Embedding Hamiltonian Cycles into Folded Hypercubes with Faulty Links

Wang, Dajin

doi:10.1006/jpdc.2000.1681

Cited by 78 publications

(27 citation statements)

References 8 publications

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“…Owing to their higher node degree, these networks also have higher connectivity, so have better fault tolerance and better diagnostic capabilities compared to hypercubes. For technical details of these favorable properties of enhanced cubes see [1,2,4,[7][8][9][10].…”

Section: Introductionmentioning

confidence: 98%

Complete binary trees in folded and enhanced cubes

Choudum

Nandini

2004

Networks

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Section: Introductionmentioning

confidence: 98%

Complete binary trees in folded and enhanced cubes

Choudum

Nandini

2004

Networks

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“…One variant that has been the focus of a great deal of research is the folded hypercube, which can be constructed from a hypercube by adding an edge joining every pair of vertices that are the farthest apart, i.e., two vertices with complementary addresses. The folded hypercube has been shown to be able to improve a system's performance over a regular hypercube in many measurements, such as diameter, fault diameter, connectivity, and so on [3,20].…”

Section: Introductionmentioning

confidence: 99%

“…Hence, the issue of fault-tolerant cycle embedding in an n-dimensional folded hypercube F Q n has been studied in [2,5,7,8,9,10,11,12,13,14,20,19]. Embedding cycles in networks is important as many network algorithms utilize cycles as data structure.…”

Section: Introductionmentioning

confidence: 99%

Edge-pancyclicity and edge-bipancyclicity of faulty folded hypercubes

Kuo

Stewart

2016

Theoretical Computer Science

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Additional information:Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractLet F v and F e be sets of faulty vertices and faulty edges, respectively, in the folded hypercube F Q n so that |F v | + |F e | ≤ n − 2, for n ≥ 2. Choose any fault-free edge e. If n ≥ 3 then there is a fault-free cycle of length l in F Q n containing e, for every even l ranging from 4 to 2 n − 2|F v |; if n ≥ 2 is even then there is a fault-free cycle of length l in F Q n containing e, for every odd l ranging from n + 1 to 2 n − 2|F v | − 1.

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“…The n-dimensional folded hypercube is (n Ϫ 1)-link Hamiltonian [21]. The n-dimensional star graph is (n Ϫ 3)-link Hamiltonian [20].…”

Section: Introductionmentioning

confidence: 99%

Fault‐tolerant cycle embedding in hierarchical cubic networks

Fu¹,

Chen²

2003

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A hierarchical cubic network was proposed as an alternative to the hypercube. By HCN(n), we denote the hierarchical cubic network that contains 2 n n-dimensional hypercubes. In this paper, using Gray codes, we construct fault-free Hamiltonian cycles in an HCN(n) with n ؊ 1 link faults. Since the HCN(n) is regular of degree n ؉ 1, the result is optimal. We also construct longest fault-free cycles of length 2 2n ؊ 1 in an HCN(n) with a one-node fault and fault-free cycles of length at least 2 2n ؊ 2f in an HCN(n) with f-node faults, where 2 2n is the number of nodes in the HCN(n), f ≤ n ؊ 1 if n ‫؍‬ 3 or 4 and f ≤ n if n ≥ 5. Our results can be applied to the hierarchical folded-hypercube network as well.

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Embedding Hamiltonian Cycles into Folded Hypercubes with Faulty Links

Cited by 78 publications

References 8 publications

Complete binary trees in folded and enhanced cubes

Complete binary trees in folded and enhanced cubes

Edge-pancyclicity and edge-bipancyclicity of faulty folded hypercubes

Fault‐tolerant cycle embedding in hierarchical cubic networks

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