Approximation Algorithms for Survivable Multicommodity Flow Problems with Applications to Network Design

Multicommodity flow (MF) problems have a wide variety of applications in areas such as VLSI circuit design, network design, etc., and are therefore very well studied. The fractional MF problems are polynomial time solvable while integer versions are NP-complete. However, exact algorithms to solve the fractional MF problems have high computational complexity. Therefore approximation algorithms to solve the fractional MF problems have been explored in the literature to reduce their computational complexity. Using these approximation algorithms and the randomized rounding technique, polynomial time approximation algorithms have been explored in the literature. In the design of high-speed networks, such as optical wavelength division multiplexing (WDM) networks, providing survivability carries great significance. Survivability is the ability of the network to recover from failures. It further increases the complexity of network design and presents network designers with more formidable challenges. In this work we formulate the survivable versions of the MF problems. We build approximation algorithms for the survivable multicommodity flow (SMF) problems based on the framework of the approximation algorithms for the MF problems presented in [1] and [2]. We discuss applications of the SMF problems to solve survivable routing in capacitated networks

Approximation Algorithms for Survivable Multicommodity Flow Problems with Applications to Network Design

Multicommodity flow (MF) problems have a wide variety of applications in areas such as VLSI circuit design, network design, etc., and are therefore very well studied. The fractional MF problems are polynomial time solvable while integer versions are NP-complete. However, exact algorithms to solve the fractional MF problems have high computational complexity. Therefore approximation algorithms to solve the fractional MF problems have been explored in the literature to reduce their computational complexity. Using these approximation algorithms and the randomized rounding technique, polynomial time approximation algorithms have been explored in the literature. In the design of high-speed networks, such as optical wavelength division multiplexing (WDM) networks, providing survivability carries great significance. Survivability is the ability of the network to recover from failures. It further increases the complexity of network design and presents network designers with more formidable challenges. In this work we formulate the survivable versions of the MF problems. We build approximation algorithms for the survivable multicommodity flow (SMF) problems based on the framework of the approximation algorithms for the MF problems presented in [1] and [2]. We discuss applications of the SMF problems to solve survivable routing in capacitated networks

Approximation algorithms for optimal routing in wavelength routed WDM network.

Finding an optimum routing scheme, so that a given logical topology for a wavelength routed WDM network handles all traffic requirements in an efficient manner, is an important problem in optical network design. One major design objective is to minimize the congestion of the network, defined as the traffic on the logical link which has the maximum traffic. This is known to be a hard problem taking an enormous amount of time even for moderate sized networks and is intractable for larger networks. The approach we have outlined is that of obtaining an approximate solution to the problem rather than an exact solution. We have developed three closely related approximate algorithms to solve this problem. These three algorithms significantly improved the running time for finding the minimum congestion. We based our approach on the approximation fraction multi-commodity algorithm by Lisa Fleischer [F99] to calculate the primal and dual solutions for the linear program to solve the multi-commodity flow problem. We have compared our algorithm with the standard linear program solution obtained using CPLEX. The experiments show that our algorithms require, on the average, only less than 10% of the time CPLEX uses for networks with 25 nodes or less. Our algorithms perform well for larger networks which CPLEX cannot handle.Dept. of Computer Science. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2004 .L85. Source: Masters Abstracts International, Volume: 43-03, page: 0884. Advisers: Subir Bandyopadhyay; Arunita Jackel. Thesis (M.Sc.)--University of Windsor (Canada), 2004

Dynamic Network Topologies

Demand for effective network defense capabilities continues to increase as cyber attacks occur more and more frequently and gain more and more prominence in the media. Current security practices stop after data encryption and network address filtering. Security at the lowest level of network infrastructure allows for greater control of how the network traffic flows around the network. This research details two methods for extending security practices to the physical layer of a network by modifying the network infrastructure. The first method adapts the Advanced Encryption Standard while the second method uses a Steiner tree. After the network connections are updated, the traffic is re-routed using an approximation algorithm to solve the resulting multicommodity flow problem. The results show that modifying the network connections provides additional security to the information. Additionally, this research extends on previous research by addressing enterprise-size networks; networks between 5 and 1000 nodes with 1 through 5 interfaces are tested. While the final configuration depends greatly on the starting network infrastructure, the speed of the execution time enables administrators to make infrastructure adjustments in response to active cyber attacks

LOGICAL TOPOLOGY DESIGN FOR SURVIVABILITY IN IP-OVER-WDM NETWORKS

IP-over-WDM networks integrate Wavelength Division Multiplexing (WDM) technology with Internet Protocol (IP) and are widely regarded as the architecture for the next generation high-speed Internet. The problem of designing an IP-over-WDM network can be modeled as an embedding problem in which an IP network is embedded in a WDM network by establishing all optical paths between IP routers in the WDM network. Survivability is considered a vital requirement in such networks, which can be achieved by embedding the IP network in the WDM network in such a way that the IP network stays connected in the presence of failure or failures in the WDM network. Otherwise, some of the IP routers may not be reachable.The problem can be formulated as an Integer Linear Program (ILP), which can be solved optimally but is NP-complete. In this thesis, we have studied and proposed various efficient algorithms that can be used to make IP-over-WDM networks survivable in the presence of a single WDM link (optical fiber cable or cables) failure.First we evaluate an existing approach, named Survivable Mapping Algorithm by Ring Trimming (SMART), which provides survivability for an entire network by successively considering pieces of the network. The evaluation provides much insight into the approach, which allowed us to propose several enhancements. The modified approach with enhancements leads to better performance than the original SMART.We have also proposed a hybrid algorithm that guarantees survivability, if the IP and the WDM networks are at least 2-edge connected. The algorithm uses a combination of proactive (protection) and reactive (restoration) mechanisms to obtain a survivable embedding for any given IP network in any given WDM network.Circuits and cutsets are dual concepts. SMART approach is based on circuits. The question then arises whether there exists a dual methodology based on cutsets. We investigate this question and provide much needed insight. We provide a unified algorithmic framework based on circuits and cutsets. We also provide new methodologies based on cutsets and give a new proof of correctnessof SMART. We also develop a method based on incidence sets that are a special case of cutsets. Noting that for some IP networks a survivable embedding may not exist, the option of adding new IP links is pursued. Comparative evaluations of all the algorithms through extensive simulations are also given in this dissertation

NETWORK DESIGN UNDER DEMAND UNCERTAINTY

A methodology for network design under demand uncertainty is proposed in this dissertation. The uncertainty is caused by the dynamic nature of the IP-based traffic which is expected to betransported directly over the optical layer in the future. Thus, there is a need to incorporate the uncertainty into a design modelexplicitly. We assume that each demand can be represented as a random variable, and then develop an optimization model to minimizethe cost of routing and bandwidth provisioning. The optimization problem is formulated as a nonlinear Multicommodity Flow problemusing Chance-Constrained Programming to capture both the demand variability and levels of uncertainty guarantee. Numerical work ispresented based on a heuristic solution approach using a linear approximation to transform the nonlinear problem to a simpler linearprogramming problem. In addition, the impact of the uncertainty on a two-layer network is investigated. This will determine how theChance-Constrained Programming based scheme can be practically implemented. Finally, the implementation guidelines for developingan updating process are provided