A parallel routing algorithm on recursive cube of rings networks employing Hamiltonian circuit Latin square

Choi, Dongmin; Lee, Okbin; Chung, Ilyong

doi:10.1016/j.ins.2007.10.028

Cited by 5 publications

(3 citation statements)

References 13 publications

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“…Nevertheless, under a natural condition this graph is indeed a Cayley graph as we will see later. In [4] the vertexdisjoint paths problem for recursive cubes of rings was solved by using Hamiltonian circuit Latin squares, and in [27] the recursive construction of them was given. The diameter problem for recursive cubes of rings has attracted considerable attention: An upper bound was given in [27,Property 5] but shown to be incorrect in [31, Example 6]; and another upper bound was given in [31,Theorem 13] but it was unknown whether it gives the exact value of the diameter.…”

Section: Introductionmentioning

confidence: 99%

Recursive cubes of rings as models for interconnection networks

Mokhtar

Zhou

2017

Discrete Applied Mathematics

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We study recursive cubes of rings as models for interconnection networks. We first redefine each of them as a Cayley graph on the semidirect product of an elementary abelian group by a cyclic group in order to facilitate the study of them by using algebraic tools. We give an algorithm for computing shortest paths and the distance between any two vertices in recursive cubes of rings, and obtain the exact value of their diameters. We obtain sharp bounds on the Wiener index, vertex-forwarding index, edge-forwarding index and bisection width of recursive cubes of rings. The cube-connected cycles and cube-of-rings are special recursive cubes of rings, and hence all results obtained in the paper apply to these well-known networks.

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Section: Introductionmentioning

confidence: 99%

Recursive cubes of rings as models for interconnection networks

Mokhtar

Zhou

2017

Discrete Applied Mathematics

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“…Graph decomposition regarding complete graph has attracted the researchers [1][2][3][4]. Among these, complete graph decomposition into Hamiltonian circuit (HC) is attention-grabbing due to its vast advantages such as analyzing interconnection network in multicomputer [5], privacy data mining [6], butterfly network [7], and DNA physical mapping [8].…”

Section: Introductionmentioning

confidence: 99%

Some new theoretical work on Half Butterfly Method for Hamiltonian circuit in complete graph

2017

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“…Routing algorithms were subsequently proposed for RCR interconnection networks (e.g. [16]. It was shown in [14], [15] that RCR networks can possess such desirable properties as scalability, symmetry, uniform node degrees, low diameter, and high bisection width.…”

Section: Introductionmentioning

confidence: 99%

Recursive-Cube-of-Rings (RCR) Revisited: Properties and Enhancement

Xie,

Li,

Wang

et al. 2013

Preprint

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We study recursive-cube-of-rings (RCR), a class of scalable graphs that can potentially provide rich inter-connection network topology for the emerging distributed and parallel computing infrastructure. Through rigorous proof and validating examples, we have corrected previous misunderstandings on the topological properties of these graphs, including node degree, symmetry, diameter and bisection width. To fully harness the potential of structural regularity through RCR construction, new edge connecting rules are proposed. The modified graphs, referred to as Class-II RCR, are shown to possess uniform node degrees, better connectivity and better network symmetry, and hence will find better application in parallel computing.

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A parallel routing algorithm on recursive cube of rings networks employing Hamiltonian circuit Latin square

Cited by 5 publications

References 13 publications

Recursive cubes of rings as models for interconnection networks

Recursive cubes of rings as models for interconnection networks

Some new theoretical work on Half Butterfly Method for Hamiltonian circuit in complete graph

Recursive-Cube-of-Rings (RCR) Revisited: Properties and Enhancement

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