Embedding meshes into crossed cubes

Fan, Jianxi; Jia, Xiaohua

doi:10.1016/j.ins.2006.12.010

Cited by 61 publications

(29 citation statements)

References 29 publications

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“…In the second embedding, edge (1010,0000) in the complete binary tree is mapping to a path P : 1010− > 0010− > 0000 of LT Q 4 . Every node of CBT 4 is mapping to a node in LT Q 4 and every edge of CBT 4 except edge (1010,0000) is mapping to an edge in LT Q 4 . By the definition of dilation, the dilation of the second embedding is 2.…”

Section: Lemmamentioning

confidence: 99%

Embedding Complete Binary Trees into Locally Twisted Cubes

Han¹,

Fan²,

You

et al. 2012

AEF

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Abstract. The locally twisted cube is a newly introduced interconnection network for parallel computing, which possesses many desirable properties. In this paper, the problem of embedding complete binary trees into locally twisted cubes is studied. Let LT Q n (V, E) denote the n-dimensional locally twisted cube. We find the following result in this paper: for any integer n ≥ 2, we show that a complete binary tree with 2 n − 1 nodes can be embedded into the LT Q n with dilation 2.

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Section: Lemmamentioning

confidence: 99%

Embedding Complete Binary Trees into Locally Twisted Cubes

Han¹,

Fan²,

You

et al. 2012

AEF

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“…Furthermore, by changing their links between some nodes, the variants of hypercubes, such as Möbius cubes [9], crossed cubes [20], and twisted cubes [1] were proposed, which have better properties [12], [13], [14], [16], [29].…”

Section: Introductionmentioning

confidence: 99%

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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“…The expansion is defined as the ratio of the number of vertices in the host graph to the number of vertices in the guest graph. Architecture simulation can be modelled as a graph embedding, which embeds the guest architecture into the host architecture of the simulation [2][3][4][5]7,9].…”

Section: Introductionmentioning

confidence: 99%