A Note on Iterated Rounding for the Survivable Network Design Problem

In this note we consider the survivable network design problem (SNDP) in undirected graphs. We make two contributions. The first is a new counting argument in the iterated rounding based 2-approximation for edge-connectivity SNDP (EC-SNDP) originally due to Jain. The second contribution is to make some connections between hypergraphic version of SNDP (Hypergraph-SNDP) introduced by Zhao, Nagamochi and Ibaraki, and edge and node-weighted versions of EC-SNDP and element-connectivity SNDP (Elem-SNDP). One useful consequence is a 2-approximation for Elem-SNDP that avoids the use of set-pair based relaxation and analysis

Logical topology design for IP rerouting: ASONs versus static OTNs

IP-based backbone networks are gradually moving to a network model consisting of high-speed routers that are flexibly interconnected by a mesh of light paths set up by an optical transport network that consists of wavelength division multiplexing (WDM) links and optical cross-connects. In such a model, the generalized MPLS protocol suite could provide the IP centric control plane component that will be used to deliver rapid and dynamic circuit provisioning of end-to-end optical light paths between the routers. This is called an automatic switched optical (transport) network (ASON). An ASON enables reconfiguration of the logical IP topology by setting up and tearing down light paths. This allows to up- or downgrade link capacities during a router failure to the capacities needed by the new routing of the affected traffic. Such survivability against (single) IP router failures is cost-effective, as capacity to the IP layer can be provided flexibly when necessary. We present and investigate a logical topology optimization problem that minimizes the total amount or cost of the needed resources (interfaces, wavelengths, WDM line-systems, amplifiers, etc.) in both the IP and the optical layer. A novel optimization aspect in this problem is the possibility, as a result of the ASON, to reuse the physical resources (like interface cards and WDM line-systems) over the different network states (the failure-free and all the router failure scenarios). We devised a simple optimization strategy to investigate the cost of the ASON approach and compare it with other schemes that survive single router failures

Risk based resilient network design

This paper presents a risk-based approach to resilient network design. The basic design problem considered is that given a working network and a fixed budget, how best to allocate the budget for deploying a survivability technique in different parts of the network based on managing the risk. The term risk measures two related quantities: the likelihood of failure or attack, and the amount of damage caused by the failure or attack. Various designs with different risk-based design objectives are considered, for example, minimizing the expected damage, minimizing the maximum damage, and minimizing a measure of the variability of damage that could occur in the network. A design methodology for the proposed risk-based survivable network design approach is presented within an optimization model framework. Numerical results and analysis illustrating the different risk based designs and the tradeoffs among the schemes are presented. © 2011 Springer Science+Business Media, LLC

Approximating Source Location and Star Survivable Network Problems

In Source Location (SL) problems the goal is to select a mini-mum cost source set $S \subseteq V$ such that the connectivity (or flow) $\psi(S,v)$ from $S$ to any node $v$ is at least the demand $d_v$ of $v$. In many SL problems $\psi(S,v)=d_v$ if $v \in S$, namely, the demand of nodes selected to $S$ is completely satisfied. In a node-connectivity variant suggested recently by Fukunaga, every node $v$ gets a "bonus" $p_v \leq d_v$ if it is selected to $S$. Fukunaga showed that for undirected graphs one can achieve ratio $O(k \ln k)$ for his variant, where $k=\max_{v \in V}d_v$ is the maximum demand. We improve this by achieving ratio \min\{p^*\lnk,k\}\cdot O(\ln (k/q^*)) for a more general version with node capacities, where $p^*=\max_{v \in V} p_v$ is the maximum bonus and $q^*=\min_{v \in V} q_v$ is the minimum capacity. In particular, for the most natural case $p^*=1$ considered by Fukunaga, we improve the ratio from $O(k \ln k)$ to $O(\ln^2k)$. We also get ratio $O(k)$ for the edge-connectivity version, for which no ratio that depends on $k$ only was known before. To derive these results, we consider a particular case of the Survivable Network (SN) problem when all edges of positive cost form a star. We give ratio $O(\min\{\ln n,\ln^2 k\})$ for this variant, improving over the best ratio known for the general case $O(k^3 \ln n)$ of Chuzhoy and Khanna