The hierarchical Petersen network: a new interconnection network with fixed degree

Seo, Jung-Hyun; Kim, Jong-Seok; Chang, Hyung Jae; Lee, Hyeong-Ok

doi:10.1007/s11227-017-2186-4

Cited by 11 publications

(7 citation statements)

References 38 publications

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“…In a connected graph G, a Hamiltonian cycle is a cycle that includes all vertices. If an interconnection network has a Hamiltonian path or a Hamiltonian cycle, it can be easily implemented as a ring or linear array, which can be used as a pipeline that is useful for parallel processing [16].…”

Section: Interconnection Network and Fixed Degree Graphmentioning

confidence: 99%

Full Binary Tree-Based Fixed Degree Graph Design and Parallel Algorithm

Seong,

Jang,

Lee

2023

IEEE Access

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Interconnection network is a network that connects processors and is an important factor in determining the performance of a parallel processing system. One measure of interconnection network evaluation is network cost, defined as degree * diameter. The interconnection networks proposed so far can be classified into mesh, hypercube, and star graph types based on the number of nodes. The interconnection network 𝑇𝑟𝑒𝑒 − 𝑏𝑎𝑠𝑒 𝐺𝑟𝑎𝑝ℎ(𝑇𝐺 𝑛 ) proposed in this study is a graph based on a full binary tree with a fixed degree of three, and the node address is expressed using n binary numbers. In this study, routing algorithms, Hamiltonian cycle, node disjoint parallel path, etc. are analyzed for 𝑇𝑟𝑒𝑒 − 𝑏𝑎𝑠𝑒 𝐺𝑟𝑎𝑝ℎ(𝑇𝐺 𝑛 ). 𝑇𝐺 𝑛 graph has network cost 𝑂(6𝑛) with a fixed degree of three and diameter 2𝑛 − 2. From the network cost viewpoint, 𝑇𝐺 𝑛 has around 50% improvement results compared to existing fixed degree graphs such as mesh, torus, honeycomb mesh and shuffle-exchange permutation.

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Section: Interconnection Network and Fixed Degree Graphmentioning

confidence: 99%

Full Binary Tree-Based Fixed Degree Graph Design and Parallel Algorithm

Seong,

Jang,

Lee

2023

IEEE Access

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“…The hypercube class has been commercialized as iPSC/2, iPSC/860, and n-CUBE/2; the mesh class as MasPar Intel Paragon, XP/ S, Touchstone DELTA System, and Mosaic C; and the three-dimensional mesh class as Cray T3D, MIT's J-Machine, and Tera Computer. 2 In the systems mentioned in the preceding paragraph, electronic signals are transmitted along the communication links. After the emergence of optical communication, an optical transpose interconnection system (OTIS), which combines the advantages of both electronic communication and optical communication, was proposed by Marsden et al 3 The OTIS network is implemented using free-space optoelectronic technology.…”

Section: Introductionmentioning

confidence: 99%

Petersen-star networks modeled by optical transpose interconnection system

Seo

Lee

2021

International Journal of Distributed Sensor Networks

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One method to create a high-performance computer is to use parallel processing to connect multiple computers. The structure of the parallel processing system is represented as an interconnection network. Traditionally, the communication links that connect the nodes in the interconnection network use electricity. With the advent of optical communication, however, optical transpose interconnection system networks have emerged, which combine the advantages of electronic communication and optical communication. Optical transpose interconnection system networks use electronic communication for relatively short distances and optical communication for long distances. Regardless of whether the interconnection network uses electronic communication or optical communication, network cost is an important factor among the various measures used for the evaluation of networks. In this article, we first propose a novel optical transpose interconnection system–Petersen-star network with a small network cost and analyze its basic topological properties. Optical transpose interconnection system–Petersen-star network is an undirected graph where the factor graph is Petersen-star network. OTIS–PSN n has the number of nodes 102n, degree n+3, and diameter 6 n − 1. Second, we compare the network cost between optical transpose interconnection system–Petersen-star network and other optical transpose interconnection system networks. Finally, we propose a routing algorithm with a time complexity of 6 n − 1 and a one-to-all broadcasting algorithm with a time complexity of 2 n − 1.

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“…In contrast, for sorting problems or WSNs with a logical connection structure, the diameter is a more important measure than the degree. In other fields, other evaluation measures may be more important [1]. In the interconnection network for parallel computing, since degree refers to the number of communication ports, the hardware installation cost increases when the degree increases.…”

Section: Introductionmentioning

confidence: 99%

“…Network cost Definition 3. The swap operation for S is SOk(S) = Sk+1 … S2k−1S2kS1S2S3 … Sk−1Sks2k+1 … sn−2sn−1sn, k = 2 0 , 2 1 , 2 2 , ⋯, 2 n/2 .…”

Section: Introductionmentioning

confidence: 99%

Design and Analysis of a Symmetric Log Star Graph with a Smaller Network Cost Than Star Graphs

Seo

Lee

2021

Electronics

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Graphs are used as models to solve problems in fields such as mathematics, computer science, physics, and chemistry. In particular, torus, hypercube, and star graphs are popular when modeling the connection structure of processors in parallel computing because they are symmetric and have a low network cost. Whereas a hypercube has a substantially smaller diameter than a torus, star graphs have been presented as an alternative to hypercubes because of their lower network cost. We propose a novel log star (LS) that is symmetric and has a lower network cost than a star graph. The LS is an undirected, recursive, and regular graph. In LSn, the number of nodes is n! while the degree is 2log2n − 1 and the diameter is 0.5n(log2n)2 + 0.75nlog2n. In this study, we analyze the basic topological properties of LS. We prove that LSn is a symmetrical connected graph and analyzed its subgraph characteristics. Then, we propose a routing algorithm and derive the diameter and network cost. Finally, the network costs of the LS and star graph-like networks are compared.

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The hierarchical Petersen network: a new interconnection network with fixed degree

Cited by 11 publications

References 38 publications

Full Binary Tree-Based Fixed Degree Graph Design and Parallel Algorithm

Full Binary Tree-Based Fixed Degree Graph Design and Parallel Algorithm

Petersen-star networks modeled by optical transpose interconnection system

Design and Analysis of a Symmetric Log Star Graph with a Smaller Network Cost Than Star Graphs

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