The survivable k-node-connected network design problem: Valid inequalities and Branch-and-Cut

Mahjoub, Meriem; Diarrassouba, Ibrahima; Mahjoub, Ali Ridha; Taktak, Raouia

doi:10.1016/j.cie.2017.03.007

Cited by 3 publications

(2 citation statements)

References 18 publications

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“…It should also be noticed that, contrarily to the survivable network design problem without hop constraints (or the kNCSP with L ≥ |V | − 1), our experiments cannot permit to conclude on the impact of an increasing of the connectivity k on the resolution of the problem. In fact, previous experiments done for the survivable network design problem (see [3] and [29], for example) have concluded that the problem without considering hop constraints seems to become easier when k increases. In our case (the kNDHP with L < |V | − 1), the impact of the connectivity on the resolution is less clear.…”

Section: Resultsmentioning

confidence: 99%

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k-node-disjoint hop-constrained survivable networks: polyhedral analysis and branch and cut

Diarrassouba

Mahjoub

et al. 2018

Ann. Telecommun.

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Given a graph with weights on the edges, a set of origin and destination pairs of nodes, and two integers L ≥ 2 and k ≥ 2, the k-node-disjoint hop-constrained network design problem is to find a minimum weight subgraph of G such that between every origin and destination there exist at least k node-disjoint paths of length at most L. In this paper, we consider this problem from a polyhedral point of view. We propose an integer linear programming formulation for the problem for L ∈ {2, 3} and arbitrary k, and investigate the associated polytope. We introduce new valid inequalities for the problem for L ∈ {2, 3, 4}, and give necessary and sufficient conditions for these inequalities to be facet defining. We also devise separation algorithms for these inequalities. Using these results, we propose a branch-and-cut algorithm for solving the problem for both L = 3 and L = 4 along with some computational results.

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Section: Resultsmentioning

confidence: 99%

“…Here, the type of each node is either 1 or 2. In [29], Mahjoub et al consider the k-node-connected subgraph problem. They give valid inequalities and propose a branch-and-cut algorithm.…”

Section: Edge and Node Versions Without Boundsmentioning

confidence: 99%

k-node-disjoint hop-constrained survivable networks: polyhedral analysis and branch and cut

Diarrassouba

Mahjoub

et al. 2018

Ann. Telecommun.

Self Cite

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Extended formulation and Branch-and-Cut-and-Price algorithm for the two connected subgraph problem with disjunctive constraints

Almathkour,

Diarrassouba,

Hadhbi

2024

Ann Oper Res

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Design of survivable networks with low connectivity requirements

Almathkour,

Magnouche,

Mahjoub

et al. 2024

Int Trans Operational Res

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In this paper, we consider the survivable network design problem when the connectivity types are in {0, 1, 2, 3}. The problem has wide applications in telecommunication networks. We consider the problem from a polyhedral point of view. We describe several classes of valid inequalities and give necessary conditions and sufficient conditions for these inequalities to be facet defining. We also develop separation routines for these inequalities. Using these results, we devise a branch‐and‐cut algorithm along with an extensive computational study is presented.

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The survivable k-node-connected network design problem: Valid inequalities and Branch-and-Cut

Cited by 3 publications

References 18 publications

k-node-disjoint hop-constrained survivable networks: polyhedral analysis and branch and cut

k-node-disjoint hop-constrained survivable networks: polyhedral analysis and branch and cut

Extended formulation and Branch-and-Cut-and-Price algorithm for the two connected subgraph problem with disjunctive constraints

Design of survivable networks with low connectivity requirements

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