Constructing independent spanning trees for locally twisted cubes

Liu, Yi-Jiun; Lan, James K.; Chou, Well Y.; Chen, Chiuyuan

doi:10.1016/j.tcs.2010.12.061

Cited by 43 publications

(16 citation statements)

References 18 publications

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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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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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“…As a result, the research on ISTs is majorly focused on special graphs. It was proved that there exist n ISTs rooted at any vertex on an n-dimensional hypercube [27,29,34,37] and some variants of the n-dimensional hypercube, such as a locally twisted cube [17,25], twisted cube [35,33], crossed cube [5], Möbius cube [4], and parity cube [32] of n dimensions.…”

Section: Graph Terminology and Notationmentioning

confidence: 99%

Dimension-adjacent trees and parallel construction of independent spanning trees on crossed cubes

Cheng

Fan

Jia

et al. 2013

Journal of Parallel and Distributed Computing

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“…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%

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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Constructing independent spanning trees for locally twisted cubes

Cited by 43 publications

References 18 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

Dimension-adjacent trees and parallel construction of independent spanning trees on crossed cubes

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

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