Constructing spanning trees in augmented cubes

Mane, S. A.; Kandekar, S. A.; Waphare, B. N.

doi:10.1016/j.jpdc.2018.08.006

Cited by 31 publications

(6 citation statements)

References 30 publications

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“…Also, with the help of constructions, it has been confirmed that certain classes of graphs possess two CISTs, e.g., 4-connected maximal planar graphs [13], Cartesian product of any 2-connected graphs [14], 4-regular chordal rings [2], [23], crossed cubes [5], and several hypercube-variant networks [21]. In addition, more graphs possessing multiple CISTs can be found in [6], [12], [16], [19], [20], [22]. In this paper, we investigate the problem of constructing two CISTs in balanced hypercubes (defined later in Sect.…”

Section: Introductionmentioning

confidence: 91%

Constructing Two Completely Independent Spanning Trees in Balanced Hypercubes

Yang

Pai

Chang

et al. 2019

IEICE Trans. Inf. & Syst.

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A set of spanning trees of a graphs G are called completely independent spanning trees (CISTs for short) if for every pair of vertices x, y ∈ V(G), the paths joining x and y in any two trees have neither vertex nor edge in common, except x and y. Constructing CISTs has applications on interconnection networks such as fault-tolerant routing and secure message transmission. In this paper, we investigate the problem of constructing two CISTs in the balanced hypercube BH n , which is a hypercube-variant network and is superior to hypercube due to having a smaller diameter. As a result, the diameter of CISTs we constructed equals to 9 for BH 2 and 6n − 2 for BH n when n 3. key words: interconnection networks, completely independent spanning trees, balanced hypercubes, diameter

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Section: Introductionmentioning

confidence: 91%

Constructing Two Completely Independent Spanning Trees in Balanced Hypercubes

Yang

Pai

Chang

et al. 2019

IEICE Trans. Inf. & Syst.

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“…Moreover, k n (G) is exactly the spanning tree packing number of G. Therefore, the generalized connectivity is a common generalization of the classical connectivity and spanning tree packing number. The research about S−Steiner trees, spanning tree packing number, generalized connectivity and pendant tree connectivity of graphs plays a key role in effective information transportation in terms of parallel routing design for large-scale networks, see [2,3,4,6,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,27,28,29,30].…”

Section: Introductionmentioning

confidence: 99%

Pendant 3-tree Connectivity of Augmented Cubes

Mane,

Kandekar

2021

Preprint

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The Steiner tree problem in graphs has applications in network design or circuit layout. Given a set S of vertices, |S| ≥ 2, a tree connecting all vertices of S is called an S-Steiner tree (tree connecting S). The reliability of a network G to connect any S vertices (|S| number of vertices) in G can be measure by this parameter. For an S-Steiner tree, if the degree of each vertex in S is equal to one, then that tree is called a pendant S-Steiner tree. Two pendant S-Steiner trees T and T ′ are said to be internally disjoint ifThe local pendant tree-connectivity τG(S) is the maximum number of internally disjoint pendant S-Steiner trees in G. For an integer k with 2 ≤ k ≤ n, the pendant k-tree-connectivity is defined as τ k (G) = min{τG(S) : S ⊆ V (G), |S| = k}. In this paper, we study the pendant 3tree connectivity of Augmented cubes which are modification of hypercubes invented to increase the connectivity and decrease the diameter hence superior to hypercubes. We show that τ3(AQn) = 2n − 3. , which attains the upper bound of τ3(G) given by Hager, for G = AQn.

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“…However, Hasunuma [12] early proved that the problem of determining whether there exists k CISTs in a graph is NP-complete, even for k = 2 (i.e., a dual-CIST). For more researches on constructing a dual-CIST or multiple CISTs on interconnection networks, please refer to [20,[22][23][24][25][26] and references quoted therein. In particular, the works in [22][23][24][25] discussed in-depth the configuration of protection routing.…”

Section: Introductionmentioning

confidence: 99%

Transmission Failure Analysis of Multi-Protection Routing in Data Center Networks with Heterogeneous Edge-Core Servers

Li¹,

Wanling²,

Chang³

et al. 2021

Preprint

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The recently proposed RCube network is a cube-based server-centric data center network (DCN), including two types of heterogeneous servers, called core servers and edge servers. Remarkably, it takes the latter as backup servers to deal with server failures and thus achieve high availability. This paper first points out that RCube is suitable as a candidate topology of DCNs for edge computing. Three transmission types are among core and edge servers based on the demand for applications' computation and instant response. We then employ protection routing to analyze the transmission failure of RCube DCNs. Unlike traditional protection routing, which only tolerates a single link or node failure, we use the multi-protection routing scheme to improve fault-tolerance capability. To configure a protection routing in a network, according to Tapolcai's suggestion, we need to construct two completely independent spanning trees (CISTs), which are edge-disjoint and innervertex-disjoint spanning trees. It is well-known that the problem of determining whether there exists a dual-CIST (i.e., two CISTs) in a network is NP-complete. A logic graph of RCube, denoted by L-RCube(n, m, k), is a network with a recursive structure. Each basic building element consists of n core servers and m edge servers, where the order k is the number of recursions applied in the structure. In this paper, we provide algorithms to construct min{n, (n + m)/2 } CISTs in L-RCube(n, m, k) for n + m 4 and n > 1. From a combination of the multiple CISTs, we can configure the desired multi-protection routing. In our simulation, we configure up to 10 protection routings for RCube DCNs. As far as we know, in past research, there were at most three protection routings developed in other network structures. Finally, we summarize some crucial analysis viewpoints about the transmission efficiency of DCNs with heterogeneous edge-core servers from the simulation results.

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Constructing spanning trees in augmented cubes

Cited by 31 publications

References 30 publications

Constructing Two Completely Independent Spanning Trees in Balanced Hypercubes

Constructing Two Completely Independent Spanning Trees in Balanced Hypercubes

Pendant 3-tree Connectivity of Augmented Cubes

Transmission Failure Analysis of Multi-Protection Routing in Data Center Networks with Heterogeneous Edge-Core Servers

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