Open Access
A cutting plane algorithm for multicomoodity survivable network design problems
Geir Dahl,Mechthild Stoer +1 more
TLDR
A cutting plane algorithm is presented for solving the following telecommunications network design problem: given point-to-point traffic demands in a network, specified survivability requirements and a discrete cost/capacity function for each link, find minimum cost capacity expansions satisfying the given demands.Abstract:
We present a cutting plane algorithm for solving the following telecommunications network design problem: given point-to-point traffic demands in a network, specified survivability requirements and a discrete cost/capacity function for each link, find minimum cost capacity expansions satisfying the given demands. This algorithm is based on the polyhedral study described in [19]. In this article we describe the underlying problem, the model and the main ingredients in our algorithm. This includes: initial formulation, feasibility test, separation for strong cutting planes, and primal heuristics. Computational results for a set of real-world problems are reported.read more
Citations
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Routing, Flow, And Capacity Design In Communication And Computer Networks
Michal Pioro,Deepankar Medhi +1 more
TL;DR: Throughout, the authors focus on the traffic demands encountered in the real world of network design, and their generic approach allows problem formulations and solutions to be applied across the board to virtually any type of backbone communication or computer network.
Journal ArticleDOI
Cutting planes in integer and mixed integer programming
TL;DR: This survey presents cutting planes that are useful or potentially useful in solving mixed integer programs and the use of valid inequalities for classes of problems with structure, such as network design, is explored.
Proceedings ArticleDOI
Strengthening integrality gaps for capacitated network design and covering problems
TL;DR: The authors show that by adding additional inequalities, the ratio between the optimal integer solution and the optimal solution to the linear program relaxation can be improved significantly, and provide a polynomial-time approximation algorithm to achieve this bound.
Journal ArticleDOI
Design of Survivable Networks: A survey
Hervé Kerivin,A. Ridha Mahjoub +1 more
TL;DR: This paper attempts to survey some of the models and the optimization methods used for solving survivable network models, and particularly cutting plane based algorithms.
Journal ArticleDOI
Routing of Uncertain Traffic Demands
Walid Ben-Ameur,Hervé Kerivin +1 more
TL;DR: A flexible model where traffic belongs to a polytope is introduced, which can be considered as a mathematical framework for a new flexible virtual private network service offer and also introduces a new concept: the routing of apolytope.
References
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Book
Knapsack Problems: Algorithms and Computer Implementations
Silvano Martello,Paolo Toth +1 more
TL;DR: This paper focuses on the part of the knapsack problem where the problem of bin packing is concerned and investigates the role of computer codes in the solution of this problem.
Book
Routing, Flow, And Capacity Design In Communication And Computer Networks
Michal Pioro,Deepankar Medhi +1 more
TL;DR: Throughout, the authors focus on the traffic demands encountered in the real world of network design, and their generic approach allows problem formulations and solutions to be applied across the board to virtually any type of backbone communication or computer network.
Book
Design of Survivable Networks
TL;DR: In this paper, a survey of survivability models using node types is presented, including basic inequalities, lifting theorems, partition inequalities, and node partition inequalities for survivability under connectivity constraints.
Journal ArticleDOI
Cutting planes in integer and mixed integer programming
TL;DR: This survey presents cutting planes that are useful or potentially useful in solving mixed integer programs and the use of valid inequalities for classes of problems with structure, such as network design, is explored.