Approximable 1-Turn Routing Problems in All-Optical Mesh Networks

In all-optical networks, several communications can be transmitted through the same fiber link provided that they use different wavelengths. The MINIMUM ALL-OPTICAL ROUTING problem (given a list of pairs of nodes standing for as many point to point communication requests, assign to each request a route along with a wavelength so as to minimize the overall number of assigned wavelengths) has been paid a lot of attention and is known to be N P–hard. Rings, trees and meshes have thus been investigated as specific networks, but leading to just as many N P–hard problems. This paper investigates 1-turn routings in meshes (paths are allowed one turn only). We first show the MINIMUM LOAD 1-TURN ROUTING problem to be N P–hard but 2-APX (more generally, the MINIMUM LOAD k-CHOICES ROUTING problem is N P–hard but k-APX), then that the MINIMUM 1-TURN PATHS COLOURING problem is 4-APX (more generally, any d-segmentable routing of load L in a hypermesh of dimension d can be coloured with 2d(L−1)+1 colours at most). >From there, we prove the MINIMUM ALL-OPTICAL 1-TURN ROUTING problem to be APX

Protection and restoration algorithms for WDM optical networks

Currently, Wavelength Division Multiplexing (WDM) optical networks play a major role in supporting the outbreak in demand for high bandwidth networks driven by the Internet. It can be a catastrophe to millions of users if a single optical fiber is somehow cut off from the network, and there is no protection in the design of the logical topology for a restorative mechanism. Many protection and restoration algorithms are needed to prevent, reroute, and/or reconfigure the network from damages in such a situation. In the past few years, many works dealing with these issues have been reported. Those algorithms can be implemented in many ways with several different objective functions such as a minimization of protection path lengths, a minimization of restoration times, a maximization of restored bandwidths, etc. This thesis investigates, analyzes and compares the algorithms that are mainly aimed to guarantee or maximize the amount of remaining bandwidth still working over a damaged network. The parameters considered in this thesis are the routing computation and implementation mechanism, routing characteristics, recovering computation timing, network capacity assignment, and implementing layer. Performance analysis in terms of the restoration efficiency, the hop length, the percentage of bandwidth guaranteed, the network capacity utilization, and the blocking probability is conducted and evaluated

Design and provisioning of WDM networks for traffic grooming

Wavelength Division Multiplexing (WDM) is the most viable technique for utilizing the enormous amounts of bandwidth inherently available in optical fibers. However, the bandwidth offered by a single wavelength in WDM networks is on the order of tens of Gigabits per second, while most of the applications\u27 bandwidth requirements are still subwavelength. Therefore, cost-effective design and provisioning of WDM networks require that traffic from different sessions share bandwidth of a single wavelength by employing electronic multiplexing at higher layers. This is known as traffic grooming. Optical networks supporting traffic grooming are usually designed in a way such that the cost of the higher layer equipment used to support a given traffic matrix is reduced. In this thesis, we propose a number of optimal and heuristic solutions for the design and provisioning of optical networks for traffic grooming with an objective of network cost reduction. In doing so, we address several practical issues. Specifically, we address the design and provisioning of WDM networks on unidirectional and bidirectional rings for arbitrary unicast traffic grooming, and on mesh topologies for arbitrary multipoint traffic grooming. In multipoint traffic grooming, we address both multicast and many-to-one traffic grooming problems. We provide a unified frame work for optimal and approximate network dimensioning and channel provisioning for the generic multicast traffic grooming problem, as well as some variants of the problem. For many-to-one traffic grooming we propose optimal as well as heuristic solutions. Optimal formulations which are inherently non-linear are mapped to an optimal linear formulation. In the heuristic solutions, we employ different problem specific search strategies to explore the solution space. We provide a number of experimental results to show the efficacy of our proposed techniques for the traffic grooming problem in WDM networks

