Cayley graphs and interconnection networks

Heydemann, Marie-Claude

doi:10.1007/978-94-015-8937-6_5

Cited by 180 publications

(199 citation statements)

References 83 publications

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“…While the modelling of a network by such graphs does not take into account implementation factors of the network, it does provide an effective means of abstraction to study many relevant network properties [6,9,12,19,20].…”

Section: Introductionmentioning

confidence: 99%

Non-existence of bipartite graphs of diameter at least 4 and defect 2

Pineda-Villavicencio

2010

J Algebr Comb

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Section: Introductionmentioning

confidence: 99%

Non-existence of bipartite graphs of diameter at least 4 and defect 2

Pineda-Villavicencio

2010

J Algebr Comb

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“…Node-symmetry means, amongst other things, that each individual processor can be supplied with the same program, routing is vastly simplified (as is the implementation of communication patterns such as many-to-many), and network analysis is easier [15,35]. Implicit is the assumption that every processor is working on the same computational task.…”

Section: Symmetry In Distributed-memory Multiprocessorsmentioning

confidence: 99%

“…Implicit is the assumption that every processor is working on the same computational task. Furthermore, algebraic characterizations of networks as Cayley graphs, so that node-symmetry immediately follows, can yield an even more beneficial environment (see, for example, [2,35,43,67]). On the other hand, link-symmetry can yield well balanced traffic loads [15].…”

Section: Symmetry In Distributed-memory Multiprocessorsmentioning

confidence: 99%

The influence of datacenter usage on symmetry in datacenter network design

Stewart

Erickson

2017

J Supercomput

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We undertake the first formal analysis of the role of symmetry, interpreted broadly, in the design of server-centric datacenter networks. Although symmetry has been mentioned by other researchers, we explicitly relate it to various specific, structural, graph-theoretic properties of datacenter networks. Our analysis of symmetry is motivated by the need to ascertain the usefulness of a datacenter network as regards the support of network virtualization and prevalent communication patterns in multitenanted clouds. We argue that a number of structural concepts relating to symmetry from general interconnection networks, such as recursive-definability, the existence and dynamic construction of spanning trees, pancyclicity, and variations in Hamiltonicity, are appropriate topological metrics to use in this regard. In relation to symmetry, we highlight the relevance of algebraic properties and algebraic constructions within datacenter network design. Built upon our analysis of symmetry, we outline the first technique to embed guest datacenter networks in a host datacenter network that is specifically oriented towards server-centric datacenter networks. In short, we provide the graph-theoretic foundations for the design of server-centric datacenter networks so as to support network virtualization and communication patterns in cloud computing.

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“…The exact values of the forwarding index of many important classes of graphs have been computed [2,4,5,6,8]. For more complete results on forwarding indices, we can refer to the survey of Xu et Al.…”

Section: Introductionmentioning

confidence: 99%