Problèmes de routages dans les réseaux optiques

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

Efficient structural outlooks for vertex product networks

In this thesis, a new classification for a large set of interconnection networks, referred to as "Vertex Product Networks" (VPN), is provided and a number of related issues are discussed including the design and evaluation of efficient structural outlooks for algorithm development on this class of networks. The importance of studying the VPN can be attributed to the following two main reasons: first an unlimited number of new networks can be defined under the umbrella of the VPN, and second some known networks can be studied and analysed more deeply. Examples of the VPN include the newly proposed arrangement-star and the existing Optical Transpose Interconnection Systems (OTIS-networks). Over the past two decades many interconnection networks have been proposed in the literature, including the star, hyperstar, hypercube, arrangement, and OTIS-networks. Most existing research on these networks has focused on analysing their topological properties. Consequently, there has been relatively little work devoted to designing efficient parallel algorithms for important parallel applications. In an attempt to fill this gap, this research aims to propose efficient structural outlooks for algorithm development. These structural outlooks are based on grid and pipeline views as popular structures that support a vast body of applications that are encountered in many areas of science and engineering, including matrix computation, divide-and- conquer type of algorithms, sorting, and Fourier transforms. The proposed structural outlooks are applied to the VPN, notably the arrangement-star and OTIS-networks. In this research, we argue that the proposed arrangement-star is a viable candidate as an underlying topology for future high-speed parallel computers. Not only does the arrangement-star bring a solution to the scalability limitations from which the Abstract existing star graph suffers, but it also enables the development of parallel algorithms based on the proposed structural outlooks, such as matrix computation, linear algebra, divide-and-conquer algorithms, sorting, and Fourier transforms. Results from a performance study conducted in this thesis reveal that the proposed arrangement-star supports efficiently applications based on the grid or pipeline structural outlooks. OTIS-networks are another example of the VPN. This type of networks has the important advantage of combining both optical and electronic interconnect technology. A number of studies have recently explored the topological properties of OTIS-networks. Although there has been some work on designing parallel algorithms for image processing and sorting, hardly any work has considered the suitability of these networks for an important class of scientific problems such as matrix computation, sorting, and Fourier transforms. In this study, we present and evaluate two structural outlooks for algorithm development on OTIS-networks. The proposed structural outlooks are general in the sense that no specific factor network or problem domain is assumed. Timing models for measuring the performance of the proposed structural outlooks are provided. Through these models, the performance of various algorithms on OTIS-networks are evaluated and compared with their counterparts on conventional electronic interconnection systems. The obtained results reveal that OTIS-networks are an attractive candidate for future parallel computers due to their superior performance characteristics over networks using traditional electronic interconnects

Designing data center networks for high throughput

Data centers with tens of thousands of servers now support popular Internet services, scientific research, as well as industrial applications. The network is the foundation of such facilities, giving the large server pool the ability to work together on these applications. The network needs to provide high throughput between servers to ensure that computations are not slowed down by network bottlenecks, with servers waiting on data from other servers. This work address two broad, related questions about high-throughput data center network design: (a) how do we measure and benchmark various network designs for throughput? and (b) how do we design such networks for near-optimal throughput? The problem of designing high-throughput networks has received a lot of attention, with multiple interesting architectures being proposed every year. However, there is no clarity on how one should benchmark these networks and how they compare to each other. In fact, this work shows that commonly used measurement approaches, in particular, cut-metrics like bisection bandwidth, do not predict throughput accurately. In contrast, we directly evaluate the throughput of networks on both uniform and (heretofore unknown) nearly-worst-case traffic matrices, and include here a comparison of 10 networks using this approach. Further, prior work has not addressed a fundamental question: how far are we from throughput-optimal design? In this work, we propose the first upper bound on network throughput for any topology with identical switches. Although designing optimal topologies is infeasible, we demonstrate that random graphs achieve throughput surprisingly close to this bound -- within a few percent at the scale of a few thousand servers for uniform traffic. Our approach also addresses important practical concerns in the design of data center networks, such as incremental expansion and heterogeneous design – as more and varied equipment is added to a data center over the years in response to evolving needs, how do we best accommodate such equipment? Our networks can achieve the same incremental growth at 40% of the expense such growth would incur with past techniques for Clos networks. Further, our approach to designing heterogeneous topologies (i.e., where all the network switches are not identical) achieves 43% higher throughput than a comparable VL2 topology, a heterogeneous network already deployed in Microsoft’s data centers. We acknowledge that the use of random graphs also poses challenges, particularly with regards to efficient routing and physical cabling. We thus present here high-efficiency routing and cabling schemes for such networks as well