Optical control plane: theory and algorithms

In this thesis we propose a novel way to achieve global network information dissemination in which some wavelengths are reserved exclusively for global control information exchange. We study the routing and wavelength assignment problem for the special communication pattern of non-blocking all-to-all broadcast in WDM optical networks. We provide efficient solutions to reduce the number of wavelengths needed for non-blocking all-to-all broadcast, in the absence of wavelength converters, for network information dissemination. We adopt an approach in which we consider all nodes to be tap-and-continue capable thus studying lighttrees rather than lightpaths. To the best of our knowledge, this thesis is the first to consider “tap-and-continue” capable nodes in the context of conflict-free all-to-all broadcast. The problem of all to-all broadcast using individual lightpaths has been proven to be an NP-complete problem [6]. We provide optimal RWA solutions for conflict-free all-to-all broadcast for some particular cases of regular topologies, namely the ring, the torus and the hypercube. We make an important contribution on hypercube decomposition into edge-disjoint structures. We also present near-optimal polynomial-time solutions for the general case of arbitrary topologies. Furthermore, we apply for the first time the “cactus” representation of all minimum edge-cuts of graphs with arbitrary topologies to the problem of all-to-all broadcast in optical networks. Using this representation recursively we obtain near-optimal results for the number of wavelengths needed by the non-blocking all-to-all broadcast. The second part of this thesis focuses on the more practical case of multi-hop RWA for non- blocking all-to-all broadcast in the presence of Optical-Electrical-Optical conversion. We propose two simple but efficient multi-hop RWA models. In addition to reducing the number of wavelengths we also concentrate on reducing the number of optical receivers, another important optical resource. We analyze these models on the ring and the hypercube, as special cases of regular topologies. Lastly, we develop a good upper-bound on the number of wavelengths in the case of non-blocking multi-hop all-to-all broadcast on networks with arbitrary topologies and offer a heuristic algorithm to achieve it. We propose a novel network partitioning method based on “virtual perfect matching” for use in the RWA heuristic algorithm

Multicasting in All-Optical WDM Networks

n this dissertation, we study the problem of (i) routing and wavelength assignment, and (ii) traffic grooming for multicast traffic in Wavelength Division Multiplexing (WDM) based all-optical networks. We focus on the 'static' case where the set of multicast traffic requests is assumed to be known in advance. For the routing and wavelength assignment problem, we study the objective of minimizing the number of wavelengths required; and for the traffic grooming problem, we study the objectives of minimizing (i) the number of wavelengths required, and (ii) the number of electronic components required. Both the problems are known to be hard for general fiber network topologies. Hence, it makes sense to study the problems under some restrictions on the network topology. We study the routing and wavelength assignment problem for bidirected trees, and the traffic grooming problem for unidirectional rings. The selected topologies are simple in the sense that the routing for any multicast traffic request is trivially determined, yet complex in the sense that the overall problems still remain hard. A motivation for selecting these topologies is that they are of practical interest since most of the deployed optical networks can be decomposed into these elemental topologies. In the first part of the thesis, we study the the problem of multicast routing and wavelength assignment in all-optical bidirected trees with the objective of minimizing the number of wavelengths required in the network. We give a 5/2-approximation algorithm for the case when the degree of the bidirected tree is at most 3. We give another algorithm with approximation ratio 10/3, 3 and 2 for the case when the degree of the bidirected tree is equal to 4, 3 and 2, respectively. The time complexity analysis for both these algorithms is also presented. Next we prove that the problem is hard even for the two restricted cases when the bidirected tree has (i) depth 2, and (ii) degree 2. Finally, we present another hardness result for a related problem of finding the clique number for a class for intersection graphs. In the second part of the thesis, we study the problem of multicast traffic grooming in all-optical unidirectional rings. For the case when the objective is to minimize the number of wavelengths required in the network, given an 'a'-approximation algorithm for the circular arc coloring problem, we give an algorithm having asymptotic approximation ratio 'a' for the multicast traffic grooming problem. We develop an easy to calculate lower bound on the minimum number of electronic components required to support a given set of multicast traffic requests on a given unidirectional ring network. We use this lower bound to analyze the worst case performance of a pair of simple grooming schemes. We also study the case when no grooming is carried out in order to get an estimate on the maximum number of electronic components that can be saved by applying intelligent grooming. Finally, we present a new grooming scheme and compare its average performance against other grooming schemes via simulations. The time complexity analysis for all the grooming schemes is also presented

