Independent spanning trees of product graphs

Obokata, Koji; Iwasaki, Yukihiro; Bao, Feng; Igarashi, Yoshihide

doi:10.1007/3-540-62559-3_27

Cited by 27 publications

(20 citation statements)

References 4 publications

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“…Independent spanning trees have been studied in several topologies, including chordal rings [14], de Bruijn and Kautz digraphs [15], [16], and product graphs [17].…”

Section: Related Workmentioning

confidence: 99%

Completely independent spanning trees for enhancing the robustness in ad-hoc Networks

Moinet¹,

Darties²,

Gastineau³

et al. 2017

2017 IEEE 13th International Conference on Wireless and Mobile Computing, Networking and Communications (WiMob)

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Abstract-We investigate the problem of computing Completely Independent Spanning Trees (CIST) under a practical approach. We aim to show that despite CISTs are very challenging to exhibit in some networks, they present a real interest in ad-hoc networks and can be computed to enhance the network robustness. We propose an original ILP formulation for CISTs and we show through simulation results on representative network models that several CISTs can be computed when the network density is sufficiently high. These results tend to reinforce the interest of CISTs for various network operations such as robustness, load-balancing, traffic splitting, . . . As an important point, our results show that both the density and the number of nodes have an impact on the number of CISTs that can be found on ad-hoc networks.

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“…Independent spanning trees have been studied in several topologies, including chordal rings [14], de Bruijn and Kautz digraphs [15], [16], and product graphs [17].…”

Section: Related Workmentioning

confidence: 99%

Completely independent spanning trees for enhancing the robustness in ad-hoc Networks

Moinet¹,

Darties²,

Gastineau³

et al. 2017

2017 IEEE 13th International Conference on Wireless and Mobile Computing, Networking and Communications (WiMob)

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“…For a graph (or network) G, the independent spanning trees (IST) problem attempts to construct a maximal set of ISTs rooted at any node r of G and such that the cardinality of the set of ISTs matches the connectivity of G. Although the problem is hard for general graphs, several results are known for some special classes of graphs (especially, the graph classes related to interconnection networks), such as k-connected graphs with k ≤ 4 [5,6,14,30], product graphs [21], planar graphs [13], chordal rings [15,26], deBruijn and Kautz graphs [10,11], hypercubes [24,29], star graphs [23], recursive circulant graphs [27,28], and multidimensional tori [25]. In this article, we deal with the IST problem on a class of graphs called folded hyper-stars.…”

Section: Introductionmentioning

confidence: 99%

Independent spanning trees on folded hyper‐stars

Yang

Chang

2010

Networks

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Fault-tolerant broadcasting and secure message distribution are important issues for numerous applications in networks. It is a common idea to design multiple independent spanning trees (ISTs) as a broadcasting scheme or a distribution protocol for receiving high levels of fault-tolerance and security. Recently, hyper-stars were introduced as a competitive model of interconnection network for both hypercubes and star graphs. The class of folded hyper-stars is a strengthened variation of hyper-stars obtained by adding additional links to connect complemented nodes. Both hyper-stars and folded hyper-stars have been shown to have lower network cost (measured by the product of degree and diameter) than hypercubes, folded hypercubes, and other variants. In this article, we propose an algorithm to construct k + 1 ISTs on a regular folded hyper-star FHS(2k , k ), where the number of ISTs matches the connectivity of FHS(2k , k ). In particular, for k ≥ 4, the constructed k ISTs have height 2k − 2, and the other one has height k + 1.

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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 of product graphs

Cited by 27 publications

References 4 publications

Completely independent spanning trees for enhancing the robustness in ad-hoc Networks

Completely independent spanning trees for enhancing the robustness in ad-hoc Networks

Independent spanning trees on folded hyper‐stars

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

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