Survivable Network Design Research Articles

Approximation algorithm for optimal location of concentrators and design of Capacitated Survivable Backbone Networks

We focus on the problem of selecting concentrator locations to minimise the access network costs. This falls under the general class of Uncapacitated Facility Location (UFL) problem. We present an approximation algorithm along with some computational results. We also study the problem of designing a Capacitated Survivable Backbone Network (CSBN) with the property that there is at least one route present between all the communicating node pairs in the case of a single link failure. Mathematical formulation to efficiently solve the survivable backbone network design problem is presented. The methodologies developed are applied to a real world setting obtaining optimal or near-optimal results.

Genetic Algorithm for the Topological Design of Survivable Optical Transport Networks

We develop a genetic algorithm for the topological design of survivable optical transport networks with minimum capital expenditure. Using the developed genetic algorithm we can obtain near-optimal topologies in a short time. The quality of the obtained solutions is assessed using an integer linear programming model. Two initial population generators, two selection methods, two crossover operators, and two population sizes are analyzed. Computational results obtained using real telecommunications networks show that by using an initial population that resembles real optical transport networks a good convergence is achieved.

Approximating survivable networks with β-metric costs

The Survivable Network Design ( SND) problem seeks a minimum-cost subgraph that satisfies prescribed node-connectivity requirements. We consider SND on both directed and undirected complete graphs with β- metric costs when c ( x z ) ⩽ β [ c ( x y ) + c ( y z ) ] for all x , y , z ∈ V , which varies from uniform costs ( β = 1 / 2 ) to metric costs ( β = 1 ). For the k- Connected Subgraph ( k- CS) problem our ratios are: 1 + 2 β k ( 1 − β ) − 1 2 k − 1 for undirected graphs, and 1 + 4 β 3 k ( 1 − 3 β 2 ) − 1 2 k − 1 for directed graphs and 1 2 ⩽ β < 1 3 . For undirected graphs this improves the ratios β 1 − β of Böckenhauer et al. (2008) [3] and 2 + β k n of Kortsarz and Nutov (2003) [11] for all k ⩾ 4 and 1 2 + 3 k − 2 2 ( 4 k 2 − 7 k + 2 ) ⩽ β ⩽ k 2 ( k + 1 ) 2 − 2 . We also show that SND admits the ratios 2 β 1 − β for undirected graphs, and 4 β 3 1 − 3 β 2 for directed graphs with 1 / 2 ⩽ β < 1 / 3 . For two important particular cases of SND, so-called Subset k- CS and Rooted SND, our ratios are 2 β 3 1 − 3 β 2 for directed graphs and β 1 − β for subset k- CS on undirected graphs.

Solving survivable two-layer network design problems by metric inequalities

We address the problem of designing a multi-layer network with survivability requirements. We are given a two-layer network: the lower layer represents the potential physical connections that can be activated, the upper layer is made of logical connections that can be set up using physical links. We are given origin-destination demands (commodities) to be routed at the upper layer. We are also given a set of failure scenarios and, for every scenario, an associated subset of commodities. The goal is to install minimum cost integer capacities on the links of both layers in order to ensure that the commodities can be routed simultaneously on the network. In addition, in every failure scenario the routing of the associated commodities must be guaranteed. We consider two variants of the problem and develop a branch-and-cut scheme based on the capacity formulation. Computational results on instances derived from the SNDLib for single node failure scenarios are discussed.

Cross-Layer Approach to Survivable DWDM Network Design

All-optical networks, in which the electrical regeneration bottlenecks are removed, are seen as the next-generation backbone networks. Any link failure in these high-speed environments, if not dealt with promptly, is catastrophic and can cause the loss of gigabits of data. While techniques to improve the survivability of optical networks are now well-established, such is not the case with all-optical networks. In these environments, the absence of regeneration implies that physical impairments accumulate over long paths. So-called cross-layer techniques mitigate the physical impairments’ impact on the network layer performance. In this work, we apply cross-layer techniques, previously successfully applied to the impairment-constrained routing and wavelength assignment problem [IEEE J. Sel. Areas Commun., vol. 26, p. 32, 2008], to the problem of improving the survivability of all-optical networks facing link failures. To the best of our knowledge, cross-layer survivability of all-optical networks has never been studied before. We present algorithms that improve the network survivability over non-cross-layer algorithms by decreasing both the blocking probability and the vulnerability of the network to failures. Our mechanisms are evaluated with extensive simulations for a realistic regional-sized network. The cross-layer algorithms are computationally intensive, and to alleviate this issue we propose two new compound restoration algorithms as well as two novel quality-of-transmission-aware protection schemes that exhibit low blocking probability and have a moderate vulnerability ratio and time complexity.

