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

Survivable Virtual Topology Routing under Shared Risk Link Groups in WDM Networks

Network survivability is one of the most important issues in the design of optical WDM networks. In this work we study the problem of survivable routing of a virtual topology on a physical topology with Shared Risk Link Groups (SRLG). The survivable virtual topology routing problem against single-link failures in the physical topology is proved to be NP-complete in [1]. We prove that survivable virtual topology routing problem against SRLG/node failures is also NP-complete. We present an improved integer linear programming (ILP) formulation (in comparison to [1]) for computing the survivable routing under SRLG/node failures. Using an ILP solver, we computed the survivable virtual topology routing against link and SRLG failures for small and medium sized networks efficiently. As even our improved ILP formulation becomes intractable for large networks, we present a congestion-based heuristic and a tabu search heuristic (which uses the congestion-based heuristic solution as the initial solution) for computing survivable routing of a virtual topology. Our experimental results show that tabu search heuristic coupled with the congestion based heuristic (used as initial solution) provides fast and near-optimal solutions

Least-cost Disjoint Paths with Dependent Cost Structure in Wavelength Continuous Optical WDM Networks

One of the important issues in establishing a fault tolerant connection in a wavelength division multiplexing optical network is computing a pair of disjoint working and protection paths and a free wavelength along the paths. While most of the earlier research focused only on computing disjoint paths, in this work we consider computing both disjoint paths and a free wavelength along the paths. The concept of dependent cost structure (DCS) of protection paths to enhance their resource sharing ability was proposed in our earlier work. In this work we extend the concept of DCS of protection paths to wavelength continuous networks. We formalize the problem of computing disjoint paths with DCS in wavelength continuous networks and prove that it is NP-complete. We present an iterative heuristic that uses a layered graph model to compute disjoint paths with DCS and identify a free wavelength

A Scalable Approach for Survivable Virtual Topology Routing in Optical WDM Networks

The survivable virtual topology routing problem is to route a virtual topology graph on a optical fiber physical topology such that the virtual topology remains connected when failures occur in the physical topology. In this work we study the problem of survivable virtual topology routing under single node/SRLG (Shared Risk Link Group) failure model. We prove that the survivable virtual topology routing problem under node/SRLG failures is NP-complete. We present an improved integer linear programming (ILP) formulation for computing the survivable routing of a virtual topology graph. However, ILP is not scalable when the network size scales more than a few tens of nodes. In this work, we present sub-classes of graphs which more accurately model an actual network and for which a survivable routing can be easily computed solving an ILP. We successfully computed the survivable routing of virtual topologies belonging to these sub-classes against link/SRLG failures for topologies of size up to 24 nodes

IMSH: An Iterative Heuristic for SRLG Diverse Routing in WDM Mesh Networks

Survivable routing of a connection involves computation of a pair of diverse routes such that at most one mute fails when failures occur in the network topology. A subset of links in the network that share the risk of failure at the same time are said to belong to a Shared Risk Link Group (SRLG) [3]. A network with shared risk link groups defined over its links is an SRLG network. A failure of an SRLG is equivalent to the failure of all the links in the SRLG. For a connection to he survivable in an SRLG network its working and protection paths must he routed on SRLG diverse paths. SRLG diverse routing problem has been proved to he NP-complete in [1]. According to the quality of service requirement of a survivable connection request, dedicated protection or shared protection can be used to establish the connection request. With dedicated protection, the connection is established on both the SRLG diverse working and protection paths. The simplest heuristic for computing SRLG diverse path pair is the two-step approach, hut it suffers from the trap topology problem. In [Z] an iterative heuristic (ITSH) using the two-step approach was proposed to compute least cost SRLG diverse path pair. Suurballe’s algorithm computes a pair of least cost link-disjoint paths between a node pair. In this work we present a modified Suurballe’s heuristic for computing the SRLG diverse routes between a node pair. We then propose an iterative heuristic (IMSH) which uses the modified Suurballe’s heuristic for computing the least cost SRLG diverse routes. We also present an 1/2-cost-improvement optimality check criterion for dedicated protection

Fault-tolerance using shared path protection in wavelength division multiplexing optical transport networks

Wavelength division multiplexing (WDM) fiber optical networks in the future are intended to provide bandwidths in the range of 500-2000 Gbps with the number of wavelengths multiplexed onto a single fiber ranging from 100-200. The enormous bandwidth capacity of WDM networks have made fault-tolerance/survivability in these networks extremely important. The goal of fault-tolerant design of a network is to build a network that is resilient to failures such as link, node, fiber conduit, etc., that occur in a network. In this dissertation, we focus on three main issues, survivable virtual topology design, fault-tolerant routing in optical networks and static survivable network design. The objective of the survivable virtual topology design problem is to route a given virtual topology on the physical topology such that when single point failures occur in the physical network, the virtual topology is still connected. We propose a scalable solution to the survivable virtual topology problem. In our experiments we successfully computed survivable routing of 45-edge virtual topologies on physical topologies of sizes up to 24 nodes within 2 min. To provide fault-tolerance to a connection, one needs to compute a link/node diverse path pair between the source and destination nodes of the connection. Such a routing is called fault-tolerant routing. The path used for routing the traffic is called the working path and the other diverse path is called the backup path. To enable resource sharing among the backup paths of multiple fault-tolerant connections, we introduce and formalize the concept of dependent cost structure (DCS) of a backup path on its working path and current network status. We present an iterative heuristic to compute diverse path pairs and our simulations show that our heuristic greatly increases the resource sharing ability of backup paths and thus reduces blocked calls and resource consumption. The goal of the static survivable network design problem is to provision the given set of traffic demands in a network such as an optical WDM network or a high-speed capacitated network. We present approximation algorithms for three versions of survivable network design problems. To the best of our knowledge this is the first work that presents approximation algorithms to survivable network design problems