Joint optimization of topology, switching, routing and wavelength assignment

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (p. 279-285).To provide end users with economic access to high bandwidth, the architecture of the next generation metropolitan area networks (MANs) needs to be judiciously designed from the cost perspective. In addition to a low initial capital investment, the ultimate goal is to design networks that exhibit excellent scalability - a decreasing cost-per-node-per-unit-traffic as user number and transaction size increase. As an effort to achieve this goal, in this thesis we search for the scalable network architectures over the solution space that embodies the key aspects of optical networks: fiber connection topology, switching architecture selection and resource dimensioning, routing and wavelength assignment (RWA). Due to the inter-related nature of these design elements, we intended to solve the design problem jointly in the optimization process in order to achieve over-all good performance. To evaluate how the cost drives architectural tradeoffs, an analytical approach is taken in most parts of the thesis by first focusing on networks with symmetric and well defined structures (i.e., regular networks) and symmetric traffic patterns (i.e., all-to-all uniform traffic), which are fair representations that give us suggestions of trends, etc.(cont.) We starts with a examination of various measures of regular topologies. The average minimum hop distance plays a crucial role in evaluating the efficiency of network architecture. From the perspective of designing optical networks, the amount of switching resources used at nodes is proportional to the average minimum hop distance. Thus a smaller average minimum hop distance translates into a lower fraction of pass-through traffic and less switching resources required. Next, a first-order cost model is set up and an optimization problem is formulated for the purpose of characterizing the tradeoffs between fiber and switching resources. Via convex optimization techniques, the joint optimization problem is solved analytically for (static) uniform traffic and symmetric networks. Two classes of regular graphs - Generalized Moore Graphs and A-nearest Neighbors Graphs - are identified to yield lower and upper cost bounds, respectively. The investigation of the cost scalability further demonstrates the advantage of the Generalized Moore Graphs as benchmark topologies: with linear switching cost structure, the minimal normalized cost per unit traffic decreases with increasing network size for the Generalized Moore Graphs and their relatives.(cont.) In comparison, for less efficient fiber topologies (e.g., A-nearest Neighbors) and switching cost structures (e.g., quadratic cost), the minimal normalized cost per unit traffic plateaus or even increases with increasing network size. The study also reveals other attractive properties of Generalized Moore Graphs in conjunction with minimum hop routing - the aggregate network load is evenly distributed over each fiber. Thus, Generalized Moore Graphs also require the minimum number of wavelengths to support a given uniform traffic demand. Further more, the theoretical works on the Generalized Moore Graphs and their close relatives are extended to study more realistic design scenarios in two aspects. One aspect addresses the irregular topologies and (static) non-uniform traffic, for which the results of Generalized Moore networks are used to provide useful estimates of network cost, and are thus offering good references for cost-efficient optical networks. The other aspect deals with network design under random demands. Two optimization formulations that incorporate the traffic variability are presented.(cont.) The results show that as physical architecture, Generalized Moore Graphs are most robust (in cost) to the demand uncertainties. Analytical results also provided design guidelines on how optimum dimensioning, network connectivity, and network costs vary as functions of risk aversion, service level requirements, and probability distributions of demands.by Kyle Chi Guan.Ph.D

Dynamic routing of reliability-differentiated connections in WDM optical networks

Master'sMASTER OF ENGINEERIN

WRHT: Efficient All-reduce for Distributed DNN Training in Optical Interconnect System

Communication efficiency plays an important role in accelerating the distributed training of Deep Neural Networks (DNN). All-reduce is the key communication primitive to reduce model parameters in distributed DNN training. Most existing all-reduce algorithms are designed for traditional electrical interconnect systems, which cannot meet the communication requirements for distributed training of large DNNs. One of the promising alternatives for electrical interconnect is optical interconnect, which can provide high bandwidth, low transmission delay, and low power cost. We propose an efficient scheme called WRHT (Wavelength Reused Hierarchical Tree) for implementing all-reduce operation in optical interconnect system, which can take advantage of WDM (Wavelength Division Multiplexing) to reduce the communication time of distributed data-parallel DNN training. We further derive the minimum number of communication steps and communication time to realize the all-reduce using WRHT. Simulation results show that the communication time of WRHT is reduced by 75.59%, 49.25%, and 70.1% respectively compared with three traditional all-reduce algorithms simulated in optical interconnect system. Simulation results also show that WRHT can reduce the communication time for all-reduce operation by 86.69% and 84.71% in comparison with two existing all-reduce algorithms in electrical interconnect system.Comment: This paper is under the submission of GLOBECOM 202

