The k-edge connected subgraph problem I: Polytopes and critical extreme points

Biha, Mohamed Didi; Mahjoub, Ali Ridha

doi:10.1016/j.laa.2003.11.007

Cited by 11 publications

(2 citation statements)

References 27 publications

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“…As a consequence, they obtain a characterization of the graphs for which the linear programming relaxation of that problem is integral. Didi Biha and Mahjoub extend the results of Fonlupt and Mahjoub to the case

k \geq 3

and introduce some graph reduction operations. Kerivin et al study that problem in the more general case where each node of the graph has a specific connectivity requirement.…”

Section: Introductionmentioning

confidence: 93%

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Integer programming formulations for thek-edge-connected 3-hop-constrained network design problem

et al. 2015

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In this article, we study the k -edge-connected L-hopconstrained network design problem. Given a weighted graph G = (V , E ), a set D of pairs of nodes, two integers L ≥ 2 and k ≥ 2, the problem consists in finding a minimum weight subgraph of G containing at least k edge-disjoint paths of length at most L between every pair {s, t } ∈ D. We consider the problem in the case where L = 2, 3 and |D| ≥ 2. We first discuss integer programming formulations introduced in the literature. Then, we introduce new integer programming formulations for the problem that are based on the transformation of the initial undirected graph into directed layered graphs. We present a theoretical comparison of these formulations in terms of LP-bound. Finally, these formulations are tested using CPLEX and compared in a computational study for k = 3, 4, 5.

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k \geq 3

and introduce some graph reduction operations. Kerivin et al study that problem in the more general case where each node of the graph has a specific connectivity requirement.…”

Section: Introductionmentioning

confidence: 93%

“…They introduce several classes of valid inequalities and discuss the separation algorithm for these inequalities. They devise a branch‐and‐cut algorithm using the reduction operations of and give some computational results for k = 3, 4, 5. A complete survey on the k ‐edge‐connected subgraph problem can be found in .…”

Section: Introductionmentioning

confidence: 99%

Integer programming formulations for thek-edge-connected 3-hop-constrained network design problem

et al. 2015

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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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