Capacitated Network Design—Polyhedral Structure and Computation

Bienstock, Daniel; Günlük, Oktay

doi:10.1287/ijoc.8.3.243

Cited by 168 publications

(148 citation statements)

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“…In the classical combinatorial network design problem integer capacities (corresponding to batches of bit rates, e. g., 40 Gbps) have to be installed on the network links at minimum cost such that all traffic demands can be realized by flow simultaneously without exceeding the link capacities. Given a single traffic matrix, this problem has been studied extensively in the literature, see [8,10,23,24,37,47,59] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Robust network design: Formulations, valid inequalities, and computations

2013

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Traffic in communication networks fluctuates heavily over time. Thus, to avoid capacity bottlenecks, operators highly overestimate the traffic volume during network planning. In this paper we consider telecommunication network design under traffic uncertainty, adapting the robust optimization approach of [21]. We present three different mathematical formulations for this problem, provide valid inequalities, study the computational implications, and evaluate the realized robustness.To enhance the performance of the mixed-integer programming solver we derive robust cutset inequalities generalizing their deterministic counterparts. Instead of a single cutset inequality for every network cut, we derive multiple valid inequalities by exploiting the extra variables available in the robust formulations. We show that these inequalities define facets under certain conditions and that they completely describe a projection of the robust cutset polyhedron if the cutset consists of a single edge.For realistic networks and live traffic measurements we compare the formulations and report on the speed up by the valid inequalities. We study the "price of robustness" and evaluate the approach by analyzing the real network load. The results show that the robust optimization approach has the potential to support network planners better than present methods.

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Section: Introductionmentioning

confidence: 99%

Robust network design: Formulations, valid inequalities, and computations

2013

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“…Specific applications include the network loading problem [3,13,15,19], the facility location problem with multiple capacity options [17,18], and the merge-in-transit problem [7].…”

Section: Introductionmentioning

confidence: 99%

A Comparison of Mixed-Integer Programming Models for Nonconvex Piecewise Linear Cost Minimization Problems

2003

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We study a generic minimization problem with separable non-convex piecewise linear costs, showing that the linear programming (LP) relaxation of three textbook mixed integer programming formulations each approximates the cost function by its lower convex envelope. We also show a relationship between this result and classical Lagrangian duality theory.Key words: piecewise-linear, integer programming, linear relaxation, Lagrangian relaxation. Resum6Nous considerons un probleme de minimisation gen6rique dans lequel l'objectif consiste d'une somme separable de fonctions lineaires par morceaux non convexes. Nous montrons que les relaxations lineaires de trois modeles classiques de programmation en nombres entiers sont equivalentes puisqu'elles fournissent comme approximation de l'objectif son enveloppe convexe inf6rieure. Nous etablissons galement une relation entre ce rsultat et la th6orie de la dualite lagrangienne classique.Mots-cls : lineaire par morceaux, progrmmation en nombres entiers, relaxation lin6aire, relaxation lagrangienne.ii

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“…The authors in [22] and [23] study a variation of the capacitated network design problem with the objective of installing additional capacity to route all the specified point-topoint traffic demands at minimum cost. The authors in [24] present a survey of models and algorithms for multicommodity capacitated network design problems.…”

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confidence: 99%

Approximation Algorithms for Survivable Multicommodity Flow Problems with Applications to Network Design

Todimala

Ramamurthy

2006

Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications

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Abstract-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 N P-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.

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Capacitated Network Design—Polyhedral Structure and Computation

Cited by 168 publications

References 10 publications

Robust network design: Formulations, valid inequalities, and computations

Robust network design: Formulations, valid inequalities, and computations

A Comparison of Mixed-Integer Programming Models for Nonconvex Piecewise Linear Cost Minimization Problems

Approximation Algorithms for Survivable Multicommodity Flow Problems with Applications to Network Design

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