Orientation-based models for {0,1,2}-survivable network design: theory and practice

We consider {0,1,2}-Survivable Network Design problems with node-connectivity constraints. In the most prominent variant, we are given an edge-weighted graph and two customer sets \({\fancyscript{R}_1}\) and \({\fancyscript{R}_2}\) ; we ask for a minimum cost subgraph that connects all customers, and guarantees two-node-connectivity for the \({\fancyscript{R}_2}\) customers. We also consider an alternative of this problem, in which 2-node-connectivity is only required w.r.t. a certain root node, and its prize-collecting variant. The central result of this paper is a novel graph-theoretical characterization of 2-node-connected graphs via orientation properties. This allows us to derive two classes of ILP formulations based on directed graphs, one using multi-commodity flow and one using cut-inequalities. We prove the theoretical advantages of these directed models compared to the previously known ILP approaches. We show that our two concepts are equivalent from the polyhedral point of view. On the other hand, our experimental study shows that the cut formulation is much more powerful in practice. Moreover, we propose a collection of benchmark instances that can be used for further research on this topic.

SNDlib 1.0Survivable Network Design Library

This article describes the Survivable Network Design Library (SNDlib), a data library for fixed telecommunication network design available at . In the current version 1.0, the library contains data...

The generalized minimum edge‐biconnected network problem: Efficient neighborhood structures for variable neighborhood search

AbstractWe consider the generalized minimum edge‐biconnected network problem where the nodes of a graph are partitioned into clusters and exactly one node from each cluster is required to be connected in an edge‐biconnected way. Instances of this problem appear, for example, in the design of survivable backbone networks. We present different variants of a variable neighborhood search approach that utilize different types of neighborhood structures, each of them addressing particular properties as spanned nodes and/or the edges between them. For the more complex neighborhood structures, we apply efficient techniques—such as a graph reduction—to essentially speed up the search process. For comparison purposes, we use a mixed integer linear programming formulation based on multi‐commodity flows to solve smaller instances of this problem to proven optimality. Experiments on such instances indicate that the variable neighborhood search is also able to identify optimal solutions in the majority of test runs, but within substantially less time. Tests on larger Euclidean and random instances with up to 1,280 nodes, which could not be solved to optimality by mixed integer programming, further document the efficiency of the variable neighborhood search. In particular, all proposed neighborhood structures are shown to contribute significantly to the search process. © 2010 Wiley Periodicals, Inc. NETWORKS, 2010

Tabu Search Algorithm for Survivable Network Design Problem with Simultaneous Unicast and Anycast Flows

Tabu Search Algorithm for Survivable Network Design Problem with Simultaneous Unicast and Anycast FlowsIn this work we focus on the problem of survivable network design for simultaneous unicast and anycast flows. This problem follows from the growing popularity of network services applying the anycast paradigm. The anycasting is defined as one-to-one-of-many transmission and is applied in Domain Name Service (DNS), peer-to-peer (P2P) systems, Content Delivery Networks (CDN). In this work we formulate two models that enables joint optimization of network capacity, working and backup connections for both unicast and anycast flows. The goal is to minimize the network cost required to protect the network against failures using the single backup path approach. In the first model we consider modular link cost, in the second we are given a set of link proposal and we must select only one of them. Because these problems are NP-hard, therefore optimal solutions of branch-and-bounds or branch-and-cut methods can be generated for relatively small networks. Consequently, we propose a new heuristic algorithm based on Tabu Search method. We present results showing the effectiveness the proposed heuristic compared against optimal results. Moreover, we report results showing that the use of anycast paradigm can reduce the network cost.

Simpler analysis of LP extreme points for traveling salesman and survivable network design problems

We consider the Survivable Network Design Problem (SNDP) and the Symmetric Traveling Salesman Problem (STSP). We give simpler proofs of the existence of a 1 2 -edge and 1-edge in any extreme point of the natural LP relaxations for the SNDP and STSP, respectively. We formulate a common generalization of both problems and show our results by a new counting argument. We also obtain a simpler proof of the existence of a 1 2 -edge in any extreme point of the set-pair LP relaxation for the element connectivity Survivable Network Design Problem ( SNDP e l t ).

