Optimal attack and reinforcement of a network
Journal of the ACM (JACM)
Survivable networks, linear programming relaxations and the parsimonious property
Mathematical Programming: Series A and B
The Steiner tree problem I: formulations, compositions and extension of facets
Mathematical Programming: Series A and B
A combinatorial algorithm for minimizing symmetric submodular functions
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Separation of Partition Inequalities
Mathematics of Operations Research
A combinatorial algorithm minimizing submodular functions in strongly polynomial time
Journal of Combinatorial Theory Series B
A combinatorial strongly polynomial algorithm for minimizing submodular functions
Journal of the ACM (JACM)
Critical Extreme Points of the 2-Edge Connected Spanning Subgraph Polytope
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
Separating from the dominant of the spanning tree polytope
Operations Research Letters
On the minimal steiner tree subproblem and its application in branch-and-price
CPAIOR'05 Proceedings of the Second international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Separation of partition inequalities with terminals
Discrete Optimization
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Given a graph G=(V,E) with edge costs and an integer vector r@?Z"+^V associated with the nodes of V, the survivable network design problem is to find a minimum cost subgraph of G such that between every pair of nodes s,t of V, there are at least min{r(s),r(t)} edge-disjoint paths. In this paper we consider that problem when r@?{1,2}^V. This case is of particular interest to the telecommunication industry. We show that the separation problem for the so-called partition inequalities reduces to minimizing a submodular function. This yields a polynomial time separation algorithm for these inequalities in that case.