### Abstract

The notion of a logically routed network was developed to overcome the bottlenecks encountered during the design of a large purely optical network. In the last few years, researchers have proposed the use of torus, Perfect Shuffle, Hypercube, de Bruijn graph, Kautz graph, and Cayley graph as an overlay structure on top of a purely optical network. All these networks have regular structures. Although regular structures have many virtues, it is often difficult in a realistic setting to meet these stringent structural requirements. In this paper, we propose generalized multimesh (GM), a semiregular structure, as an alternate to the proposed architectures. In terms of simplicity of interconnection and routing, this architecture is comparable to the torus network. However, the new architecture exhibits significantly superior topological properties to the torus. For example, whereas a two-dimensional (2-D) torus with N nodes has a diameter of Θ (N^{0.5}), a generalized multimesh network with the same number of nodes and links bas a diameter of Θ (N^{0.25}). In this paper, we also introduce a new metric, flow number, that can be used to evaluate topologies for optical networks. For optical networks, a topology with a smaller flow number is preferable, as it is an indicator of the number of wavelengths necessary for full connectivity. We show that the flow numbers of a 2-D torus, a multimesh, and a de Bruijn network, are Θ (N^{1.5}), Θ (N^{1.25}), and Θ (N log N), respectively, where N is the number of nodes in the network. The advantage of the generalized multimesh over the de Bruijn network lies in the fact that, unlike the de Bruijn network, this network can be constructed for any number of nodes and is incrementally expandable.

Original language | English (US) |
---|---|

Pages (from-to) | 913-925 |

Number of pages | 13 |

Journal | Journal of Lightwave Technology |

Volume | 19 |

Issue number | 7 |

DOIs | |

State | Published - Jul 2001 |

### Fingerprint

### Keywords

- De Bruijn graph
- Flow number
- Multihop networks
- Multimesh (MM)
- Optical networks
- Torus

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Atomic and Molecular Physics, and Optics

### Cite this

*Journal of Lightwave Technology*,

*19*(7), 913-925. https://doi.org/10.1109/50.933285

**A new architecture and a new metric for lightwave networks.** / Sen, Arunabha; Bandyopadhyay, Subir; Sinha, Bhabani P.

Research output: Contribution to journal › Article

*Journal of Lightwave Technology*, vol. 19, no. 7, pp. 913-925. https://doi.org/10.1109/50.933285

}

TY - JOUR

T1 - A new architecture and a new metric for lightwave networks

AU - Sen, Arunabha

AU - Bandyopadhyay, Subir

AU - Sinha, Bhabani P.

PY - 2001/7

Y1 - 2001/7

N2 - The notion of a logically routed network was developed to overcome the bottlenecks encountered during the design of a large purely optical network. In the last few years, researchers have proposed the use of torus, Perfect Shuffle, Hypercube, de Bruijn graph, Kautz graph, and Cayley graph as an overlay structure on top of a purely optical network. All these networks have regular structures. Although regular structures have many virtues, it is often difficult in a realistic setting to meet these stringent structural requirements. In this paper, we propose generalized multimesh (GM), a semiregular structure, as an alternate to the proposed architectures. In terms of simplicity of interconnection and routing, this architecture is comparable to the torus network. However, the new architecture exhibits significantly superior topological properties to the torus. For example, whereas a two-dimensional (2-D) torus with N nodes has a diameter of Θ (N0.5), a generalized multimesh network with the same number of nodes and links bas a diameter of Θ (N0.25). In this paper, we also introduce a new metric, flow number, that can be used to evaluate topologies for optical networks. For optical networks, a topology with a smaller flow number is preferable, as it is an indicator of the number of wavelengths necessary for full connectivity. We show that the flow numbers of a 2-D torus, a multimesh, and a de Bruijn network, are Θ (N1.5), Θ (N1.25), and Θ (N log N), respectively, where N is the number of nodes in the network. The advantage of the generalized multimesh over the de Bruijn network lies in the fact that, unlike the de Bruijn network, this network can be constructed for any number of nodes and is incrementally expandable.

AB - The notion of a logically routed network was developed to overcome the bottlenecks encountered during the design of a large purely optical network. In the last few years, researchers have proposed the use of torus, Perfect Shuffle, Hypercube, de Bruijn graph, Kautz graph, and Cayley graph as an overlay structure on top of a purely optical network. All these networks have regular structures. Although regular structures have many virtues, it is often difficult in a realistic setting to meet these stringent structural requirements. In this paper, we propose generalized multimesh (GM), a semiregular structure, as an alternate to the proposed architectures. In terms of simplicity of interconnection and routing, this architecture is comparable to the torus network. However, the new architecture exhibits significantly superior topological properties to the torus. For example, whereas a two-dimensional (2-D) torus with N nodes has a diameter of Θ (N0.5), a generalized multimesh network with the same number of nodes and links bas a diameter of Θ (N0.25). In this paper, we also introduce a new metric, flow number, that can be used to evaluate topologies for optical networks. For optical networks, a topology with a smaller flow number is preferable, as it is an indicator of the number of wavelengths necessary for full connectivity. We show that the flow numbers of a 2-D torus, a multimesh, and a de Bruijn network, are Θ (N1.5), Θ (N1.25), and Θ (N log N), respectively, where N is the number of nodes in the network. The advantage of the generalized multimesh over the de Bruijn network lies in the fact that, unlike the de Bruijn network, this network can be constructed for any number of nodes and is incrementally expandable.

KW - De Bruijn graph

KW - Flow number

KW - Multihop networks

KW - Multimesh (MM)

KW - Optical networks

KW - Torus

UR - http://www.scopus.com/inward/record.url?scp=0035392832&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035392832&partnerID=8YFLogxK

U2 - 10.1109/50.933285

DO - 10.1109/50.933285

M3 - Article

AN - SCOPUS:0035392832

VL - 19

SP - 913

EP - 925

JO - Journal of Lightwave Technology

JF - Journal of Lightwave Technology

SN - 0733-8724

IS - 7

ER -