Bus interconnection networks

Bermond, Jean‐Claude; Ergincan, Fahir Ö.

doi:10.1016/0166-218x(95)00046-t

Cited by 25 publications

(15 citation statements)

References 38 publications

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“…As a result, faulttolerant routing has become one of the central issues in the study of the networks [3,4,15,16]. For a specific routing problem, we say a graph can tolerate I faulty nodes if after deleting at most l arbitrary nodes from the graph the required routing paths exist for the routing problem.…”

Section: Introductionmentioning

confidence: 99%

Cluster fault-tolerant routing in star graphs

Peng

2000

Networks

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Fault‐tolerant routing is a key issue in computer/communication networks. We say a network (graph) can tolerate / faulty nodes for a routing problem if after removing at most / arbitrary faulty nodes from the graph the routing paths exist for the routing problem. However, the bound / is usually a worst‐case measure and it is of great interest to find the routing paths when more than / faulty nodes exist. Cluster fault‐tolerant (CFT) routing was proposed as an approach for this purpose. In the CFT routing, we reduce the number of “faults” that a routing problem has to deal with using subgraphs to cover the faulty nodes. In particular, we consider the number and the size (diameter) of faulty subgraphs rather than the number of faulty nodes that a graph can tolerate. In this paper, we show that a subgraph of diameter 2 can be viewed as a single “fault” for the following routing problems in the star graph: Given a source node s and t target nodes t1, …, tk, find k node‐disjoint paths from s to ti (1 ≤ i ≤ k), and given k node pairs (s1, t1), …, (sk, tk), find k node‐disjoint paths si → ti (1 ≤ i ≤ k). Since a subgraph of diameter 2 of the n‐dimensional star graph Gn may have n nodes, the above result implies that the number of faulty nodes that Gn can tolerate is n times larger than the worst‐case measure if the faulty nodes can be covered by certain subgraphs. We also give algorithms which find the paths for the two routing problems. © 2000 John Wiley & Sons, Inc.

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Section: Introductionmentioning

confidence: 99%

Cluster fault-tolerant routing in star graphs

Peng

2000

Networks

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“…The vertices are the integer modulo n and the hyperarcs are the integer modulo m. Vertex i is incident to the hyperarcs E j with j ≡ di + α (mod m), Figure 1 shows GB 2 (2,6,3,4) and Figure 2 shows GB 2 (2,36,3,24). Note that condition (1) is needed in order to insure that i and i + n have the same out-neighborhood.…”

Section: Generalized De Bruijn and Kautz Dihypergraphsmentioning

confidence: 99%

“…This is useful to prove results using induction. We generalized this definition and used it in an unpublished manuscript (first version in 1993) which was announced in [6]). Unfortunately, this manuscript was never completely finished and never published.…”

Section: Introductionmentioning

confidence: 99%

“…They have been proposed as the underlying physical topologies for optical networks, as well as dense logical topologies for Logically Routed Networks (LRN) because of ease of routing, load balancing, and congestion reduction properties inherent in de Bruijn and Kautz networks. More recently, Jean-Jacques brought to our attention the web site (http://punetech.com/building-eka-the-worlds-fastestprivately-funded-supercomputer/) where it is explained how hypergraphs and the results of [6] were used for the design of the supercomputer EKA (http: //en.wikipedia.org/wiki/EKA (supercomputer)).…”

Section: Introductionmentioning

confidence: 99%

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Line Directed Hypergraphs

Bermond

Ergincan

Syska

2012

Cryptography and Security: From Theory to Applications

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Abstract. In this article we generalize the concept of line digraphs to line dihypergraphs. We give some general properties in particular concerning connectivity parameters of dihypergraphs and their line dihypergraphs, like the fact that the arc connectivity of a line dihypergraph is greater than or equal to that of the original dihypergraph. Then we show that the De Bruijn and Kautz dihypergraphs (which are among the best known bus networks) are iterated line digraphs. Finally we give short proofs that they are highly connected.

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“…In 2009, J-J. Quisquater brought to our attention the web site (http://punetech.com/building-eka-theworlds-fastest-privately-funded-supercomputer/ ) where it is explained how these hypergraphs and the results of [18] were used for the design of the supercomputer EKA in 2007 (http://en.wikipedia.or wiki/EKA (supercomputer)).…”

Section: Introductionmentioning

confidence: 99%

Eulerian and Hamiltonian Dicycles in Directed Hypergraphs

Araújo

Bermond

Ducoffe

2014

Discrete Math. Algorithm. Appl.

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In this article, we generalize the concepts of Eulerian and Hamiltonian digraphs to directed hypergraphs. A dihypergraph H is a pair (V(H), E(H)), where V(H) is a non-empty set of elements, called vertices, and E(H) is a collection of ordered pairs of subsets of V(H), called hyperarcs. It is Eulerian (resp. Hamiltonian) if there is a dicycle containing each hyperarc (resp. each vertex) exactly once. We first present some properties of Eulerian and Hamiltonian dihypergraphs. For example, we show that deciding whether a dihypergraph is Eulerian is an NP-complete problem. We also study when iterated line dihypergraphs are Eulerian and Hamiltonian. Finally, we study when the generalized de Bruijn dihypergraphs are Eulerian and Hamiltonian. In particular, we determine when they contain a complete Berge dicycle, i.e. an Eulerian and Hamiltonian dicycle.

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Bus interconnection networks

Cited by 25 publications

References 38 publications

Cluster fault-tolerant routing in star graphs

Cluster fault-tolerant routing in star graphs

Line Directed Hypergraphs

Eulerian and Hamiltonian Dicycles in Directed Hypergraphs

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