Optimal Routing and Hamiltonian Cycle in Petersen-Torus Networks

Seo, Jung-Hyun; Lee, Hyeong-Ok; Jang, Moonsuk

doi:10.1109/iccit.2008.53

Cited by 5 publications

(1 citation statement)

References 6 publications

(6 reference statements)

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“…This viewpoint can be extend to more complicated topologies, such as the Peterson Torus [32]. where 0 ≤ x < a, 0 ≤ y < b, and 0 ≤ p < 10.…”

Section: G-connected-hmentioning

confidence: 99%

Ramanujan Graphs and the Spectral Gap of Supercomputing Topologies

Aksoy¹,

Bruillard²,

Young³

et al. 2019

Preprint

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Graph eigenvalues play a fundamental role in controlling structural properties, such as bisection bandwidth, diameter, and fault tolerance, which are critical considerations in the design of supercomputing interconnection networks. This motivates considering graphs with optimal spectral expansion, called Ramanujan graphs, as potential candidates for interconnection networks. In this work, we explore this possibility by comparing Ramanujan graph properties against those of a wide swath of current and proposed supercomputing topologies. We derive analytic expressions for the spectral gap, bisection bandwidth, and diameter of these topologies, some of which were previously unknown. We find the spectral gap of existing topologies are well-separated from the optimal achievable by Ramanujan topologies, suggesting the potential utility of adopting Ramanujan graphs as interconnection networks.

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“…This viewpoint can be extend to more complicated topologies, such as the Peterson Torus [32]. where 0 ≤ x < a, 0 ≤ y < b, and 0 ≤ p < 10.…”

Section: G-connected-hmentioning

confidence: 99%

Ramanujan Graphs and the Spectral Gap of Supercomputing Topologies

Aksoy¹,

Bruillard²,

Young³

et al. 2019

Preprint

View full text Add to dashboard Cite

show abstract

Ramanujan graphs and the spectral gap of supercomputing topologies

et al. 2020

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A High-Performance and Cost-Efficient Interconnection Network for High-Density Servers

Bao¹,

Fu²,

Chen³

et al. 2013

2013 IEEE 10th International Conference on High Performance Computing and Communications &Amp; 2013 IEEE International Conferen

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The flourishing large-scale and high-throughput web applications have emphasized the importance of high-density servers for their distinct advantages, such as high computing density, low power and low space requirements. To achieve above advantages, an efficient intra-server interconnection network is necessary. Most state-of-the-art high-density servers adopt the fully-connected intra-server network to achieve high network performance. Unfortunately, this solution is very expensive due to the high degree of nodes.To address this problem, we exploit the theory optimized moore graph to interconnect the chips within a server. Considering the size of applications, the 50-size moore graph, namely the Hoffman-Singleton graph, is extensively discussed in this paper. The simulation results show that it could attain comparative performance as the fully-connected network with much lower cost. In practice, however, chips could be integrated onto multiple boards. Thus, the graph should be divided into self-connected sub-graphs with the same size. Unfortunately, state-of-the-art solutions do not consider the production problem and generate heterogeneous subgraphs. To address this problem, we propose two equivalent-partition solutions for Hoffman-Singleton graph depending on the density of boards. Finally, we propose and evaluate a deadlock-free routing algorithm for each partition scheme.

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Optimal Routing and Hamiltonian Cycle in Petersen-Torus Networks

Cited by 5 publications

References 6 publications

Ramanujan Graphs and the Spectral Gap of Supercomputing Topologies

Ramanujan Graphs and the Spectral Gap of Supercomputing Topologies

Ramanujan graphs and the spectral gap of supercomputing topologies

A High-Performance and Cost-Efficient Interconnection Network for High-Density Servers

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