Congestion-free embedding of 2(n−k) spanning trees in an arrangement graph

Chen, Yuh‐Shyan; Juang, Tong‐Ying; Shen, Ying-Ying

doi:10.1016/s1383-7621(00)00041-2

Cited by 16 publications

(10 citation statements)

References 12 publications

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“…Clearly, if x ⩽ 7, then x 3 = 0. In this case, we have j = 3 and parent(T 3 , x) = x+2 3 = x+8 for x ∈ {1, 2, 4}; j = 2 and parent(T 3 , x) = x + 2 2 = 7 for x = 3; j = 1 and parent(T 3 , x) = x + 2 1 = 7 for x = 5; j = 0 and parent(T 3 , x) = x + 2 0 = 7 for x = 6; and j = * and parent(…”

Section: Constructing Spanning Trees In Folded Hypercubesmentioning

confidence: 99%

Broadcasting secure messages via optimal independent spanning trees in folded hypercubes

Yang

Chan

Chang

2011

Discrete Applied Mathematics

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a b s t r a c tFault-tolerant broadcasting and secure message distribution are important issues for network applications. It is a common idea to design multiple spanning trees with a specific property in the underlying graph of a network to serve as a broadcasting scheme or a distribution protocol for receiving high levels of fault-tolerance and security. An ndimensional folded hypercube, denoted by FQ n , is a strengthening variation of hypercube by adding additional links between nodes that have the furthest Hamming distance. In, [12], Ho(1990) proposed an algorithm for constructing n + 1 edge-disjoint spanning trees each with a height twice the diameter of FQ n . Yang et al. (2009), [29] recently proved that Ho's spanning trees are indeed independent, i.e., any two spanning trees have the same root, say r, and for any other node v ̸ = r, the two different paths from v to r, one path in each tree, are internally node-disjoint. In this paper, we provide another construction scheme to produce n + 1 independent spanning trees of FQ n , where the height of each tree is equal to the diameter of FQ n plus one. As a result, the heights of independent spanning trees constructed in this paper are shown to be optimal.

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Section: Constructing Spanning Trees In Folded Hypercubesmentioning

confidence: 99%

Broadcasting secure messages via optimal independent spanning trees in folded hypercubes

Yang

Chan

Chang

2011

Discrete Applied Mathematics

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“…By so doing, even when a node cannot receive the description due to the departure of a node in its upper position, the descendant node can still receive the descriptions from other trees. In THAG, participating nodes are grouped into a number of Arrangement Graphs (AGs) [13], [14]. In each AG, several node-disjoint multicast trees are embedded.…”

Section: B Multiple-tree Multicastmentioning

confidence: 99%

“…An AG is an undirected graph and has desired properties, such as symmetric vertex, symmetric edge, strong resilience, and maximal fault-tolerance [14]. An AG is denoted by , and specified by integers and .…”

Section: A Node-disjoint Trees In Hierarchical Arrangement Graphmentioning

confidence: 99%

“…In [7], the approach which uses a Topology-aware Hierarchical Arrangement Graph (THAG) has been proposed for the construction of multiple multicast trees. In THAG, all participating nodes are divided into a number of Arrangement Graphs (AGs) [13], [14], and several node-disjoint multicast trees are embedded in each AG. An AG is an undirected graph which possesses desired properties for overlay topology.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Robust and Efficient Stream Delivery for Application Layer Multicasting in Heterogeneous Networks

Kobayashi

Nakayama

Ansari

et al. 2009

IEEE Trans. Multimedia

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Abstract-Application Layer Multicast (ALM) is highly expected to replace IP multicasting as the new technological choice for content delivery. Depending on the streaming application, ALM nodes will construct a multicast tree and deliver the stream through this tree. However, if a node resides in the tree leaves, it cannot deliver the stream to its descendant nodes. In this case, Quality of Service (QoS) will be compromised dramatically. To overcome this problem, Topology-aware Hierarchical Arrangement Graph (THAG) was proposed. By employing Multiple Description Coding (MDC), THAG first splits the stream into a number of descriptions, and then uses Arrangement Graph (AG) to construct node-disjoint multicast trees for each description. However, using a constant AG size in THAG creates difficulty in delivering descriptions appropriately across a heterogeneous network. In this paper, we propose a method, referred to as Network-aware Hierarchical Arrangement Graph (NHAG), to change the AG size dynamically to enhance THAG performance, even in heterogeneous networks. Finally, we evaluate the proposed scheme by experiments using the network simulator ns-2. By comparing our proposed method to THAG and SplitStream, we show that our method provides better performance in terms of throughput and QoS. The results indicate that our approach is more reliable than other methods in heterogeneous networks.

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“…Two spanning trees in a graph are said to be edge-disjoint if they are rooted at the same node without sharing any common edge. All the while, the construction of a set of pairwise edge-disjoint spanning trees in a particular family of networks has received a great deal of attention [2,8,9,12,16,20].…”

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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Congestion-free embedding of 2(n−k) spanning trees in an arrangement graph

Cited by 16 publications

References 12 publications

Broadcasting secure messages via optimal independent spanning trees in folded hypercubes

Broadcasting secure messages via optimal independent spanning trees in folded hypercubes

Robust and Efficient Stream Delivery for Application Layer Multicasting in Heterogeneous Networks

Independent spanning trees on folded hyper‐stars

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