Optimal attack and reinforcement of a network
Journal of the ACM (JACM)
Integer and combinatorial optimization
Integer and combinatorial optimization
Integer polyhedra arising from certain network design problems with connectivity constraints
SIAM Journal on Discrete Mathematics
An integer polytope related to the design of survivable communication networks
SIAM Journal on Discrete Mathematics
Design of Survivable Networks with Bounded Rings
Design of Survivable Networks with Bounded Rings
Solving the Two-Connected Network with Bounded Meshes Problem
Operations Research
Graphs and Hypergraphs
Particle swarm optimisation for the design of two-connected networks with bounded rings
International Journal of High Performance Systems Architecture
Improved formulations for the ring spur assignment problem
INOC'11 Proceedings of the 5th international conference on Network optimization
Benders Decomposition for the Hop-Constrained Survivable Network Design Problem
INFORMS Journal on Computing
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We study the problem of designing at minimum cost a two-connected network such that each edge belongs to a cycle using at most K edges. This problem is a particular case of the two-connected networks with bounded meshes problem studied by Fortz, Labbé and Maffioli (Operations Research, vol. 48, no. 6, pp. 866–877, 2000).In this paper, we compute a lower bound on the number of edges in a feasible solution, we show that the problem is strongly NP-complete for any fixed K, and we derive a new class of facet defining inequalities. Numerical results obtained with a branch-and-cut algorithm using these inequalities show their effectiveness for solving the problem.