Independent spanning trees vs. edge-disjoint spanning trees in locally twisted cubes

Lin, Jia-Cian; Yang, Jinn‐Shyong; Hsu, Cheng–Che; Chang, Jou–Ming

doi:10.1016/j.ipl.2010.03.012

Cited by 38 publications

(11 citation statements)

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“…The conjecture has been proved true for kconnected graphs with k 4 [3,4,11,23] and some classes of graphs or digraphs (in particular, interconnection networks) such as planar graphs [10], product graphs [15], chordal rings [12,19], star graphs [16], de Bruijn and Kautz 0020-0190/$ -see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.ipl.2010.11.018 digraphs [6], recursive circulant graphs [20,21], hypercubes [22], locally twisted cubes [14] and torus [17], etc.…”

Section: J01354)mentioning

confidence: 99%

Parallel construction of optimal independent spanning trees on Cartesian product of complete graphs

Chen

2011

Information Processing Letters

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Section: J01354)mentioning

confidence: 99%

Parallel construction of optimal independent spanning trees on Cartesian product of complete graphs

Chen

2011

Information Processing Letters

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“…The embedding capabilities are important in evaluating an interconnection wireless networks. The many-to-one embedding of the guest graph G into a host graph H is a mapping from many vertices of G into one vertex of H and mapping each edge of G into one path of H. Graph embedding is useful because an algorithm designed for H can be applied to G directly (Abraham et al, 1991;Cheng-Kuan et al, 2008;Lin et al, 2010;Xu et al, 2010). In comparison with a Multiply-Twisted Hypercube, the Pancake configuration offers good and simple simulations of other interconnection wireless networks (Miller et al, 1994;Senoussi et al, 1997).…”

Section: Figure 1 Crossbow's Telosb Motementioning

confidence: 99%

New Approach Construction for Wireless ZigBee Sensor Based on Embedding Pancake Graphs

Femmam¹,

Faouzi²,

Benakila³

2012

NCT

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Wireless Sensor Networks (WSN) based on the IEEE 802.15.4 standard are constantly expanding. Applications like production control, building control are more and more based on WSN because of their energy efficiency, self organizing capacity and protocol flexibility. However, the construction of Cluster-Tree networks based on the beacon mode Pancake graphs is still undefined by the IEEE 802.15.4 standard. In order to enable the construction of such topology, i.e., Beacon Cluster-Tree based on Pancake graphs, we present, in this paper, a new topology construction approach.The Pancake is one of the Cayley graphs that were proposed as alternative to the Hypercube for interconnecting processors in parallel computers. This network offers attractive and desirable properties: Vertex symmetry, small degree and diameter, extensibility, high connectivity, easy routing, regularity of topology, fault-tolerance, and embed ability of other topologies. We present in this work the many-to-one embedding of Multiply-Twisted Hypercube into the Pancake networks with dilation 5 as a new approach for wireless networks. The presented approach is based on the exploitation of RF front-end capabilities in treating multipath signals and, thus, avoiding the introduction of beacon or Super Frames scheduling algorithms. Avoiding the introduction of scheduling algorithms ensures a simple solution that could be easily implemented and executed by ZigBee sensor nodes.

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“…A message can be divided into t packets where each packet is sent by node r to its destination using a different spanning tree. Thus, each node in the network receives at most one of the t packets except the destination node that receives all the t packets [20][24] [25]. In [1], AlBdaiwi et.…”

Section: Introductionmentioning

confidence: 99%

Node-independent spanning trees in Gaussian networks

Hussain

AlBdaiwi

Černý

2017

Journal of Parallel and Distributed Computing

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Message broadcasting in networks could be carried over spanning trees. A set of spanning trees in the same network is node independent if two conditions are satisfied. First, all trees are rooted at node r. Second, for every node u in the network, all trees' paths from r to u are node-disjoint, excluding the end nodes r and u. Independent spanning trees have applications in fault-tolerant communications and secure message distributions.Gaussian networks and two-dimensional toroidal networks share similar topological characteristics. They are regular of degree four, symmetric, and node-transitive. Gaussian networks, however, have relatively lesser network diameter that could result in a better performance. This promotes Gaussian networks to be a potential alternative for twodimensional toroidal networks.In this paper, we present constructions for node independent spanning trees in dense Gaussian networks. Based on these constructions, we design routing algorithms that can be used in fault-tolerant routing and secure message distribution. We also design fault-tolerant algorithms to construct these trees in parallel.

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Independent spanning trees vs. edge-disjoint spanning trees in locally twisted cubes

Cited by 38 publications

References 31 publications

Parallel construction of optimal independent spanning trees on Cartesian product of complete graphs

Parallel construction of optimal independent spanning trees on Cartesian product of complete graphs

New Approach Construction for Wireless ZigBee Sensor Based on Embedding Pancake Graphs

Node-independent spanning trees in Gaussian networks

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