors in a representation of the symplectic algebra. Such design of topologies can conveniently reconstruct the mesh and hypercube, widely used as network topologies, as well as many other classes of graphs potentially suitable for network topologies.

Keywords: Supercomputer network topologies; graph theory; group theory; roots and weights lattices; symplectic algebra (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijmpcx:v:29:y:2018:i:07:n:s0129183118500481

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DOI: 10.1142/S0129183118500481

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