Independent spanning trees on folded hyper‐stars

Yang, Jinn‐Shyong; Chang, Jou–Ming

doi:10.1002/net.20389

Cited by 13 publications

(5 citation statements)

References 26 publications

(36 reference statements)

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“…From then on, this conjecture has been shown to be true for k-connected graphs with k 4 (see [11,13,20,48] for k = 2, 3, 4, respectively) and is still open for k 5. Also, this conjecture has been confirmed for several restricted classes of graphs, e.g., graphs related to planarity [18,19,25,26], graphs defined by Cartesian product [6,27,29,30,34,40,44], variations of hypercubes [5,[8][9][10]24,32,33,38,49], special Cayley graphs [22,23,28,39,42,43], and chordal ring [21,41]. In particular, [5,[7][8][9][10][32][33][34]40,49] are published after 2012.…”

Section: Introductionmentioning

confidence: 87%

A fully parallelized scheme of constructing independent spanning trees on Möbius cubes

Yang

Chang

et al. 2014

J Supercomput

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A set of spanning trees in a graph is said to be independent (ISTs for short) if all the trees are rooted at the same node r and for any other node v( = r ), the paths from v to r in any two trees are node-disjoint except the two end nodes v and r . It was conjectured that for any n-connected graph there exist n ISTs rooted at an arbitrary node. Let N = 2 n be the number of nodes in the n-dimensional Möbius cube M Q n . Recently, for constructing n ISTs rooted at an arbitrary node of M Q n , Cheng et al. (Comput J 56(11):1347(Comput J 56(11): -1362(Comput J 56(11): , 2013 and (J Supercomput 65 (3):1279-1301, 2013), respectively, proposed a sequential algorithm to run in O(N log N ) time and a parallel algorithm that takes O(N ) time using log N processors. However, the former algorithm is executed in a recursive fashion and thus is hard to be parallelized. Although the latter algorithm can simultaneously construct n ISTs, it is not fully parallelized for the construction of each spanning tree. In this paper, we present a nonrecursive and fully parallelized approach to construct n ISTs rooted at an arbitrary node of M Q n in O(log N ) time using N nodes of M Q n as processors. In particular, we derive useful properties from the description of paths in ISTs, which make the proof of independency to become easier than ever before.

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Section: Introductionmentioning

confidence: 87%

A fully parallelized scheme of constructing independent spanning trees on Möbius cubes

Yang

Chang

et al. 2014

J Supercomput

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“…For examples, it has better scalability, simple routing algorithm, maximum fault‐tolerance and lower network cost (defined as the product of its degree and diameter) than the hypercube and its variations . Many properties of hyper‐star and folded hyper‐star graphs were introduced in . Please note that there is a similarly named network called hyperstar , which is completely different from the hyper‐star studied in this paper.…”

Section: Introductionmentioning

confidence: 99%

Hyper‐star graphs: Some topological properties and an optimal neighbourhood broadcasting algorithm

Zhang

Qiu

Kim

2015

Concurrency and Computation

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Summary Hyper‐star graph HS(2n,n) was introduced to be a competitive model to both hypercubes and star graphs. In this paper, we study its properties by (1) giving a closed form solution to the surface area of HS(2n,n), (2) discussing its Hamiltonicity by establishing an isomorphism between the graph and the well‐known middle levels problem, and (3) showing that full binary trees can be embedded into HS(2n,n) with dilation 1. We also develop a single‐port optimal neighbourhood broadcasting algorithm for HS(2n,n). Copyright © 2015 John Wiley & Sons, Ltd.

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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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Independent spanning trees on folded hyper‐stars

Cited by 13 publications

References 26 publications

A fully parallelized scheme of constructing independent spanning trees on Möbius cubes

A fully parallelized scheme of constructing independent spanning trees on Möbius cubes

Hyper‐star graphs: Some topological properties and an optimal neighbourhood broadcasting algorithm

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

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