A Lagrangean Relaxation Algorithm for Flow Optimization in Survivable MPLS Networks

The problem that this paper investigates, namely, the working route assignment (WRA) problem, is one that arises naturally from problems of survivable network design that have recently received significant attention in data networking community. We consider an existing MPLS backbone transport network, which is in an operational phase and augmenting its resources is not possible. To address the issue of network survivability we apply restoration, i.e. after a network failure broken connections are dynamically restored. The main goal of our work is twofold. First, we want to develop an effective objective function for optimization of working routes in order to scale network flows and prepare the network for future failures and restoration. Second, we plan to find an efficient method to solve the WRA problem with this new objective function. Therefore, a function called RCL (Residual Capacity and Lost Flow in Link) facilitating the function LFL (Lost Flow in Link) developed previously by the author is formulated. Next, we present an approximation approach, called Lagrangean relaxation with heuristics (LRH) aimed to solve WRA with RCL as objective function. We further draw comparisons between LRH and an existing heuristic based on Flow Deviation algorithm. We also examine the performance of RCL against other functions in the context of network survivability. The results of simulation tests demonstrate that the new algorithm provides sub-optimal results, which are significantly better than other heuristic and the new function RCL can be effectively applied for assignment of working routes in survivable MPLS networks.

SNDlib 1.0—Survivable Network Design Library

AbstractThis article describes the Survivable Network Design Library (SNDlib), a data library for fixed telecommunication network design available at http://sndlib.zib.de. In the current version 1.0, the library contains data related to 22 networks which, combined with a set of selected planning parameters, leads to 830 network design problem instances. In this article, we discuss the data concepts of SNDlib and describe a mathematical model for each design problem considered in the library. We also provide information on characteristic features and the origin of the SNDlib problem instances. © 2009 Wiley Periodicals, Inc. NETWORKS, 2010

Survivable ATM mesh networks: Techniques and performance evaluation

The Capacity and Flow Assignment problem in self-healing ATM networks is an interesting one from a Generalized Multi-Protocol Label Switching (GMPLS) prospective since IP and ATM protocols are destined to co-exist together in this unified platform. This paper continues the investigation of the path-based design approach of the network survivability problem in existing ATM mesh networks. Our contribution consists in quantifying (1) the effects the selection of candidate paths per node pair has on the restoration ratio, (2) the effect of restoration schemes on the restoration ratio, (3) the effect of failure scenarios on the restoration ratio, and finally (4) the effect of network connectivity on the restoration ratio. Numerical results are presented under representative network topologies, various traffic demands and spare capacity distribution schemes. They provide additional guidelines for the design of survivable ATM mesh-type networks, from a network reliability viewpoint.

Design of survivable WDM networks using pre-configured protection structures with unrestricted shapes

We propose a novel protection approach for the design of link-protection schemes in survivable Wavelength Division Multiplexing mesh networks by merging the well-known p-cycle- and p-tree-protection structures. So doing, we aim at gathering the advantages of p-cycles in terms of protection capabilities, and of p-trees in terms of protection flexibilities (local re-routing, scalability) in a single protection scheme. As opposed to existing protection schemes based on protection structures with a pre-defined shape, the building blocks of the new scheme are protection structures with unrestricted shapes. Thus, they allow more flexibility in provisioning spare capacity, and provide higher capacity efficiency when compared to the shaped-protection schemes that have been proposed so far. In order to cope with the size of the solution space which includes all the possible protection structures, we propose an efficient and scalable optimization technique in large-scale systems named column generation (CG). In our CG-based optimization approach, the shape of a candidate protection structure is dynamically decided during the optimization process according to a link spare capacity budget. Experimental results on different network instances show that the protection plan resulting from the merging of p-cycle and p-tree structures is, on average, ~15% less capacity redundant and ~15% more reliable than the pure p-cycle one. It also requires, on average, ~30% less protection structures. In addition, those structures provide backup paths ~30% smaller than those of the p-cycle-based scheme.