On-Chip Optical Interconnection Networks for Multi/Manycore Architectures

The rapid development of multi/manycore technologies offers the opportunity for highly parallel architectures implemented on a single chip. While the first, low-parallelism multicore products have been based on simple interconnection structures (single bus, very simple crossbar), the emerging highly parallel architectures will require complex, limited-degree interconnection networks. This thesis studies this trend according to the general theory of interconnection structures for parallel machines, and investigates some solutions in terms of performance, cost, fault-tolerance, and run-time support to shared-memory and/or message passing programming mechanisms

Towards Scalable Cost-Effective Service and Survivability Provisioning in Ultra High Speed Networks

Optical transport networks based on wavelength division multiplexing (WDM) are considered to be the most appropriate choice for future Internet backbone. On the other hand, future DOE networks are expected to have the ability to dynamically provision on-demand survivable services to suit the needs of various high performance scientific applications and remote collaboration. Since a failure in aWDMnetwork such as a cable cut may result in a tremendous amount of data loss, efficient protection of data transport in WDM networks is therefore essential. As the backbone network is moving towards GMPLS/WDM optical networks, the unique requirement to support DOE’s science mission results in challenging issues that are not directly addressed by existing networking techniques and methodologies. The objectives of this project were to develop cost effective protection and restoration mechanisms based on dedicated path, shared path, preconfigured cycle (p-cycle), and so on, to deal with single failure, dual failure, and shared risk link group (SRLG) failure, under different traffic and resource requirement models; to devise efficient service provisioning algorithms that deal with application specific network resource requirements for both unicast and multicast; to study various aspects of traffic grooming in WDM ring and mesh networks to derive cost effective solutions while meeting application resource and QoS requirements; to design various diverse routing and multi-constrained routing algorithms, considering different traffic models and failure models, for protection and restoration, as well as for service provisioning; to propose and study new optical burst switched architectures and mechanisms for effectively supporting dynamic services; and to integrate research with graduate and undergraduate education. All objectives have been successfully met. This report summarizes the major accomplishments of this project. The impact of the project manifests in many aspects: First, the project addressed many essential problems that arisen in current and future WDM optical networks, and provided a host of innovative solutions though there was no invention or patent filing. This project resulted in more than 2 dozens publications in major journals and conferences (including papers in IEEE Transactions and journals, as well as a book chapter). Our publications have been cited by many peer researchers. In particular, one of our conference papers was nominated for the best paper award of IEEE/Create-Net Broadnets (International Conference on Broadband Communications, Networks, and Systems) 2006. Second, the results and solutions of this project were well received by DOE Labs where presentations were given by the PI. We hope to continue the collaboration with DOE Labs in the future. Third, the project was the first to propose and extensively study multicast traffic grooming, new traffic models such as sliding scheduled traffic model and scheduled traffic model. Our research has sparkled a flurry of recent studies and publications by the research community in these areas. Fourth, the project has benefited a diverse population of students by motivating, engaging, enhancing their learning and skills. The project has been conducted in a manner conducive to the training of students both at graduate and undergraduate levels. As a result, one Ph.D., Dr. Abdur Billah, was graduated. Another Ph.D. student, Tianjian Li, will graduate in January 2007. In addition, four MS students were graduated. One undergraduate student, Jeffrey Alan Shininger, completed his university honors project. Fifth, thanks to the support of this ECPI project, the PI has obtained additional funding from the National Science Foundation, the Air Force Research Lab, and other sources. A few other proposals are pending. Finally, this project has also significantly impacted the curricula and resulted in the enhancement of courses at the graduate and undergraduate levels, therefore strengthening the bond between research and education