Independent spanning trees on even networks

Kim, Jong-Seok; Lee, Hyeong-Ok; Cheng, Eddie; Lipták, László

doi:10.1016/j.ins.2011.02.012

Cited by 23 publications

(7 citation statements)

References 33 publications

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“…Hypercubes and its variants [9,15,17,21,22,24,25,28,36,37] form the basic classes of interconnection networks. The class of star graphs [1] and the class of alternating group graphs [23] were introduced to be competitive models of hypercubes.…”

Section: Introductionmentioning

confidence: 99%

A kind of conditional vertex connectivity of Cayley graphs generated by 2-trees

Cheng

Lipták

Yang

et al. 2011

Information Sciences

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Section: Introductionmentioning

confidence: 99%

A kind of conditional vertex connectivity of Cayley graphs generated by 2-trees

Cheng

Lipták

Yang

et al. 2011

Information Sciences

Self Cite

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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: 79%

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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“…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 even networks

Cited by 23 publications

References 33 publications

A kind of conditional vertex connectivity of Cayley graphs generated by 2-trees

A kind of conditional vertex connectivity of Cayley graphs generated by 2-trees

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

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

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