THE CONDITIONAL NODE CONNECTIVITY OF THE k-ARY n-CUBE

Day, Khaled

doi:10.1142/s0219265904001003

Cited by 59 publications

(22 citation statements)

References 7 publications

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“…With the assumption that each node was incident with at least one fault-free node, the connectivities of hypercubes [9], k-ary n-cubes [6], cube-connected cycles [20], undirected de Bruijn networks [20], and Kautz networks [20] were computed. Moreover, the fault diameters of hypercubes [18] and star graphs [21] were obtained.…”

Section: Discussionmentioning

confidence: 99%

Embedding fault-free cycles in crossed cubes with conditional link faults

Hung

Chen

2008

J Supercomput

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The crossed cube, which is a variation of the hypercube, possesses some properties that are superior to those of the hypercube. In this paper, we show that with the assumption of each node incident with at least two fault-free links, an ndimensional crossed cube with up to 2n − 5 link faults can embed, with dilation one, fault-free cycles of lengths ranging from 4 to 2 n . The assumption is meaningful, for its occurrence probability is very close to 1, and the result is optimal with respect to the number of link faults tolerated. Consequently, it is very probable that algorithms executable on rings of lengths ranging from 4 to 2 n can be applied to an n-dimensional crossed cube with up to 2n − 5 link faults.

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Section: Discussionmentioning

confidence: 99%

Embedding fault-free cycles in crossed cubes with conditional link faults

Hung

Chen

2008

J Supercomput

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“…The idea states that each node has at least one non-faulty neighbor. Under this forbidden faulty set condition, the number of tolerable faulty nodes is significantly larger with a slight increase in the fault diameter [24]. The forbidden faulty set analysis of restricted connectivity and fault tolerance assumes that a set of nodes cannot be faulty at the same time.…”

Section: Conditional Connectivity and Forbidden Faulty Setmentioning

confidence: 99%

Coverage and Connectivity in 3D Wireless Sensor Networks

Mansoor

Ammari

2013

The Art of Wireless Sensor Networks

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A wireless sensor network (WSN) is categorized as three-dimensional (3D) when variation in the height of deployed sensor nodes is not negligible as compared to length and breadth of deployment field. The fundamental problem in such 3D networks is to find an optimal way to deploy sensor nodes needed to maintain full (or targeted degree of) coverage of monitored volume and reliable connectivity as desired by network designers. The solution should yield lower bound on number of nodes needed to achieve full coverage and connectivity. However, optimizing coverage and connectivity in 3D WSNs comes with its inherent complexities and intrinsic design challenges. 3D WSNs are not only difficult to visualize but their analysis is also computationally intensive. This literature summarizes major work conducted in the domain of coverage and connectivity in 3D WSNs. It studies different placement strategies, fundamental characteristics, modeling schemes, analytical methods, limiting factors, and practical constraints dealing with coverage and connectivity in 3D WSNs.

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“…The design of the interconnection network topology significantly determines the performance of the system. A lot of interconnection networks have been proposed in the past decades, for example, hypercube [1] crossed cube [2], twisted cube [3], [4], torus [5], k-ary n-cube [6], [7], [8] and star graph [9]. The k-ary n-cube, denoted by Q k n , is one of the most common interconnection networks due to its desirable properties [10], [11], [12], such as its ability to reduce message latency and ease of implementation.…”

Section: Introductionmentioning

confidence: 99%

Hamiltonian Cycle and Path Embeddings in 3-Ary n-Cubes Based on K1,2-Structure Faults

Lin

Fan

2016

2016 IEEE Trustcom/BigDataSE/Ispa

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The k-ary n-cube is one of the most attractive interconnection networks for parallel and distributed computing system. In this paper, we investigate hamiltonian cycle and path embeddings in 3-ary n-cubes Q 3 n based on K1,2-structure faults, which means each faulty element is isomorphic to a connected graph K1,2 or a connected subgraph of the connected graph. We show that for two arbitrary distinct healthy nodes of a faulty Q 3 n , there exists a fault-free hamiltonian path connecting these two nodes if the number of faulty element is at most n − 2 and each faulty element is isomorphic to K1,2 or a connected subgraph of K1,2. We also show that there exists a fault-free hamiltonian cycle if the number of faulty element is at most n − 1 and each faulty element is isomorphic to K1,2 or a connected subgraph of K1,2. These results mean that the 3-ary n-cube Q 3 n can tolerate up to 3(n − 2) faulty nodes such that Q 3 n − V (F ) is still hamiltonian and hamiltonian-connected, where F denotes the faulty set of Q 3 n .

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THE CONDITIONAL NODE CONNECTIVITY OF THE k-ARY n-CUBE

Cited by 59 publications

References 7 publications

Embedding fault-free cycles in crossed cubes with conditional link faults

Embedding fault-free cycles in crossed cubes with conditional link faults

Coverage and Connectivity in 3D Wireless Sensor Networks

Hamiltonian Cycle and Path Embeddings in 3-Ary n-Cubes Based on K1,2-Structure Faults

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