TY - JOUR

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

AU - Sen, Arunabha

AU - Bandyopadhyay, Subir

AU - Sinha, Bhabani P.

N1 - Funding Information:
Manuscript received April 12, 2000; revised March 20, 2001. The work of S. Bandyopadhyay was supported by the National Sciences and Engineering Research Council of Canada under a Research Grant. A. Sen is with the Department of Computer Science and Engineering, Arizona State University, Tempe, AZ 85287 USA (e-mail: asen@asu.edu). S. Bandyopadhyay is with the School of Computer Science, University of Windsor, Windsor, ON N9B 3P4, Canada. B. P. Sinha is with the Advanced Computing and Microelectronics Unit, Indian Statistical Institute, Calcutta 700035, India. Publisher Item Identifier S 0733-8724(01)05309-9.

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

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U2 - 10.1109/50.933285

DO - 10.1109/50.933285

M3 - Article

AN - SCOPUS:0035392832

SN - 0733-8724

VL - 19

SP - 913

EP - 925

JO - Journal of Lightwave Technology

JF - Journal of Lightwave Technology

IS - 7

ER -