Shared-p-cycles method for design of survivable WDM networks

In future high-capacity wavelength division multiplexed (WDM) optical networks, the failure of a network component such as a fiber link can lead to severe disruption in the networks’ traffic. Hence, it is imperatively important to provide fast and full protection in WDM optical networks. In this paper, we propose a new approach, called shared preconfigured protection cycles (shared-p-cycles), for the design of survivable WDM networks. We develop an integer linear program (ILP) formulation to solve the problem of shared-p-cycles design for WDM networks with and without wavelength conversion. Numerical results show that the shared-p-cycles design is more efficient in the use of spare capacity and requires much less spare capacity than the conventional p-cycles design.

Incremental survivable network design with topology augmentation in SDH/SONET mesh networks

An incremental capacity allocation with topology augmentation problem is investigated in this article to maximize the service restorability in SDH/SONET mesh networks. To tackle the optimal design problem, two schemes are proposed, i.e., minimal backup path provisioning with topology augmentation (MBPP-TA), and global path pair provisioning with topology augmentation (GPPP-TA). Both schemes are formulated as integer linear programming (ILP) models, and are implemented using the proposed two-step linear programming (LP) approaches. Numerical results show that the two-step LP approaches achieve better solutions with significantly less execution time than the direct ILP approach. Moreover, results show that GPPP-TA provides better solutions than MBPP-TA at the cost of longer computation time.

A note on Rooted Survivable Networks

The (undirected) Rooted Survivable Network Design ( Rooted SND) problem is: given a complete graph on node set V with edge-costs, a root s ∈ V , and (node-)connectivity requirements { r ( t ) : t ∈ T ⊆ V } , find a minimum cost subgraph G that contains r ( t ) internally-disjoint st-paths for all t ∈ T . For large values of k = max t ∈ T r ( t ) Rooted SND is at least as hard to approximate as Directed Steiner Tree [Y. Lando, Z. Nutov, Inapproximability of survivable networks, Theoret. Comput. Sci. 410 (21–23) (2009) 2122–2125]. For Rooted SND, [J. Chuzhoy, S. Khanna, Algorithms for single-source vertex-connectivity, in: FOCS, 2008, pp. 105–114] gave recently an approximation algorithm with ratio O ( k 2 log n ) . Independently, and using different techniques, we obtained at the same time a simpler primal–dual algorithm with the same ratio.

Compacting cuts

For a graph ( V , E ), existing compact linear formulations for the minimum cut problem require Θ(| V || E |) variables and constraints and can be interpreted as a composition of | V | − 1 polyhedra for minimum s - t cuts in much the same way as early approaches to finding globally minimum cuts relied on | V | − 1 calls to a minimum s - t cut algorithm. We present the first formulation to beat this bound, one that uses O (| V | 2 ) variables and O (| V | 3 ) constraints. An immediate consequence of our result is a compact linear relaxation with O (| V | 2 ) constraints and O (| V | 3 ) variables for enforcing global connectivity constraints. This relaxation is as strong as standard cut-based relaxations and has applications in solving traveling salesman problems by integer programming as well as finding approximate solutions for survivable network design problems using Jain's iterative rounding method. Another application is a polynomial-time verifiable certificate of size n for for the NP-complete problem of l 1 -embeddability of a rational metric on an n -set (as opposed to a certificate of size n 2 known previously).

Maximal covering with network survivability requirements in wireless mesh networks

This paper introduces an approach for survivable network design of citywide wireless broadband. Our primary interest is in methodology for ensuring maximal coverage and reliable provision of services based on network connectivity. From a public perspective, ubiquitous and reliable provision of broadband services is important. Thus our approach will be particularly relevant to decision makers in local municipalities who are looking to deploy wireless broadband networks with cheaper installation costs and easier deployment, instead of ground wires such as cable or fiber optics. More formally, we present a maximal wireless covering problem with survivability constraints based on network connectivity using binary integer programming. Under some modeling assumptions, the developed model is applied to structuring a wireless mesh network in the city of Dublin, Ohio as an application. Results demonstrate tradeoffs between coverage and network survivability given a fixed number of selected facility locations. Also, performance of our method highlights computational challenges in solving such combinatorial spatial optimization problems exactly.

On DRC covering — a survey

This paper surveys the cycle covering problem of a graphs motivated by the design of survivable WDM networks, where the requests are routed on sub-networks which are protected independently from each other. The problem is stated as follows. Find a cycle partition or a cycle covering satisfying disjoint routing constraint of the edges of logical graph with an associated routing over physical graph such that the number of cycles is minimized. We give the value or lower bound of the number of cycles in a DRC-covering.