Dense group networks

Campbell, L. Andrew

doi:10.1016/0166-218x(92)90125-t

Cited by 14 publications

(9 citation statements)

References 4 publications

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“…The problem on hypernetworks we are considering is known as the ðD; D; rÞ-hypergraph problem which consists of finding ðD; D; rÞ-hypergraphs with the maximum number of nodes or finding large ðD; D; rÞ-hypergraphs. In the case r ¼ 2 (conventional graph case), the ðD; D; rÞ-hypergraph problem is known as the ðD; DÞ-graph problem, which has been extensively studied, and many large ðD; DÞ-graphs constructed so far correspond to Cayley graphs (e.g., [3], [4]). …”

Section: Preliminariesmentioning

confidence: 99%

Switch-Centric Data Center Network Structures Based on Hypergraphs and Combinatorial Block Designs

Fang

Zhang

et al. 2015

IEEE Trans. Parallel Distrib. Syst.

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Fat trees are considered suitable structures for data center interconnection networking. Such structures are rigid, and hard to scale up and scale out. A good data center network structure should have high scalability, efficient switch utilization, and high reliability. In this paper we present a class of data center network structures based on hypergraph theory and combinatorial block design theory. We show that our data center network structures are more flexible and scalable than fat trees. Using switches of the same size, our data center network structures can connect more nodes than fat trees, and it is possible to construct different structures with tradeoffs among inter-cluster communication capacity, reliability, the number of switches used, and the number of connected nodes.

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Section: Preliminariesmentioning

confidence: 99%

Switch-Centric Data Center Network Structures Based on Hypergraphs and Combinatorial Block Designs

Fang

Zhang

et al. 2015

IEEE Trans. Parallel Distrib. Syst.

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“…Notice that, because M = 3, it is impossible for each vertex of K 4 to have an edge-intercopy of B 6,6 . These vertices, according to …”

Section: Another Large H Q (K H ) Graphmentioning

confidence: 98%

“…Figure 5 shows the graph that we call B 6,6 . This graph is used to join the copies of K 4 to obtain the H 4 (K 4 ) graph.…”

Section: Another Large H Q (K H ) Graphmentioning

confidence: 98%

“…The graph H 4 (K 4 ) is constructed by replacing the vertices x ij0 , i = 0, 1, j = 0, 1, 2 with the vertices of one stable set of B 6,6 , and the vertices x ij0 , i = 2, 3, j = 0, 1, 2 with the vertices of the other stable set of B 6,6 ; see Figure 6. Observe that the vertex x is depicted in two places, so that the graph can be more easily drawn.…”

Section: Another Large H Q (K H ) Graphmentioning

confidence: 99%

“…Many ( , D)-graphs correspond to Cayley graphs (see, i.e., [6,7,[14][15][16]25]), and have been found with computer help. However, the use of these computers is only efficient when the degree and the diameter are in general not too large.…”

Section: Introductionmentioning

confidence: 99%

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On large (Δ, 6)-Graphs

Martí¹

2005

Networks

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In this article, a new method is proposed for obtaining large-diameter 6 graphs by replacing some vertices of a Moore bipartite diameter 6 graph by complete K h graphs. These complete graphs are joined to the remaining nonmodified graph and to each other by means of new edges. More precisely, these new edges are those of a bipartite diameter 3 graph, together with some appropriate extra edges. The degree and the diameter of the graph so constructed coincide with those of the original one. The construction put forward here gives rise to some of the largest known diameter 6 graphs.

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