Parallel construction of optimal independent spanning trees on hypercubes

Yang, Jinn‐Shyong; Tang, Shyue-Ming; Chang, Jou–Ming; Wang, Yue-Li

doi:10.1016/j.parco.2006.12.001

Cited by 69 publications

(43 citation statements)

References 16 publications

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“…Comparing with the result in [25], all the (n − 1)! sets of ISTs can provide optimal reliable broadcasting for Q n .…”

Section: Theoremmentioning

confidence: 77%

“…. , n − 1; the set of ISTs in [30] is similar to that in [28] for Q n , which can be constructed by the descending CDP n − 1, n − 2, . .…”

Section: Observationmentioning

confidence: 99%

“…Consequently, researchers are interested in the study of ISTs for various special networks. Conjecture 1 has been solved for some restricted classes of networks, such as planar networks [15], product networks [23], hypercubes [25], [28], [30], Möbius cubes [5], [6], locally twisted cubes [22], crossed cubes [4], [7], twisted cubes [27], even networks [18], odd networks [19], and etc.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Circular Dimensional-Permutations and Reliable Broadcasting for Hypercubes and Möbius Cubes

Cheng

Fan

Yang

et al. 2013

Lecture Notes in Computer Science

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Abstract. Reliable broadcasting for interconnection networks can be achieved by constructing multiple independent spanning trees(ISTs) rooted at the same node. In this paper, we prove that there exists (n−1)! sets of ISTs rooted at an arbitrary node for Qn and Mn based on circular dimensional-permutations of 0, 1, . . . , n − 1 and n ≥ 1. At the same time, we give an parallel algorithm, called BCIST, which is the further study of IST problem for Qn and Mn in literature. Furthermore, simulation experiments of ISTs based on JUNG framework and different sets of disjoint paths between node 1 and any node v ∈ V (0-M4)\{1} for 0-M4 are also presented.

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“…Comparing with the result in [25], all the (n − 1)! sets of ISTs can provide optimal reliable broadcasting for Q n .…”

Section: Theoremmentioning

confidence: 77%

“…. , n − 1; the set of ISTs in [30] is similar to that in [28] for Q n , which can be constructed by the descending CDP n − 1, n − 2, . .…”

Section: Observationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Circular Dimensional-Permutations and Reliable Broadcasting for Hypercubes and Möbius Cubes

Cheng

Fan

Yang

et al. 2013

Lecture Notes in Computer Science

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“…Towards the conjecture that for any n -connected graph ) 1 (  n G , there are n ISTs rooted at an arbitrary vertex on G [1,2], it was only solved for 4  n [1,2,3,4], but remains open for 5  n . Thus, the results on special graphs are still the focus of researchers and many results have been obtained, such as hypercubes [5,6], crossed cubes [7], even networks [8], odd networks [9], folded hyper-stars [10], multidimensional torus networks [11], recursive circulant graphs [12], Gaussian networks [13], 2-chordal rings [14], and so on.…”

Section: Introductionmentioning

confidence: 99%

A Secure Message Transmission Scheme in an Extended Network of Crossed Cubes

Cheng¹,

Pan²,

Fan³

et al. 2017

Proceedings of the International Conference on Computer Networks and Communication Technology (CNCT 2016)

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Abstract. Secure message transmission schemes in interconnection networks can be achieved by constructing multiple vertex-disjoint paths or independent spanning trees. The extended network of crossed cube (ECC for short) has the advantages such as easy to be deployed and low ratio between number of vertices and diameter. In this paper, we have studied a secure message transmission scheme in ECC by constructing n independent spanning trees in n S and proposed a constructive algorithm with the timewhere N is the number of n S . Furthermore, the maximum length of the vertex-disjoint paths between any two vertices is shown to be n 2 +3. In addition, simulation of vertex-disjoint paths based on JUNG has also been discussed.

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“…Then, we can further study interconnection network of BC graphs [9] which include hypercubes, crossed cubes, Möbius cube, and twisted cube, etc. In the other way, Yang et al [10] gave the algorithm which can construct n ISTs in n-dimensional hypercube. Furthermore, we have solved the constuction of ISTs on a class of BC networks include hypercubes, crossed cubes, locally twisted cubes, Möbius cubes, and et al [11].…”

Section: Introductionmentioning

confidence: 99%