Forwarding and optical indices of 4-regular circulant networks

An all-to-all routing in a graph $G$ is a set of oriented paths of $G$, with exactly one path for each ordered pair of vertices. The load of an edge under an all-to-all routing $R$ is the number of times it is used (in either direction) by paths of $R$, and the maximum load of an edge is denoted by $\pi(G,R)$. The edge-forwarding index $\pi(G)$ is the minimum of $\pi(G,R)$ over all possible all-to-all routings $R$, and the arc-forwarding index $\overrightarrow{\pi}(G)$ is defined similarly by taking direction into consideration, where an arc is an ordered pair of adjacent vertices. Denote by $w(G,R)$ the minimum number of colours required to colour the paths of $R$ such that any two paths having an edge in common receive distinct colours. The optical index $w(G)$ is defined to be the minimum of $w(G,R)$ over all possible $R$, and the directed optical index $\overrightarrow{w}(G)$ is defined similarly by requiring that any two paths having an arc in common receive distinct colours. In this paper we obtain lower and upper bounds on these four invariants for $4$-regular circulant graphs with connection set $\{\pm 1,\pm s\}$, $1<s<n/2$. We give approximation algorithms with performance ratio a small constant for the corresponding forwarding index and routing and wavelength assignment problems for some families of $4$-regular circulant graphs.Comment: 19 pages, no figure in Journal of Discrete Algorithms 201

Photonics design tool for advanced CMOS nodes

Recently, the authors have demonstrated large-scale integrated systems with several million transistors and hundreds of photonic elements. Yielding such large-scale integrated systems requires a design-for-manufacture rigour that is embodied in the 10 000 to 50 000 design rules that these designs must comply within advanced complementary metal-oxide semiconductor manufacturing. Here, the authors present a photonic design automation tool which allows automatic generation of layouts without design-rule violations. This tool is written in SKILL, the native language of the mainstream electric design automation software, Cadence. This allows seamless integration of photonic and electronic design in a single environment. The tool leverages intuitive photonic layer definitions, allowing the designer to focus on the physical properties rather than on technology-dependent details. For the first time the authors present an algorithm for removal of design-rule violations from photonic layouts based on Manhattan discretisation, Boolean and sizing operations. This algorithm is not limited to the implementation in SKILL, and can in principle be implemented in any scripting language. Connectivity is achieved with software-defined waveguide ports and low-level procedures that enable auto-routing of waveguide connections.Comment: 5 pages, 10 figure

Electronic and photonic switching in the atm era

Broadband networks require high-capacity switches in order to properly manage large amounts of traffic fluxes. Electronic and photonic technologies are being used to achieve this objective both allowing different multiplexing and switching techniques. Focusing on the asynchronous transfer mode (ATM), the inherent different characteristics of electronics and photonics makes different architectures feasible. In this paper, different switching structures are described, several ATM switching architectures which have been recently implemented are presented and the implementation characteristics discussed. Three diverse points of view are given from the electronic research, the photonic research and the commercial switches. Although all the architectures where successfully tested, they should also follow different market requirements in order to be commercialised. The characteristics are presented and the architectures projected over them to evaluate their commercial capabilities.Peer ReviewedPostprint (published version

Methods and problems of wavelength-routing in all-optical networks

We give a survey of recent theoretical results obtained for wavelength-routing in all-optical networks. The survey is based on the previous survey in [Beauquier, B., Bermond, J-C., Gargano, L., Hell, P., Perennes, S., Vaccaro, U.: Graph problems arising from wavelength-routing in all-optical networks. In: Proc. of the 2nd Workshop on Optics and Computer Science, part of IPPS'97, 1997]. We focus our survey on the current research directions and on the used methods. We also state several open problems connected with this line of research, and give an overview of several related research directions

Optimization in Telecommunication Networks

Network design and network synthesis have been the classical optimization problems intelecommunication for a long time. In the recent past, there have been many technologicaldevelopments such as digitization of information, optical networks, internet, and wirelessnetworks. These developments have led to a series of new optimization problems. Thismanuscript gives an overview of the developments in solving both classical and moderntelecom optimization problems.We start with a short historical overview of the technological developments. Then,the classical (still actual) network design and synthesis problems are described with anemphasis on the latest developments on modelling and solving them. Classical results suchas Menger’s disjoint paths theorem, and Ford-Fulkerson’s max-flow-min-cut theorem, butalso Gomory-Hu trees and the Okamura-Seymour cut-condition, will be related to themodels described. Finally, we describe recent optimization problems such as routing andwavelength assignment, and grooming in optical networks.operations research and management science;

Wavelength assignment in all-optical networks for mesh topologies

All-Optical Networks employing Dense Wavelength Division Multiplexing (DWDM) are believed to be the next generation networks that can meet the ever-increasing demand for bandwidth of the end users. This thesis presents some new heuristics for wavelength assignment and converter placement in mesh topologies. Our heuristics try to assign the wavelengths in an efficient manner that results in very low blocking probability. We propose novel static and dynamic assignment schemes that outperform the assignments reported in the literature even when converters are used. The proposed on-line scheme called Round-Robin assignment outperforms previously proposed strategies such as first-fit and random assignment schemes. The performance improvement obtained with the proposed static assignments is very significant when compared with the dynamic schemes. We designed and developed a simulator in the C language that supports the 2D mesh topology with DWDM. We ran extensive simulations and compared our heuristics with those reported in the literature. We have examined converter placement in mesh topologies and proposed that placing converters at the center yields better results than uniform placement when dimension order routing is employed. We introduced a new concept called wavelength assignment with second trial that results in extremely low blocking probabilities when compared to schemes based on a single trial. Our proposed schemes are simple to implement and do not add to the cost. Thus we conclude that wavelength assignment plays more significant role in affecting the blocking probability than wavelength converters. We further conclude that static schemes without converters could easily outperform dynamic schemes thus resulting in great savings

High speed all optical networks

An inherent problem of conventional point-to-point wide area network (WAN) architectures is that they cannot translate optical transmission bandwidth into comparable user available throughput due to the limiting electronic processing speed of the switching nodes. The first solution to wavelength division multiplexing (WDM) based WAN networks that overcomes this limitation is presented. The proposed Lightnet architecture takes into account the idiosyncrasies of WDM switching/transmission leading to an efficient and pragmatic solution. The Lightnet architecture trades the ample WDM bandwidth for a reduction in the number of processing stages and a simplification of each switching stage, leading to drastically increased effective network throughputs. The principle of the Lightnet architecture is the construction and use of virtual topology networks, embedded in the original network in the wavelength domain. For this construction Lightnets utilize the new concept of lightpaths which constitute the links of the virtual topology. Lightpaths are all-optical, multihop, paths in the network that allow data to be switched through intermediate nodes using high throughput passive optical switches. The use of the virtual topologies and the associated switching design introduce a number of new ideas, which are discussed in detail