Optimal fault-tolerant communication algorithms on product networks using spanning trees

Öhring, Sabine R.; Hohndel, Dirk H.

doi:10.1109/spdp.1994.346167

Cited by 18 publications

(5 citation statements)

References 12 publications

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“…Furthermore we have recently investigated incomplete folded Petersen networks having an arbitrary number of nodes [39]. Another direction of our research is to generalize the results derived for hyper P.etersen or folded Petersen networks for a class of product networks in general [40].…”

Section: Discussionmentioning

confidence: 99%

Embeddings into Hyper Petersen Networks: YetAnother Hypercube‐Like Interconnection Topology

1995

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A new hypercube-like topology, called the hyper Petersen (HP) network, is proposed and analyzed, which is constructed from the well-known cartesian product of the binary hypercube and the Petersen graph of ten nodes.This topology is an attractive candidate for multiprocessor interconnection having such desirable properties as regularity, high symmetry and connectivity, and logarithmic diameter. For example, an n-dimensional hyper Petersen network, HPn, with N=1.25 * 2n nodes is a regular graph of degree and node-connectivity n and diameter n–1 , whereas an (n–1)-dimensional binary hypercube, Qn−1 , with the same diameter covers only 2n−1 nodes, each of degree (n–1). Thus the HP topology accommodates 2.5 times extra nodes than Qn−1 at the cost of increasing the node-degree by one. With the same degree and connectivity of n, the diameter of the HPn network is one less than that of Qn, yet having 1.25 times larger number of nodes.Efficient routing and broadcasting schemes are presented, and node-disjoint paths in HPn, are computed even under faulty conditions. The versatility of the hyper Petersen networks is emphasized by embedding rings, meshes, hypercubes and several tree-related topologies into it. Contrary to the hypercubes, rings of odd lengths, and a complete binary tree of height n–1 permit subgraph embeddings in HPn.

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Section: Discussionmentioning

confidence: 99%

Embeddings into Hyper Petersen Networks: YetAnother Hypercube‐Like Interconnection Topology

1995

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“…By using the Cartesian product to combine two known topologies with established properties, we can construct a new topology with the properties of both worlds, which is of practical interest for network design. A number of studies that investigated various topological properties of product networks, such as the connectivity, diameter, shortest path routing, and embedding [7], [8], [20], [22], [17]. In this paper, we investigate the super fault-tolerant Hamiltonicity of product networks.…”

Section: Introductionmentioning

confidence: 99%

Super Fault-Tolerant Hamiltonicity of Product Networks

Hsieh

Lin

2010

International Symposium on Parallel and Distributed Processing With Applications

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A graph G is called k-fault Hamiltonian (resp. Hamiltonian-connected) if after deleting at most k vertices and/or edges from G, the resulting graph remains Hamiltonian (resp. Hamiltonian-connected). Let δ(G) be the minimum degree of G. Given a (δ(G) − 2)-fault Hamiltonian/ (δ(G) − 3)-fault Hamiltonian-connected graph G and a (δ(H) − 2)-fault Hamiltonian/(δ(H) − 3)-fault Hamiltonian-connected graph H, we show that the Cartesian product network G × H is ( δ(G) + δ(H) − 2)-fault Hamiltonian and (δ(G) + δ(H) − 3)-faultHamiltonian-connected. We then apply our result to determine the fault-tolerant hamiltonicity and Hamiltonian-connectivity of two multiprocessor systems, namely the generalized hypercube and the nearest neighbor mesh hypercube, both of which belong to Cartesian product networks. We also demonstrate that our results are worst-case optimal with respect to the number of faults tolerated.

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“…However, his algorithm can tolerate only one failure node in binary de Bruijn networks and it cannot achieve shortest path if there is failure node on the path. Broadcasting problems on dBG have been investigated as local broadcasting [6] and arc-disjoint spanning trees [7] [8]. Nonetheless, the above can only work in a binary de Bruijn network (dBG (2,k)).…”

Section: Introductionmentioning

confidence: 99%

Efficient Routing and Broadcasting Algorithms in de Bruijn Networks

Nguyen

Lee

2004

Parallel and Distributed Processing and Applications

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Recently, routing on dBG has been investigated as shortest path and fault tolerant routing but investigation into shortest path in failure mode on dBG has been non-existent. Furthermore, dBG based broadcasting has been studied as local broadcasting and arc-disjoint spanning trees based broadcasting. However, their broadcasting algorithms can only work in dBG(2,k). In this paper, we investigate shortest path routing algorithms in the condition of existing failure, based on the Bidirectional de Bruijn graph (BdBG). And we also investigate broadcasting in BdBG for a degree greater than or equal to two 1 .

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Optimal fault-tolerant communication algorithms on product networks using spanning trees

Cited by 18 publications

References 12 publications

Embeddings into Hyper Petersen Networks: YetAnother Hypercube‐Like Interconnection Topology

Embeddings into Hyper Petersen Networks: YetAnother Hypercube‐Like Interconnection Topology

Super Fault-Tolerant Hamiltonicity of Product Networks

Efficient Routing and Broadcasting Algorithms in de Bruijn Networks

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