An Integer Polytope Related to the Design of Survivable Communication Networks

Boyd, Sylvia C.; Hao, Tianbao

doi:10.1137/0406047

Cited by 25 publications

(17 citation statements)

References 16 publications

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“…Fortz et al [54] showed that, when K ≤ 4, this problem reduces to a max-flow problem in an appropriate directed graph, and hence, can be solved in polynomial time. As a consequence, they obtained a polynomial-time separation algorithm for inequalities (20) when K ≤ 4. Unfortunately, McCormick [100] showed that the above constrained min-cut problem is NP-hard if K ≥ 13.…”

Section: Survivability With Bounded Ringsmentioning

confidence: 97%

“…Thus, Grötschel et al [76] (see also Stoer [112]) extended to the polytopes NSNDP(G, r) and LNSDP(G, r) the comb inequalities, which are valid for the polytope associated with the solutions of the TSP. Boyd and Hao [20] introduced the same class of inequalities for the 2-edge connected network polytope, and gave necessary and sufficient conditions for these inequalities to be facet-defining.…”

Section: Valid Inequalities and Their Separation Problemmentioning

confidence: 97%

“…It is not hard to see that the separation problem for inequalities (20) associated with an edge e = st reduces to finding a minimum weight edge subset that intersects all st-paths of length ≤ K − 1. Fortz et al [54] showed that, when K ≤ 4, this problem reduces to a max-flow problem in an appropriate directed graph, and hence, can be solved in polynomial time.…”

Section: Survivability With Bounded Ringsmentioning

confidence: 99%

See 2 more Smart Citations

Design of Survivable Networks: A survey

2005

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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, much research has been carried out to devise 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.

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Section: Survivability With Bounded Ringsmentioning

confidence: 97%

Section: Valid Inequalities and Their Separation Problemmentioning

confidence: 97%

Section: Survivability With Bounded Ringsmentioning

confidence: 99%

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Design of Survivable Networks: A survey

2005

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“…Mahjoub [32] introduces a general class of valid inequalities for 2ECSP(G). Boyd and Hao [6] describe a class of "comb inequalities" which are valid for 2ECSP(G). This class and that introduced by Mahjoub [32] are special cases of a more general class of inequalities given by Grötschel et al [25] for the general survivable network polytope.…”

Section: Kecsp(g) = Conv{xmentioning

confidence: 99%

A branch‐and‐cut algorithm for the k‐edge connected subgraph problem

Bendali¹,

Diarrassouba²,

Mahjoub³

et al. 2009

Networks

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International audienceIn this article, we consider the k-edge connected subgraph problem from a polyhedral point of view. We introduce further classes of valid inequalities for the associated polytope and describe sufficient conditions for these inequalities to be facet defining. We also devise separation routines for these inequalities and discuss some reduction operations that can be used in a preprocessing phase for the separation. Using these results, we develop a Branch-and-Cut algorithm and present some computational results

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“…Mahjoub [24] introduced a general class of valid inequalities for 2ECSP(G). Boyd and Hao [4] describe a class of "comb inequalities" which are valid for 2ECSP(G). This class, as well as that introduced by Mahjoub, are special cases of a more general class of inequalities given by Grötschel et al [20] for the general survivable network polytope.…”

Section: Introduction and Notationmentioning

confidence: 99%