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32
Survivable networks, linear programming relaxations and the parsimonious property
, 1993
"... We consider the survivable network design problem the problem of designing, at minimum cost, a network with edgeconnectivity requirements. As special cases, this problem encompasses the Steiner tree problem, the traveling salesman problem and the kedgeconnected network design problem. We establ ..."
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Cited by 44 (12 self)
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We consider the survivable network design problem the problem of designing, at minimum cost, a network with edgeconnectivity requirements. As special cases, this problem encompasses the Steiner tree problem, the traveling salesman problem and the kedgeconnected network design problem. We establish a property, referred to as the parsimonious property, of the linear programming (LP) relaxation of a classical formulation for the problem. The parsimonious property has numerous consequences. For example, we derive various structural properties of these LP relaxations, we present some algorithmic improvements and we perform tight worstcase analyses of two heuristics for the survivable network design problem.
WorstCase Comparison of Valid Inequalities for the TSP
 MATH. PROG
, 1995
"... We consider most of the known classes of valid inequalities for the graphical travelling salesman polyhedron and compute the worstcase improvement resulting from their addition to the subtour polyhedron. For example, we show that the comb inequalities cannot improve the subtour bound by a factor gr ..."
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Cited by 25 (1 self)
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We consider most of the known classes of valid inequalities for the graphical travelling salesman polyhedron and compute the worstcase improvement resulting from their addition to the subtour polyhedron. For example, we show that the comb inequalities cannot improve the subtour bound by a factor greater than 10/9. The corresponding factor for the class of clique tree inequalities is 8/7, while it is 4/3 for the path configuration inequalities.
Polyhedral and Computational Investigations for Designing Communication Networks with High Survivability Requirements
, 1992
"... We consider the important practical and theoretical problem of designing a lowcost ..."
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Cited by 16 (0 self)
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We consider the important practical and theoretical problem of designing a lowcost
Design of Survivable Networks with Bounded Rings
, 2000
"... This dissertation is the result of a project funded by Belgacom, the Belgian telecommunication operator, dealing with the development of new models and optimization techniques for the longterm planning of the backbone network. The minimumcost twoconnected spanning network problem consists in find ..."
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Cited by 14 (4 self)
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This dissertation is the result of a project funded by Belgacom, the Belgian telecommunication operator, dealing with the development of new models and optimization techniques for the longterm planning of the backbone network. The minimumcost twoconnected spanning network problem consists in finding a network with minimal total cost for which there exist two nodedisjoint paths between every pair of nodes. This problem, arising from the need to obtain survivable communication and transportation networks, has been widely studied. In our model, the following constraint is added in order to increase the reliability of the network : each edge must belong to a cycle of length less than or equal to a given threshold value K. This condition ensures that when traffic between two nodes has to be redirected (e.g. in case of failure of an edge), we can limit the increase of the distance between these nodes. We investigate valid inequalities for this problem and provide numerical results obtai...
Design of Survivable Networks: A survey
 In Networks
, 2005
"... For the past few decades, combinatorial optimization techniques have been shown to be powerful tools for formulating and solving optimization problems arising from practical situations. In particular, many network design problems have been formulated as combinatorial optimization problems. With the ..."
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Cited by 14 (0 self)
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For the past few decades, combinatorial optimization techniques have been shown to be powerful tools for formulating and solving optimization problems arising from practical situations. In particular, many network design problems have been formulated as combinatorial optimization problems. With the advances of optical technologies and the explosive growth of the Internet, telecommunication networks have seen an important evolution and therefore, designing survivable networks has become a major objective for telecommunication operators. Over the past years, a big amount of research has then been done for devising efficient methods for survivable network models, and particularly cutting plane based algorithms. In this paper, we attempt to survey some of these models and the optimization methods used for solving them.
Capacity and survivability models for telecommunication networks
 in Proceedings of EURO/INFORMS Meeting
, 1997
"... Designing lowcost networks that survive certain failure situations is one of the prime tasks in the telecommunication industry. In this paper we survey the development of models for network survivability used in practice in the last ten years. We show how algorithms integrating polyhedral combinato ..."
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Cited by 13 (1 self)
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Designing lowcost networks that survive certain failure situations is one of the prime tasks in the telecommunication industry. In this paper we survey the development of models for network survivability used in practice in the last ten years. We show how algorithms integrating polyhedral combinatorics, linear programming, and various heuristic ideas can help solve realworld network dimensioning instances to optimality or within reasonable quality guarantees in acceptable running times. The most general problem type we address is the following. Let a communication demand between each pair of nodes of a telecommunication network be given. We consider the problem of choosing, among a discrete set of possible capacities, which capacity to install on each of the possible edges of the network in order to (i) satisfy all demands, (ii) minimize the building cost of the network. In addition to determining the network topology and the edge capacities we have to provide, for each demand, a routing such that (iii) no path can carry more than a given percentage of the demand, (iv) no path in the routing exceeds a given length. We also have to make sure that (v) for every single node or edge failure, a certain percentage of the demand is reroutable. Moreover, for all failure situations feasible routings must be computed. The model described above has been developed in cooperation with a German mobile phone provider. We present a mixedinteger programming formulation of this model and computational results with data from practice.
An Improved Approximation Algorithm for Minimum Size 2Edge Connected Spanning Subgraphs
, 1999
"... We give a 17/12approximation algorithm for the following NPhard problem: Given an undirected graph, find a 2edge connected spanning subgraph that has the minimum number of edges. The best previous approximation guarantee was 3/2. We conjecture that there is a 4/3approximation algorithm. Thus ..."
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Cited by 12 (1 self)
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We give a 17/12approximation algorithm for the following NPhard problem: Given an undirected graph, find a 2edge connected spanning subgraph that has the minimum number of edges. The best previous approximation guarantee was 3/2. We conjecture that there is a 4/3approximation algorithm. Thus our main result gets halfway to this target.
Approximability of Dense and Sparse Instances of Minimum 2Connectivity, TSP and Path Problems
 In 13th Annual ACMSIAM Symposium on Discrete Algorithms
, 2002
"... We study the approximability of dense and sparse instances of the following problems: the minimum 2edgeconnected (2EC) and 2vertexconnected (2VC) spanning subgraph, metric TSP with distances 1 and 2 (TSP(1,2)), maximum path packing, and the longest path (cycle) problems. The approximability of ..."
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Cited by 11 (0 self)
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We study the approximability of dense and sparse instances of the following problems: the minimum 2edgeconnected (2EC) and 2vertexconnected (2VC) spanning subgraph, metric TSP with distances 1 and 2 (TSP(1,2)), maximum path packing, and the longest path (cycle) problems. The approximability of dense instances of these problems was left open in Arora et al. [3]. We characterize the approximability of all these problems by proving tight upper (approximation algorithms) and lower bounds (inapproximability). We prove that 2EC, 2VC and TSP(1,2) are Max SNPhard even on 3regular graphs, and provide explicit hardness constants, under P 6= NP. We also improve the approximation ratio for 2EC and 2VC on graphs with maximum degree 3. These are the rst explicit hardness results on sparse and dense graphs for these problems. We apply our results to prove bounds on the integrality gaps of LP relaxations for dense and sparse 2EC and TSP(1,2) problems, related to the famous metric TSP conjecture, due to Goemans [18].