Hierarchical cubic networks

Ghose, Kanad; Desai, Kiran

doi:10.1109/71.372797

Cited by 179 publications

(82 citation statements)

References 19 publications

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“…Prominent among these were the two-level special case of WK-recursive networks [7] (beyond two levels, WK-recursive and swapped networks diverge in structure and do not have much in common), hierarchical cubic networks [8], and recursively fully connected networks [9]. The unification was due to the replacement of complete-graph or hypercube component networks of the prior architectures with an arbitrary graph.…”

Section: Related Workmentioning

confidence: 99%

The Hamiltonicity of swapped (OTIS) networks built of Hamiltonian component networks

Parhami¹

2005

Information Processing Letters

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A two-level swapped (also known as optical transpose interconnect system, or OTIS) network with n 2 nodes is built of n copies of an n-node basis network constituting its clusters. A simple rule for intercluster connectivity (node j in cluster i connected to node i in cluster j for all i = j ) leads to regularity, modularity, packageability, fault tolerance, and algorithmic efficiency of the resulting networks. We prove that a swapped network is Hamiltonian if its basis network is Hamiltonian. This general closure property for Hamiltonicity under swap or OTIS composition replaces a number of proofs in the literature for specific basis networks and obviates the need for proving Hamiltonicity for many other basis networks of potential practical interest.

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Section: Related Workmentioning

confidence: 99%

The Hamiltonicity of swapped (OTIS) networks built of Hamiltonian component networks

Parhami¹

2005

Information Processing Letters

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“…The lack of scalability of the hypercube stems from the fact that the node degree is not bounded and varies as log 2 N, where N is the total number of nodes. This property makes the hypercube cost prohibitive for large N. Most hypercube-based interconnection networks proposed in the literature [9], [10], [11], [12], [13], [14], [15] suffer from similar size scalability problems.…”

Section: Introductionmentioning

confidence: 99%

A spanning multichannel linked hypercube: a gradually scalable optical interconnection network for massively parallel computing

Louri

Weech

Neocleous

1998

IEEE Trans. Parallel Distrib. Syst.

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Abstract-A new, scalable interconnection topology called the Spanning Multichannel Linked Hypercube (SMLH) is proposed. This proposed network is very suitable to massively parallel systems and is highly amenable to optical implementation. The SMLH uses the hypercube topology as a basic building block and connects such building blocks using two-dimensional multichannel links (similar to spanning buses). In doing so, the SMLH combines positive features of both the hypercube (small diameter, high connectivity, symmetry, simple routing, and fault tolerance) and the spanning bus hypercube (SBH) (constant node degree, scalability, and ease of physical implementation), while at the same time circumventing their disadvantages. The SMLH topology supports many communication patterns found in different classes of computation, such as bus-based, mesh-based, and tree-based problems, as well as hypercube-based problems. A very attractive feature of the SMLH network is its ability to support a large number of processors with the possibility of maintaining a constant degree and a constant diameter. Other positive features include symmetry, incremental scalability, and fault tolerance. It is shown that the SMLH network provides better average message distance, average traffic density, and queuing delay than many similar networks, including the binary hypercube, the SBH, etc. Additionally, the SMLH has comparable performance to other high-performance hypercubic networks, including the Generalized Hypercube and the Hypermesh. An optical implementation methodology is proposed for SMLH. The implementation methodology combines both the advantages of free space optics with those of wavelength division multiplexing techniques. A detailed analysis of the feasibility of the proposed network is also presented.

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“…, 하이퍼큐브 [4,7], Hierarchical Cubic Network(HCN) †준 회 원 : 오클라호마 주립대학교 컴퓨터과학과 박사후연구원 † †정 회 원 : (주)보고정보 기획영업팀 차장 논문접수 : 2007년 6월 24일, 심사완료：2007년 9월 22일 [11,17], Hierarchical Folded-hypercube Network(HFN) [6], …”

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Embedding Algorithm between [ 2^2n-k×2^k] Torus and HFN(n,n), HCN(n,n)

Kim¹,

Kang²

2007

The KIPS Transactions:PartA

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Hierarchical cubic networks

Cited by 179 publications

References 19 publications

The Hamiltonicity of swapped (OTIS) networks built of Hamiltonian component networks

The Hamiltonicity of swapped (OTIS) networks built of Hamiltonian component networks

A spanning multichannel linked hypercube: a gradually scalable optical interconnection network for massively parallel computing

Embedding Algorithm between [ 2^2n-k×2^k] Torus and HFN(n,n), HCN(n,n)

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Hierarchical cubic networks

Cited by 179 publications

References 19 publications

The Hamiltonicity of swapped (OTIS) networks built of Hamiltonian component networks

The Hamiltonicity of swapped (OTIS) networks built of Hamiltonian component networks

A spanning multichannel linked hypercube: a gradually scalable optical interconnection network for massively parallel computing

Embedding Algorithm between [ 22n-k×2k] Torus and HFN(n,n), HCN(n,n)

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Embedding Algorithm between [ 2^2n-k×2^k] Torus and HFN(n,n), HCN(n,n)